Model-Aware Predictive Control for Occupant-Centric Environment Optimization in Room-Level Scenarios

Abstract

Building energy consumption accounts for 30% of global energy use, making building management pivotal to achieving global sustainability. Occupants have profound impacts on the building environment. Incorporating occupant-related factors into the environmental control process is essential for optimizing the efficiency of building management systems (BMSs), which thus gives rise to the concept of occupant-centric control (OCC). Conventional methods rely on simplified models and fixed schedules that fail to satisfy environmental control and occupant requirements, while constructing credible models places strict requirements on the dataset. In this paper, we propose a Model-Aware Predictive Control (MAPC) framework that can construct credible models with limited data and provide room-level control strategies to optimize the trade-off between occupant comfort and energy consumption. The technological innovations of this research are twofold. On the one hand, we design a model construction and fine-tuning method that combines data-driven subspace projection approach with physical priors that can construct credible thermal dynamic models with limited data. On the other hand, to balance the potential conflicts between enhancing occupant comfort and saving energy, we present a hierarchical decision-making mechanism that enables adaptive multi-objective room-level control considering dynamic occupant comfort requirements and energy usage. The experimental results obtained on an EnergyPlus-based simulation dataset and a publicly available dataset demonstrate that MAPC can provide room-level control strategies based on dynamic occupant requirements and user preferences and achieve superior trade-offs between occupant comfort and energy consumption. The ablation experiments also demonstrated the superiority of MAPC in constructing reliable models on limited datasets. MAPC provides pivotal support for the advancement of the intelligent buildings and sustainable indoor environment.

1. Introduction

Because of the substantial energy demands of buildings and infrastructure that accompany the rapid development of urbanization, it has become a focal point in the sustainability debate [1]. Currently, the energy consumption of buildings accounts for 30% of the total global energy consumption, demonstrating the significant potential for achieving energy savings and sustainable development in this domain [2]. As a result, energy conservation has become one of the primary control objectives in buildings [3]. As an important tool for building environment control, the building management system (BMS) plays a significant role in controlling building energy savings [4]. Moreover, with the advancement of the technology used in BMSs, occupants’ pursuit of healthier and more comfortable building environments has accelerated [5,6]. Substantially, occupants play a crucial role in building management [7], thus giving rise to the concept of occupant-centric control (OCC). In this regard, reconciling occupant comfort with energy efficiency has become a research focus in the sustainable indoor environment domain [8,9,10,11].

Recently, considerable efforts have been made in the field of OCC. Researchers have explored several approaches to integrating environmental requirements into the building control loop [7,12,13,14]. Conventional methods often adopt the rule-based control (RBC) approach, which operates according to fixed schedules and primarily relies on empirical knowledge to adjust the control parameters. Although RBC offers heuristic management capabilities, they lack the quantitative precision required for optimized control. Thus, the proportional–integral–derivative (PID) method with explicit mathematical formulations is commonly deployed in practice to regulate indoor temperatures toward the desired setpoints [15,16,17,18,19]. As a classic control method, the effectiveness of the PID method in building environmental systems has been demonstrated through long-term practice [17]. Nonetheless, PID control operates primarily on scheduled occupancy profiles, resulting in static control strategies and control lag [15,18]. Therefore, researchers have increasingly focused on integrating dynamic occupant-related factors into control processes, expecting more proactive and optimized system operation results. This has prompted the exploration of advanced control strategies as promising pathways forward.

Substantially, the existing advanced control methods can be mainly divided into model-driven and data-driven approaches. On the one hand, as a typical model-driven control method, model predictive control (MPC) has attracted significant attention because of its inherent ability to incorporate predictive information over a finite time horizon [13,20,21,22,23,24,25,26]. Existing studies on MPC generally utilize the resistance-capacitance (RC) model to represent the heat transfer and storage processes of buildings. However, while relying on pure RC model may introduce certain inaccuracies [13], researchers have found it difficult to establish a more accurate explicit model for the building thermal dynamics. Furthermore, model-driven approaches entail substantial manual effort in development and face significant challenges in parameter quantification and acquisition. On the other hand, data-driven methods such as neural networks and reinforcement learning (RL) have attracted researchers’ attention [4,12,19,21,26,27,28,29,30,31,32]. These methods are not constrained by fixed formulaic expressions and can depict implicit relationships hidden behind the data. Although data-driven methods skillfully manage complex nonlinear systems without depending on specific models, they still face some challenges in terms of training cost, convergence speed, and dataset requirements [33]. Typically, existing methods struggle to establish thermal dynamic models with limited data, and their credibility and interpretability also pose challenges [34]. Therefore, the exploration of a building environment management framework that can reliably model the thermal dynamics using a limited dataset is urgently needed. Moreover, addressing the potential conflicts in room-level control is also highly important, as the scope of OCC is gradually shifting from single room to complex spaces [8].

In this paper, we propose a model-aware predictive control framework, named MAPC. Generally, MAPC overcomes the challenge of modeling building thermal dynamics with limited data. Moreover, MAPC can also provide adaptive multi-objective room-level control strategies considering dynamic occupant comfort and energy saving requirements. We first design a model construction and fine-tuning method for indoor thermal dynamics, which integrates the data-driven subspace projection method with physical priors. Utilizing a data-driven method, this process is able to identify abstract system state changes with limited dataset quantity and quality, while using the RC model as a physical constraint endows the model with higher reliability and interpretability. Second, to balance the potential conflicts associated with distributed control, a hierarchical decision-making framework is presented. A set of objectives and constraints is proposed for global decision-making and model optimization, with the aim of achieving an improved trade-off between global energy consumption and occupant comfort within room-level control scenarios. To evaluate our method, we utilized a simulated dataset generated from EnergyPlus named EP and a public dataset named CN-OBEE [35]. The EP dataset comprises full-year operational data simulated for a five-room commercial building located in Nanjing, while the CN-OBEE dataset encompasses measured data collected from multiple rooms of a duplex apartment located in Miyun District, Beijing. For the EP dataset, occupant comfort is evaluated using the conventional Predicted Mean Vote (PMV) index [36]. Conversely, due to the limited parameter availability in the CN-OBEE dataset, we designed an occupant comfort violation index to reflect the ability of methods to enhance occupant comfort. According to the experimental results, MAPC can provide room-level control strategies based on dynamic occupant requirements and user preferences, achieving superior trade-offs between occupant comfort and energy efficiency. To more comprehensively investigate the proposed approach, we designed ablation experiments to investigate the impact of each step on the performance of the model. We envision MAPC as an important first step toward achieving occupant-driven dynamic environmental control in buildings, thereby paving the way for sustainable indoor environments.

In summary, our contributions are summarized as follows:

• We propose a model-aware predictive control framework oriented to OCC named MAPC, addressing the challenges of constructing credible thermal dynamic models with limited data, and providing adaptive room-level environmental control strategies that meet dynamic requirements.
• To construct credible thermal dynamic models, we propose a novel modeling approach that integrates the data-driven subspace projection method with physical priors that can decouple abstract system states from limited data and utilize physical constraints to fine-tune the baseline model, effectively enhancing its reliability and interpretability.
• We propose a hierarchical framework and an adaptive room-level decision-making mechanism to balance the potential conflicts associated with distributed control and facilitate the dynamic adaptation of system objectives and constraints by allowing for occupant comfort and energy consumption requirements.
• MAPC is implemented utilizing data from an EnergyPlus simulation dataset and a publicly available dataset. It is extensively compared with different methods, and ablation experiments are conducted. The experimental results demonstrate the superiority of the MAPC method in thermal dynamics modeling and its capability to achieve better trade-offs between occupant comfort and energy consumption.

The subsequent sections are organized as follows. We first review the recent literature in Section 2. The principles and the technical details of MAPC are then explained in Section 3, which is followed by discussions on the experimental results and evaluations in Section 4 and Section 5, respectively. Finally, we provide a summary of this paper in Section 6.

2. Literature Review

With respect to buildings, researchers have reached a consensus that occupants have a significant effect on building energy efficiency and environmental control [37,38,39,40]. For example, Cuerda et al. reported that the difference in energy consumption between actual occupant data and fixed standard data can reach 15% [41]. Ma et al. deconstructed building energy consumption from three perspectives, i.e., physics, occupants, and white noise, and improved the accuracy achieved when characterizing the impact of occupants on energy consumption by more than 50% [42]. However, how to precisely elucidate the impacts of occupant-related factors and further incorporate them into building environment control is still an important scientific issue for BMS. The research efforts in this regard are as follows.

2.1. Conventional Methods

Conventional BMS primarily implement RBC [19], which means controlling the building operating parameters such as indoor temperature according to fixed operating rules and occupancy schedules. Controlling system actions through a set of heuristic rules, RBC can operate without reliance on precise mathematical models and is particularly adept at managing modal switching, enforcing safety constraints, and executing macro-level decisions. However, RBC lacks the requisite ability to precisely regulate continuous variables and maintain high steady-state fidelity. This limitation has precipitated a paradigm shift toward the PID control method [43,44]. PID control is a classic control method. Owing to its advantages of simple principles, strong robustness, and wide practicality, PID control is widely applied in fields like building lighting [43] and HVAC system [44]. For example, Sultan et al. designed a PID control strategy to process real-time temperature and humidity sensor data, output control signals for the fluid control valve of a coil, and ultimately maintain the temperature of a room at the set point [17]. However, the fixed rules and occupancy schedules make RBC methods unable to respond to dynamic occupant-related factors, resulting in static control strategies and control lag [15,18]. Meanwhile, as the scope of research shifts towards complex systems in multiple spaces, PID control may face the problems of low global performance and conflicts among multiple objectives [15].

Therefore, how to integrate dynamic occupant-related factors into the building control loop and resolve the competing objectives inherent in distributed control remain a key scientific challenge. Advanced control methods provide solutions to these problems, which primarily fall into two categories: model-driven control and data-driven control.

2.2. Model-Driven Control

Model-driven control methods utilize precise physical models for environmental management, providing the possibility of integrating dynamic occupant data into the building control loop. Among the existing approaches, MPC is a sophisticated method that has the ability to achieve the optimal control strategy by utilizing predictive information within a finite future time horizon, and this method has been widely applied to BMSs [22,45,46]. For example, Gupta et al. calculated the estimated time of arrival (ETA) of occupants on the basis of their living locations and the distance from home, and then communicated it to the MPC controller to ensure that the house reached the temperature setpoint when the occupants arrived [47]. Wang et al. designed a hierarchical nonlinear model predictive control (HNLMPC) method that can dynamically optimize the temperature setting strategy by predicting future factors including occupancy levels [26]. Additionally, Jiang et al. developed an OBMPC system. By predicting future disturbances including occupant behaviors, OBMPC calculates the optimal control strategy to reduce energy consumption levels while ensuring air quality [13].

However, MPC faces challenges such as the difficulty in obtaining accurate physical models [11]. The effectiveness of MPC relies heavily on the accuracy of the system model, but establishing an accurate explicit model for the building environment is difficult. Existing studies mostly adopt the resistance–capacitance (RC) model as the fundamental model. However, relying solely on RC models often introduces certain inaccuracies [13]. Furthermore, researchers encounter challenges in formulating more accurate explicit models for building thermal dynamics which entail parameter quantification, acquisition and extensive manual development efforts. In addition, MPC has difficulty in accommodating the heterogeneous control demands arising from diverse functional zones within buildings. Therefore, the primary challenge faced by model-driven control methods is how to construct an accurate building thermal dynamic model with limited data sources and meet heterogeneous room-level demands.

2.3. Data-Driven Control

With the support of advanced theory and intelligent algorithms, existing data-driven methods have demonstrated a series of prominent outcomes [19,21,32]. These methods are not constrained by the expression of fixed formulas, and can overcome the limitations of artificially defined finite relations, enabling them to capture the implicit relationships hidden behind the data. For example, Tohid et al. used the numerical algorithms for subspace state space system identification (N4SID) method instead of the commonly used RC model to identify the abstract thermal dynamics of the system. By optimizing the multi-step ahead prediction error (MSPE), they established high-fidelity data-driven models for large-scale building clusters [19]. Deng et al. utilized transfer learning to predict the occupancy in buildings and provided optimal control strategies [48]. Additionally, Gou et al. designed an MLP-VQGAN surrogate model that maps continuous HVAC control parameters to physical fields and proposed an adaptive ventilation strategy [49]. Furthermore, owing to its ability to implement adaptive and online learning in unknown or complex environments, RL is gradually becoming a cutting-edge method utilized in OCC [11]. For instance, Chen et al. implemented RL-based HVAC control in a test room using real-time occupancy information sensed by camera sensors and predefined schedules [50]. Moreover, Arroyo et al. innovatively combined the constraints of MPC with the long-term value-based optimization capabilities of RL, enabling constraint satisfaction and continuous learning while achieving performance similar to that of MPC in deterministic settings [21]. Similarly, Parisa et al. utilized a dynamic model identified by a long short-term memory neural network (LSTM) and designed an upper-level controller based on RL to provide global decisions [32].

However, data-driven methods such as RL still face challenges. For instance, the need for the high quantity and quality of training data is a major obstacle to addressing the problem of data scarcity and may lead to poor model robustness [33]. Furthermore, the black-box nature of RL presents significant challenges for ensuring model credibility and operational safety. Studies have demonstrated that adding certain physical constraints can effectively enhance the performance of data-driven methods on small sample datasets and guide the model to learn fundamental patterns, thereby increasing the credibility and interpretability of the model [34,51]. Therefore, a method for building thermal dynamic modeling that integrates data-driven approaches with physical priors is urgently needed.

2.4. Existing Challenges

In summary, with respect to adopting MAPC in smart buildings, several technical challenges still exist and need to be addressed. (1) How to depict the implicit dynamics of the building thermal environment from limited data. The conventional model-driven methods adopt simplified models and require knowledge of the building envelope and thermal parameters, while the effectiveness of data-driven methods depends on the quantity and quality of the datasets. This makes conventional building environment datasets inadequate to meet the training requirements. (2) How to integrate model-driven control method constrained by limited data with reliable physical priors. Although the models utilized in model-driven methods offer reliable physical priors for the training of data-driven methods, the critical challenge of harmonizing these disparate modeling paradigms persists. How to embed these physical priors into the learning framework as effective constraints or objectives remains a key scientific problem. (3) How to strike a balance between building energy efficiency and dynamic occupant comfort requirements in room-level control. This problem is challenging, as the conventional methods rely on fixed occupant schedules because of the randomness of occupant-related factors, resulting in distorted and lagged control results. Moreover, to achieve better control effects in building environmental control, the potential conflicts between objectives, such as energy efficiency and occupant comfort requirements, must be balanced. However, the conventional MPC technique lacks global optimization capabilities, and its constraints and objectives cannot be updated online, making it unable to adapt to real-world situations.

3. Methodology

3.1. Overview

To address the above issues, we seek to explore a hybrid control framework oriented toward OCC. On the one hand, in terms of model construction, it can integrate data-driven methods with physical priors, achieving the goal of depicting the building thermal dynamics with limited data. On the other hand, in terms of system operation, it also has the ability to strike a balance between conflicting objectives and provide adaptive room-level control strategies allowing for dynamic occupant comfort and energy consumption requirements.

Therefore, we establish a model-aware predictive control structure named MAPC, and its basic principles are proposed in this paper. MAPC can be divided into two processes, i.e., model construction and fine-tuning, and model implementation, as shown in Figure 1.

In terms of model construction and fine-tuning, to extract the implicit relationships between occupants and the environment from limited data, MAPC first utilizes the data-driven subspace projection method to identify the initial baseline models of the indoor environment which represent the abstract thermal dynamics of the system. Meanwhile, MAPC constructs RC physical models for each room. Afterward, MAPC incorporates the states of the RC models as physical priors into the data-driven training process. MAPC is then used to fine-tune the baseline model to obtain a credible gray-box model. Furthermore, in terms of model implementation, a hierarchical framework and an adaptive room-level decision-making mechanism are proposed to strike a balance between the conflicting objectives brought about by distributed control. This mechanism can formulate dynamic occupancy and predicted energy usage as explicit constraints and objective functions, which are then passed to MPC controllers to conduct room-level distributed model optimization.

Then, in the following sections, we will introduce the basic principles of the MAPC, deconstruct its model construction and fine-tuning principles, and explain its hierarchical operation logic.

3.2. Baseline Model Construction

Utilizing a collaborative approach involving data-driven methods and physical priors, MAPC is primarily responsible for constructing the credible state space equations for each room, given the limited quantity and quality of the dataset.

In this section, to first obtain the baseline model, we adopted the subspace projection and identification method to learn the State Space (SS) prediction model of the building thermal dynamics from the raw data. First, we will introduce the definition of the SS model.

Mathematically, a state space equation can be modeled as follows:

$$\begin{array}{c}{\displaystyle \frac{dX}{dt}}=AX+BU\\ Y=CX+DU\end{array}$$

(1)

where $X$ denotes the system state variable, $U$ denotes the system input and $Y$ denotes the system output. $A, B, C$ and $D$ represent different system matrices. Despite sharing the same mathematical structure as the RC model, the state $X$ of the SS model does not have direct physical meanings, such as the wall or air temperature. Instead, they represent abstract system states that capture the main thermodynamic dynamics of the building. However, the aforementioned state space model is continuous and requires discretization, i.e.,

$$\left\{\begin{array}{c}{X}_N(k+1)=A_N{X}_N(k)+B_N{U}_N(k)\\ Y_N(k)=C_N{X}_N(k)+D_N{U}_N(k)\end{array}\right.$$

(2)

Specifically, in this paper, the input $U_N$ includes outdoor temperature $T_{air,out}$, solar radiation $S$, and air conditioning power $Q_{HVAC}$, while the output $y$ represents indoor temperature $T_{air,in}$. All of these parameters are extracted from the raw dataset.

Next, we will illustrate the principle of the subspace projection and identification method, whose workflow is shown in Figure 2.

First of all, we divide the dataset into inputs and outputs, i.e.,

$$\left\{u(1),u(2),\dots ,u(N)\right\}, \left\{y(1),y(2),\dots y(N)\right\}$$

(3)

We define two integers $i$ and $j$, which represent the lengths of the future window and past window, respectively. Afterward, we construct Hankel matrices, i.e.,

$$U_p=\left[\begin{array}{cccc}u(1)& u(2)& \dots & u(j)\\ u(2)& u(3)& \dots & u(j+1)\\ ⋮& ⋮& \ddots & ⋮\\ u(i)& u(i+1)& \dots & u(i+j-1)\end{array}\right], Y_p=\left[\begin{array}{cccc}y(1)& y(2)& \dots & y(j)\\ y(2)& y(3)& \dots & y(j+1)\\ ⋮& ⋮& \ddots & ⋮\\ y(i)& y(i+1)& \dots & y(i+j-1)\end{array}\right]$$

(4)

$$U_f=\left[\begin{array}{cccc}u(i+1)& u(i+2)& \dots & u(i+j)\\ u(i+2)& u(i+3)& \dots & u(i+j+1)\\ ⋮& ⋮& \ddots & ⋮\\ u(2i)& u(2i+1)& \dots & u(2i+j-1)\end{array}\right], Y_f=\left[\begin{array}{cccc}y(i+1)& y(i+2)& \dots & y(i+j)\\ y(i+2)& y(i+3)& \dots & y(i+j+1)\\ ⋮& ⋮& \ddots & ⋮\\ y(2i)& y(2i+1)& \dots & y(2i+j-1)\end{array}\right]$$

(5)

where $U_p$ and $Y_p$ represent the past input matrix and past output matrix, and $U_f$ and $Y_f$ represent the future input matrix and future output matrix, respectively. Furthermore, the past matrix $W_p$ is defined as:

$$W_p={\left[U_p^T,Y_p^T\right]}^T$$

(6)

By calculating the projection $O_n$ of $Y_f$ on the space spanned by $W_p$ and $U_f$, we can obtain the system’s extended observable matrix ${\Gamma }_n$ and state vector $X_n$, i.e.,

$$O_n={\displaystyle \frac{Y_f}{{}_{U_f}W_p}}\approx {\Gamma }_n{X}_n$$

(7)

After calculating $O_n$, we further perform singular value decomposition (SVD) on it to obtain the estimated ${\Gamma }_n$ and $X_n$, i.e.,

$$O_n=U_1{\Sigma }_1{V}_1^T$$

(8)

$${\stackrel{\wedge }{\Gamma }}_n=U_1{\Sigma }_1^{1/2}, {\stackrel{\wedge }{X}}_n={\Sigma }_1^{1/2}{V}_1^T$$

(9)

Finally, the system matrix $A,B,C,D$ is solved through least squares regression, i.e.,

$$\begin{array}{c}\left[\begin{array}{c}{\stackrel{\wedge }{X}}_{i+1}\\ Y_i\end{array}\right]=\left[\begin{array}{cc}A& B\\ C& D\end{array}\right]\left[\begin{array}{c}{\stackrel{\wedge }{X}}_i\\ U_i\end{array}\right]\\ \left[\begin{array}{cc}A& B\\ C& D\end{array}\right]=\left[\begin{array}{c}{\stackrel{\wedge }{X}}_{i+1}\\ Y_i\end{array}\right]{\left[\begin{array}{c}{\stackrel{\wedge }{X}}_i\\ U_i\end{array}\right]}^T\end{array}$$

(10)

Therefore, we obtained the baseline model, which required further fine-tuning. Additionally, to align the model orders for further fine-tuning, the baseline model was identified as a third-order system.

3.3. RC-Model-Based Model Fine-Tuning

Moreover, to provide reliable physical priors, we established RC models for the thermal dynamics of each room. The RC model is an explicit equation widely recognized and used in academia to describe indoor thermal dynamics, where the state vector includes the external wall temperature $T_{wall,ext}$, the internal wall temperature $T_{wall,in}$ and the indoor air temperature $T_{air,in}$. We consider the air conditioning power $Q_{HVAC}$ as the input $U$ to the system. Furthermore, the outdoor air temperature $T_{air,out}$ and the solar radiation $S$ are considered disturbances $D$. The system matrices $A,B,E$ contain explicit thermal parameters of the buildings. With these variables, the state space model can be established, as shown in Equation (11).

$$\left[\begin{array}{c}{\dot{T}}_{wall,ext}\\ {\dot{T}}_{wall,in}\\ {\dot{T}}_{air,in}\end{array}\right]=A\left[\begin{array}{c}{T}_{wall,ext}\\ T_{wall,in}\\ T_{air,in}\end{array}\right]+B{Q}_{HVAC}+E\left[\begin{array}{c}{T}_{air,out}\\ S\end{array}\right]$$

(11)

Similarly, the aforementioned state space model is continuous and requires discretization, as shown in Equation (12):

$$\left\{\begin{array}{l}{X}_{RC}(k+1)=A_d{X}_{RC}(k)+B_d{U}_{RC}(k)+E_d{D}_{RC}(k)\\ Y_{RC}(k+1)=C_d{X}_{RC}(k)\end{array}\right.$$

(12)

where $A_d=e^{A{T}_s}$, $B_d=({\displaystyle {\displaystyle \underset{0}{\overset{T_s}{\int }}}{e}^{At}dt})B_c$ and $E_d=({\displaystyle {\displaystyle \underset{0}{\overset{T_s}{\int }}}{e}^{At}dt})E_c$, while $T_s$ is the sampling time.

We adopt the rolling window methods to adaptively update the parameters in the system matrix. By minimizing the difference between temperature prediction results and actual data, we obtain a relatively accurate calibration model.

Finally, we fine-tune the basic model identified by the subspace projection and identification method, using the RC model of the building as a physical constraint, to obtain the final explainable fine-tuned models with physical priors. First, due to discrepancies in state order and magnitude between the data-driven model and the RC model, we first apply a transformation to the state vector of the data-driven model to align it closely with the physical states of the RC model, as shown in Equation (13). Then, the loss function for training is set as shown in Equation (14):

$$\left\{\begin{array}{c}{X}_S(k+1)=T{X}_N(k+1)=T[A_N{X}_N(k)+B_N{U}_N(k)]\\ X_S (k+1)\approx X_{RC} (k+1)\end{array}\right.$$

(13)

$$J_{loss}=\min {\displaystyle {\displaystyle \sum _{k=0}^K}{[y(k)-(Cx(k)+Du(k))]}^2}+\lambda *{\displaystyle {\displaystyle \sum _{k=0}^K}{[(X_S(k)-f_{\_RC}(x(k),u(k)))]}^2}$$

(14)

where the transformation $T$ in Equation (13) was derived via joint optimization utilizing the gradient descent algorithm. Furthermore, the first term in Equation (14) ensures that the model output closely matches the actual value, aiming for high prediction accuracy. Moreover, the second term ensures that the states transition identified by the data-driven model closely approximate those predicted by the RC model, serving as a physical constraint. The hyperparameter $\lambda$ is used to balance the importance of the two terms and is determined through hyperparameter optimization. In this study, hyperparameter optimization is performed using a log-space grid search, with the search range defined over $[{10}^{-4},{10}^2]$. During each fine-tuning iteration, MAPC selects a candidate value for $\lambda$. Subsequently, the optimal fine-tuned model corresponding to this $\lambda$ is derived by minimizing the loss function. Finally, a comparative evaluation is conducted across all candidates to identify the optimal model and its associated $\lambda$ value

3.4. Model Implementation

This process is primarily responsible for collecting and preprocessing multisource data, with the aim of balancing the potential conflicts of multi-zone distributed control and providing an adaptive room-level optimization strategy for MPC in each room.

First, we introduce the conventional MPC method. MPC is an advanced control strategy that utilizes a dynamic process model to predict and optimize future system behavior over a finite time horizon, with continuous feedback correction. The three underlying components of MPC include a predictive model, rolling optimization and feedback optimization, which endow it with advantages such as advanced control and online optimization capabilities. The working process and optimization principle of MPC are shown in Figure 3. First, on the basis of the externally set expected output $y_{pre}$ and feedback signal $y_c$, MPC generates the tracking target $y_r$ for the future time window. Afterward, using the predictive model of the system, the control input $u$ and other inputs are used to predict the system output $y_m$ for the next $N$ steps. The control sequence for the future time domain is solved by minimizing the performance index $\min \mathrm{J}(k)$. Finally, only the first control input is executed on the controlled object to produce the actual output $y$, which is sent to the next moment, thus completing one control step.

In this paper, the model implementation process can be divided into an adaptive room-level decision-making mechanism and a distributed model optimization, as shown in Figure 4. After obtaining the fine-tuned models, MAPC uses them as the predictive models of MPC controllers in each room. Afterward, the decision-making mechanism provides goals and constraints based on the dynamic requirements of the architectural environment, offering control guidance and suggestions for MPC. Its control approaches are as follows.

Specifically, after accurate building thermal dynamic models are obtained, the decision-making module is responsible for dynamic planning and energy resource scheduling, with the aim of enabling adaptive room-level optimization and striking a balance between multiple objectives such as conserving energy, ensuring occupant comfort, and prioritizing room allocation.

First, this process acquires the predicted occupancy of each room, which is calculated as shown in Equation (15):

$$P_{r,h}={\displaystyle \frac{I_{r,h}}{N_r}}$$

(15)

where $I_{r,h}$ represents the occupant count in room $r$ at time step $h$, and $N_r$ represents the maximum occupancy capacity of room $r$. Then, MAPC employs appropriate metrics to quantitatively evaluate occupant comfort.

(1) On the one hand, for datasets with complete parameters, occupant thermal comfort is evaluated using the Predicted Mean Vote (PMV) index. The PMV is an internationally recognized metric and is calculated based on a heat-balance model, correlating environmental variables with human metabolic responses. The formulation is expressed as follows:

$$PMV=[0.303e^{-0.036M}+0.028]L$$

(16)

where $M$ is the occupant metabolic rate and $L$ is the occupant thermal load. In this study, to reduce computational complexity, the PMV calculation is streamlined by fixing secondary parameters [52,53], as shown below.

$$\left\{\begin{array}{c}\begin{array}{c}{I}_{cl}=0.5clo=0.078 {\mathrm{m}}^2·\mathrm{K}/\mathrm{W}\\ M=1.2met=69.8 \mathrm{W}/{\mathrm{m}}^2\\ W=0\end{array}\\ \begin{array}{c}{v}_a=0.1 \mathrm{m}/\mathrm{s}\\ RH=50\%\\ T_r=T_{in}\end{array}\end{array}\right.$$

(17)

where $I_{cl}$ is the clothing insulation, and $M$ corresponds to sedentary activity involving light brain work. $W$ represents the mechanical work which is assumed to be zero, consistent with a stationary office scenario. The air velocity $v_a$ simulated still air conditions typical of standard HVAC operation and the relative humidity $RH$ was maintained at conventional dehumidification setpoints. Finally, the mean radiant temperature $T_r$ was equivalent to the indoor air temperature.

Based on the aforementioned fixed parameters, the total sensible heat loss of occupants $Q_{sens}$ can be derived as:

$$\left\{\begin{array}{c}{Q}_{sens}={\displaystyle \frac{T_{sk}-T_{in}}{I_{cl}+1/(h_c+h_r)}}\\ T_{sk}=34 °\mathrm{C}\\ I_{cl}=0.078 {\mathrm{m}}^2·\mathrm{K}/\mathrm{W}\\ \begin{array}{c}{h}_c=3.0 \mathrm{W}/{\mathrm{m}}^2·\mathrm{K}\\ h_r=4.7 \mathrm{W}/{\mathrm{m}}^2·\mathrm{K}\end{array}\end{array}\right.$$

(18)

where T_sk denotes the mean skin temperature, while $h_c$ and $h_r$ represent the convective and radiative heat transfer coefficients, respectively.

Then, differentiating $Q_{sens}$ with respect to $T$ yields:

$${\displaystyle \frac{d{Q}_{sens}}{dT}}={\displaystyle \frac{1}{I_{cl}+1/(h_c+h_r)}}\approx -4.81 W/({\mathrm{m}}^2·°\mathrm{C})$$

(19)

$${\displaystyle \frac{dL}{dT}}=-{\displaystyle \frac{d{Q}_{sens}}{dT}}\approx 4.81 \mathrm{W}/({\mathrm{m}}^2·°\mathrm{C})$$

(20)

$${\displaystyle \frac{\partial PMV}{\partial T}}=[0.303e^{-0.036M}+0.028]L·{\displaystyle \frac{dL}{dT}}\approx 0.25 \mathrm{W}/({\mathrm{m}}^2·°\mathrm{C})$$

(21)

Finally, accounting for evaporative losses and second-order effects, we calibrated the coefficient to 0.28, yielding:

$$PMV=0.28\times (T-T_{setpoint})$$

(22)

where $T$ represents the indoor temperature, $\alpha$ represents the seasonal adjustment factor, and $T_{setpoint}$ represents the temperature set point, which is calculated by Equation (23).

$$T_{setpoint}=\left\{\begin{array}{c}{T}_{base}+(T_{max}-T_{base})\times (1-P_{r,h}) summer\hfill \\ T_{base}-(T_{base}-T_{min})\times (1-P_{r,h}) winter\hfill \end{array}\right.$$

(23)

where $T_{max}$,$T_{min}$ and $T_{base}$ are defined by the user and represent the temperature limits desired by the user.

(2) On the other hand, for datasets with limited parameter availability, we design a comfort violation index of the occupants. This index serves as a temperature-based discomfort proxy, functioning as a substitute for the conventional PMV calculation. i.e.,

$$C_o=(T_{air,in}-T_{setpoint})\times ({\lambda }_o+P_{r,h})$$

(24)

where ${\lambda }_o$ represents the basic weight of temperature violation and is also defined by the user.

After obtaining the occupant comfort violation index, we can list the objective functions for each MPC, as shown in Equation (25):

$$\left\{\begin{array}{c}{J}_{MAPC}=\min {[{\omega }_o{{\displaystyle \sum (\tilde{C}}}_o or PMV)}^2+{\omega }_e{\displaystyle \sum {\tilde{Q}}_{HVAC}^2+{\omega }_s{\displaystyle \sum \Delta {\tilde{Q}}_{HVAC}^2)}}]\\ \begin{array}{c}{\tilde{C}}_o={\displaystyle \frac{C_o}{C_{ref}}}, {\tilde{Q}}_{HVAC}={\displaystyle \frac{Q_{HVAC}}{Q_{ref}}}, \Delta {\tilde{Q}}_{HVAC}={\displaystyle \frac{\Delta Q_{HVAC}}{\Delta Q_{ref}}}\\ C_{ref}=1 °\mathrm{C}, Q_{ref}=\Delta Q_{ref}=1 \mathrm{KWh}\end{array}\end{array}\right.$$

(25)

where $C_o$ represents the occupant comfort term, $Q_{HVAC}$ represents the energy consumption term, and control smoothness term, respectively, and ${\omega }_o, {\omega }_e, {\omega }_s$ are the weights of each term, calculated by the following formula:

$$\left\{\begin{array}{l}{\omega }_o={\omega }_{o,base}\times ({\lambda }_1+P_{r,h})\\ {\omega }_e={\omega }_{e,base}\times [{\lambda }_2+(1-P_{r,h})]\\ {\omega }_s={\lambda }_3\end{array}\right.$$

(26)

where ${\lambda }_1, {\lambda }_2$ and ${\lambda }_3$ are defined by the users, which represent their control preferences. In this study, all aforementioned user-defined weighting factors are determined through iterative refinement informed by expert experience and empirical performance evaluation. Furthermore, all terms in Equation (26) are normalized by reference values $C_{ref}$, $Q_{ref}$ and $\Delta Q_{ref}$ to ensure dimensional homogeneity.

Finally, the MPC controllers in each room operate based on the corresponding models obtained through the model construction process, along with real-time environmental parameters such as occupancy and outdoor temperature, to derive an adaptive room-level control strategy that balances multiple objectives. The entire MAPC process is illustrated in Algorithm 1.

Algorithm 1 Working process of MAPC

Input: Diverse environmental data $\left\{T_{air,out},T_{air,in},S,Q_{HVAC},I_{d,h}\right\}$ Output: Adaptive room-level HVAC control strategy that balances objectives such as personnel comfort and energy consumption and simulated control results 1: MAPC uses the N4SID method to identify the base model of each room 2: MAPC identifies RC models for each room 3: MAPC selects candidate values for $\lambda$ 4: MAPC minimizes the loss function and obtains the optimal model for $\lambda$ 5: MAPC selects the best model and the corresponding $\lambda$ 6: MPC controllers perform rolling optimization 7: for ($t=0 ; t\le t_{final} ; t++$) 8:            The MPC controllers acquire and report dynamic environmental data $\left\{T_{air,out},S,P_h\right\}$ 9:        The MPC controllers solve Equation (20) and obtain the control sequence${\stackrel{·}{U}}_t$ 10:       The MPC controllers execute $U_{t,1}$ and calculate the simulation results $T_{air,in,t}$ 11:       The MPC controllers pass $T_{air,in,t}$ to the next step and continue optimization 12: end for 13: The MPC controllers obtain the final control strategy $U(t)$ and simulation results $T_{air,in}$

4. Experimental Studies

4.1. Simulation Experiment Based on EnergyPlus

4.1.1. Experimental Configuration

In this section, we verify MAPC on a simulated dataset generated by EnergyPlus. The workflow of the experiment is shown in Figure 5.

Firstly, a 3D model of a five-zone office building was developed using SketchUp. Subsequently, this model was translated into an EnergyPlus Input Data File (IDF) via the OpenStudio plugin. Then, a full-year simulation was executed, utilizing a 15 min time step to generate the training dataset. Specifically, as shown in

Table 1. EnergyPlus Simulation Parameters.

EnergyPlus Parameters	Configuration/Value
Number of Timesteps per Hour	4
Location	Nanjing, China
Number of Thermal Zones	5
Maximum Number of Occupants in Rooms	10
Constant Heating Setpoint	20
Constant Cooling Setpoint	26
Outputs	outdoor air temperature
	indoor air temperature
	HVAC energy consumption
	absorbed solar radiation

, the EnergyPlus simulation utilizes the official standard weather file for Nanjing, China. During the simulation process, the HVAC system is modeled using the Ideal Loads Air System and operates under a RBC strategy in each room. Aligned with ASHRAE Standard 55 [36], the HVAC setpoints are configured to initiate cooling when the temperature exceeds 26 °C and heating when it drops below 20 °C. The output data encompass the outdoor air temperature, indoor air temperature for each zone, HVAC energy consumption, and absorbed solar radiation.

Then, we utilize the full year of data to construct and fine-tune the model, and the simulated dataset is divided into chronological order, with 70% used for training the model, 10% for validation, and the remaining 20% for testing. That is to say, the dataset is temporally partitioned such that the first 256 days are allocated for model training, the subsequent 36 days for validation, and the final 73 days for testing. Upon completion of the model construction and fine-tuning process, the fine-tuned model is deployed as the predictive engine within MAPC. Afterward, the performance of the MAPC framework is validated during two representative weeks: February 1–7 as a typical week in winter and August 1–7 as a typical week in summer. Given the minimal operational demand on the HVAC system during the spring and autumn months, these periods were excluded from the validation scope. Regarding occupants, a stochastic occupancy model is employed to generate the simulation dataset. For the purpose of model validation, we assume perfect foresight of future occupancy fluctuations, thereby emulating the input stream of a real-world prediction module.

For each time step in the representative winter and summer weeks, a multi-objective optimization yields the adaptive control input. The derived control actions are fed into EnergyPlus for co-simulation, and the simulated actual states are subsequently returned to MAPC to initialize the next optimization cycle, thereby enabling a rolling control loop. It is important to note that the simulated HVAC system operates under a constant supply air temperature strategy. The control action is executed by varying the supply airflow rate, which converts the commanded energy input into the corresponding mass flow of conditioned air.

To demonstrate the superiority of the MAPC framework, we first establish a rule-based control (RBC) as the baseline control strategy. Under this scheme, the HVAC system operates daily from 08:00 to 18:00. Cooling is activated when the indoor temperature exceeds 26 °C in summer, and heating is triggered when it drops below 20 °C in winter. This baseline simulates a scenario of minimal thermal intervention within the building. Subsequently, we employed a conventional MPC [13] as an additional benchmark, which utilized RC model as its predictive engine. The system is treated as a set of independent subsystems, represented by a block-diagonal state matrix comprising the five room models. The objective function of the baseline MPC is defined as follows:

$$J_{Baseline}=\min {\displaystyle \sum _{r=1}^5[{\omega }_1{\displaystyle \sum {(T_{air,in\_r}(k)-T_{set})}^2}+{\omega }_2{\displaystyle \sum Q_{HVAC\_r}^2+{\omega }_3{{\displaystyle \sum diff(Q_{HVAC\_r})}}^2}]}$$

(27)

Moreover, a comprehensive summary of the hardware platform and the key parameters employed throughout the experimental validation is presented in

Table 2. Control hardware and parameters.

Hardware/Parameters	Configuration/Value
${\omega }_{o,base}$	3
${\omega }_{e,base}$	1
${\lambda }_1$	2
${\lambda }_2$	1
${\lambda }_3$	5
${\omega }_1$	50
${\omega }_2$	1
${\omega }_3$	5
Solver	PyTorch Adam (PyTorch 2.9.1, CUDA12.6)
Iterations	80
Learning Rate	2.2
Prediction Horizon	12 (3 h)
CPU	Intel Core i5-10400

. For all methods, the absolute value of the control input $Q_{HVAC}$ constrained within the range of 0 to 50 kWh. Furthermore, seasonal operational constraints were enforced: cooling was permitted exclusively in summer, while heating was allowed only in winter. Consistent with this MAPC, the conventional MPC also received occupancy rate inputs and underwent similar preprocessing as MAPC, but with lower summer cooling setpoints and higher winter heating setpoints. Maintaining indoor temperatures at higher levels during winter and lower levels during summer, this MPC strategy is employed to simulate a high-level regime of thermal regulation within the building.

It is worth noting that although a learning rate of 2.2 is unusually high for deep learning paradigms, in this study, the Adam optimizer is applied to optimize the control sequence $Q_{HVAC}$ instead of network weights. The optimization space is low-dimensional and structurally simple, with only 20 iterations. A large learning rate is therefore necessary to ensure rapid convergence. Furthermore, each MPC step initializes the optimization near the optimal solution of the previous step, meaning the starting point is already close to the optimum. Under these conditions, a large learning rate does not cause divergence.

4.1.2. Evaluation Metrics

We first choose appropriate metrics to evaluate the performance of MAPC. (1) Indoor temperature control results are used to reflect the direct impact of the control scheme on the indoor environment. These results demonstrate the precise regulation capability of this method towards the environment and whether it can meet the control requirements of the user. (2) Energy consumption is used to reflect the impact of control schemes on building energy efficiency. The lower the energy consumption, the higher the energy-saving level of the method. (3) The PMV index, which refers to the internationally standardized index used to quantify human thermal comfort. The closer PMV is to zero, the more the current environment is able to meet the occupants’ needs.

4.1.3. Overall Performance

Taking all the parameters and indicators into consideration, the primary focus is on the method’s efficacy in optimizing the trade-off between occupant comfort and energy use. In this section, we simulate and compare the results of temperature control, occupant comfort violation index, and energy consumption under each mode of MAPC with those obtained under baseline control, as shown in Figure 6.

Where the red curve represents the temperature control results of MAPC, the blue curve represents the temperature control results of conventional MPC, the green curve represents the control results of baseline RBC strategy, while the purple curve represents the occupancy of each room, respectively.

It is obvious that MAPC can provide adaptive room-level control strategies based on dynamic occupant comfort and energy consumption requirements. Specifically, the indoor temperature trajectories of each room align closely with user-defined dynamic objectives, achieving an optimized trade-off between occupant comfort and energy conservation. MAPC facilitates personalized control strategies tailored to specific zones and time steps. In scenarios characterized by high occupancy or elevated comfort requirements, MAPC prioritizes thermal comfort by tightly tracking adaptive temperature setpoints, thereby placing greater emphasis on precise temperature regulation. Conversely, during periods of low occupancy or relaxed demand, MAPC alleviates control stringency, shifting the optimization focus toward energy minimization and consequently reducing HVAC energy consumption.

In addition, to assess its capability in balancing occupant comfort with energy consumption, we also compared the PMV and energy consumption of each room under different strategies, as shown in Figure 7 and Figure 8.

Clearly, the total PMV across all zones under MAPC are consistently lower than those of the baseline MPC, regardless of the season. Specifically, compared to the baseline RBC, MAPC achieved a reduction in aggregate PMV indices, with room-specific decreases ranging from 11.2% to 52.2% in summer and 68.8% to 88.6% in winter. The average PMV reduction reached 29.4% in summer and 76.6% in winter. Moreover, relative to conventional MPC, MAPC achieved a reduction in aggregate PMV indices, with room-specific decreases ranging from 17.4% to 58.1% in summer and 31.6% to 47.9% in winter. The average PMV reduction reached 36.3% in summer and 37.9% in winter. Furthermore, given that the baseline control operates exclusively from 08:00 to 18:00 while the conventional MPC and MAPC strategies run continuously over a 24 h cycle, we conducted a dedicated comparison of the total PMV specifically within the baseline’s active window. The results demonstrate that within this period, MAPC reduces the total PMV by 56.1% in summer and 45.4% in winter compared to the baseline. Meanwhile, relative to conventional MPC, MAPC achieves reductions of 31.7% in summer and 57.4% in winter.

It can thus be concluded that although conventional MPC maintains lower temperatures during summer and higher temperatures during winter, this does not necessarily translate to superior thermal comfort. According to the PMV formulation, comfort is not a monotonic function of temperature alone. Crucially, higher occupancy levels elevate the PMV value toward the warm side +1 at a given temperature, whereas lower occupancy shifts it toward the cool side −1. MAPC’s ability to modulate control objectives based on real-time occupancy allows it to navigate this relationship, achieving a PMV trajectory that remains closer to the neutral point (0) compared to the baseline.

Furthermore, in terms of energy consumption, MAPC can balance the goals of energy conservation and meeting dynamic environmental requirements under relatively limited energy resources. In contrast to the baseline RBC which represents minimal-intervention control, MAPC strategically increases energy consumption to achieve higher occupant comfort. However, when compared to conventional MPC, it achieved a reduction in total energy consumption, with room-specific decreases ranging from 5.5% to 33.9% in summer and 18.3% to 43.4% in winter. The average energy consumption reduction reached 22.3% in summer and 32.4% in winter.

Finally, to evaluate its ability to handle highly dynamic occupant-related information, we compared the average running time of MAPC in one time step with that of conventional centralized MPC, as illustrated in Figure 9. To rigorously benchmark the runtime efficiency advantage of our proposed MAPC, we standardized all other parameters for the conventional centralized MPC to be identical to those of MAPC, excluding the control logic. This controlled variable approach effectively isolates the contribution of distributed method by eliminating confounding factors. Obviously, MAPC demonstrated significantly faster performance, with an average optimization time of 291.2 ms versus 666.0 ms for conventional centralized MPC, representing a 56.3% decrease. This result clearly demonstrates that the distributed architecture of MAPC, which operates on low-dimensional state spaces, directly translates to significant runtime savings compared to the high-dimensional optimization in conventional centralized MPC. The reduced computational latency enables MAPC to process real-time, highly dynamic occupant data rapidly and effectively, facilitating near real-time adaptation and avoiding control delays.

4.1.4. Ablation Experiments

In this section, to demonstrate the accuracy and effectiveness of the data-driven model with physical priors used by MAPC, we designed two sets of ablation experiments, removing the N4SID data-driven part and the RC model-driven parts, and comparing the predictive ability of the MAPC model with the purely model-driven model and the purely data-driven model. Furthermore, we benchmarked the proposed MAPC framework against the conventional gray-box AutoRegressive Moving Average with eXogenous inputs (ARMAX) model [13,54]. In this work, the ARMAX model is realized via a custom, in-house software implementation rather than through commercial system-identification toolboxes. Both models were evaluated using an identical input dataset to ensure a fair comparison. All experiments are conducted on the EnergyPlus dataset, which is more comprehensive, to ensure high fidelity and generalizability, as shown in Figure 10, Figure 11 and Figure 12.

Figure 10 compares the predicted outcomes of each model against the actual value. The green curve represents the MAPC fine-tuned model, the red curve represents the model that dissolved the data-driven part, the blue curve represents the model that dissolved the model-driven part, the purple curve represents the ARMAX model, and the black curve represents the actual value. Evidently, the MAPC model exhibits superior predictive accuracy in forecasting indoor temperature variations.

Furthermore, as shown in Figure 11 and Figure 12, we adopted a comprehensive suite of metrics to evaluate the model’s predictive performance, including CVRMSE, MAE, MAPE, NMBE, and RMSE, according to ASHRAE Guideline 14 [53]. Specifically, the comparison focuses exclusively on the pure open-loop prediction performance of each method. Specifically, the models forecast indoor temperature over a 12-step horizon using only the input from the first step, and all evaluation metrics are averaged over this entire prediction window.

Figure 11 illustrates the overall comparison of evaluation metrics across all rooms, while Figure 12 presents a temporal analysis of these metrics for different prediction horizons under the rolling forecast scheme. It is worth noting that the multi-step prediction results presented in Figure 12 and

Table 3. Average Model Performance Evaluation Metrics.

Model	ARMAX	RC	N4SID	MAPC
CVRMSE	18.1723	14.4627	6.7010	1.1166
MAE	2.9992	2.0908	0.8520	0.1409
MAPE	16.0505	10.5972	4.3961	0.7306
NMBE	14.0126	−7.8184	1.3251	0.1720
RMSE	3.4817	2.7680	1.2846	0.2147

represent the average performance over the entire prediction horizon. Evidently, compared to the two ablated models and the ARMAX model, the data-driven model integrating physical priors used by MAPC can better fit the real indoor temperature data, with an error distribution closer to 0. The specific evaluation metrics of the three models are shown in Table 3.

4.2. Simulation Experiment Based on CN-OBEE

4.2.1. Experimental Configuration

To enhance the credibility and authenticity of the experiments, in this section, we verify MAPC on a public room-level building environmental and occupancy dataset, named CN-OBEE. CN-OBEE provides a dataset containing a full year of data. With regard to the location, the dataset was collected in a duplex apartment inhabited by a typical urban family of three in Miyun District, Beijing. The dataset includes information on occupant presence as well as indoor and outdoor environmental data such as temperature, solar radiation, and energy consumption of various appliances. This paper utilizes data from the four typical rooms, including a Master Bedroom, a Secondary Bedroom, a Home Office and a Kitchen. The layout of the rooms is shown in Figure 13. Unfortunately, the specific room geometry was not disclosed in the original dataset. Each room is equipped with an independent split-type air conditioner. Regarding the time series, to simulate the situation of a limited dataset, we used data collected in August 2021. The time interval for indoor data is 1 min, while that for outdoor data is 1 h. The dataset was sampled at a one-minute interval. To align the time scale of the data, we assume that the outdoor data within one hour represents a smooth transition between the actual two consecutive data points. Specifically, we assume a linear ramp between consecutive hourly measurements. Under this premise, the 59 intervening samples are populated through arithmetic sequencing, i.e., classical linear interpolation across the interval bounded by the two hourly values. Missing data points are filled with the median of the surrounding data. The final dataset is divided into chronological order, with 70% used for training the model, 10% for validation, and the remaining 20% for testing.

Since the dataset records only binary occupancy presence rather than explicit occupant counts, Equation (28) is employed to estimate the room occupancy. For the purpose of model validation, we assume that MAPC has perfect foresight of this derived occupancy rate to serve as a predictive input.

$$P_h={\displaystyle \frac{{\displaystyle \sum _{d=1}^D{I}_{d,h}}}{N_h}}$$

(28)

where $I_{d,h}$ represents the occupant presence status of each room. If the room is occupied in the time interval $h$ on day $d$, then $I_{d,h}$ is 1. Otherwise,$I_{d,h}$ is set to 0.

The predicted occupancy in each room is calculated every half an hour. In addition, the input data include outdoor environmental data such as outdoor temperature, solar radiation and energy consumption. All of the outdoor environmental data are sourced from the national meteorological station in Miyun District. In this section, we conduct experiments using data from 0:00 to 8:00 on August 25th. In order to simulate the operation results under different user preferences, we design two operating modes for MAPC, i.e., the comfort mode which pays more attention to occupant comfort, and the energy saving mode which focuses more on energy conservation. The parameter settings for the formulas of each mode are shown in Equations (29) and (30).

$$T_{max}=28 °\mathrm{C}, T_{base}=24 °\mathrm{C}, {\lambda }_0=0.2$$

(29)

$$\left\{\begin{array}{l}{\lambda }_1=0.4\\ {\lambda }_2=0.1\\ {\lambda }_3=0.01\end{array} \left(\mathrm{Comfort} \mathrm{Model}\right)\right. \left\{\begin{array}{l}{\lambda }_1=0.2\\ {\lambda }_2=0.3\\ {\lambda }_3=0.01\end{array}\right. \left(\mathrm{Energy} \mathrm{Saving} \mathrm{Model}\right)$$

(30)

4.2.2. Evaluation Metrics

We still choose similar appropriate metrics to evaluate the performance of MAPC. (1) Indoor temperature control results are used to reflect the direct impact of the control scheme on the indoor environment. These results demonstrate the precise regulation capability of this method towards the environment and whether it can meet the control requirements of the user. (2) Energy consumption is used to reflect the impact of control schemes on building energy efficiency. The lower the energy consumption, the higher the energy-saving level of the method. (3) The occupant comfort violation index, which refers to the degree to which the indoor environment violates the occupants’ needs, taking the occupancy probability into account. Due to the unavailability of essential parameters required for the standard PMV formulation, this study adopts this simplified index as a proxy for thermal comfort assessment. The lower the occupant comfort violation index, the more the current environment is able to meet the occupants’ needs.

4.2.3. Overall Performance

We continued to evaluate our method’s capability to reconcile energy consumption with occupant comfort, reaffirming its effectiveness in navigating this critical trade-off. We first define the control strategies and results provided in the dataset as a baseline. This baseline control strategy represents a rule-based and low-effort manual operation, wherein occupants intervene only reactively when the indoor environment becomes intolerable. Then, we simultaneously compare the results of temperature control, occupant comfort violation index, and energy consumption under each mode of MAPC with those obtained under baseline control and conventional centralized MPC, as shown in Figure 14. In this section, the parameter configurations for the conventional MPC are kept identical to those detailed in Section 4.1, except the temperature setpoint which is fixed at 26 °C. The red dashed line in the figure represents the baseline temperature control results from the dataset and the green curve represents the temperature control results of conventional MPC, while the purple and blue curves represent the control results of the two modes of MAPC, respectively. The green dashed line represents the temperature tracking target of conventional MPC.

Obviously, MAPC can provide adaptive multi-objective room-level control strategies. The comfort mode of MAPC demonstrates superior performance in maintaining indoor temperatures closer to the desired setpoints, while the energy saving mode prioritizes energy conservation at the expense of looser temperature regulation. Moreover, compared with baseline control and conventional centralized MPC, the indoor temperature of each room under both MAPC modes can align with user-defined control dynamic objectives, providing adaptive multi-objective control strategies that balance occupant comfort and energy conservation goals. Meanwhile, MAPC can dynamically adjust personalized control strategies for each room. In rooms with high environmental requirements such as occupant comfort, MAPC can adjust control objectives to better meet occupant comfort needs, while allowing MPC controllers to focus more on temperature tracking. In the opposite situation, MAPC releases the pressure on temperature control, adopts optimization logic that focuses more on energy conservation, and reduces cooling energy consumption.

In addition, we also compared the comfort violation index of each room under different strategies, as shown in Figure 15. Clearly, mainly considering the occupant demands, the comfort mode of MAPC can maintain the lowest value in most cases, reflecting its excellent ability to meet occupant comfort requirements. The index in energy saving mode has increased, but it can still maintain a level lower than the conventional MPC during times of high demand.

Furthermore, in terms of balancing the goals of energy conservation and meeting dynamic environmental requirements under relatively limited energy resources, MAPC can use the least amount of energy to enhance occupant comfort, as shown in Figure 16. Specifically, compared with the conventional centralized MPC, the control strategy provided by the comfort mode of MAPC can reduce the occupant comfort violation index by 55.4% while only increasing energy consumption by 14.7%. Meanwhile, the energy saving mode of MAPC achieves a 44.3% reduction in the comfort violation index along with a 7.7% decrease in energy consumption.

Finally, we also compared the average running time of MAPC in one time step with that of conventional centralized MPC, as illustrated in Figure 17. Obviously, MAPC demonstrated significantly faster performance, with an average optimization time of 324.75 ms versus 1017.86 ms for conventional MPC, representing a 68.1% decrease. These results further corroborate that the distributed architecture of MAPC effectively reduces computational latency, leading to significantly shorter execution times.

5. Discussion

MAPC demonstrates significant potential for balancing energy conservation and meeting dynamic occupant requirements like thermal comfort.

Firstly, in terms of model construction, the experimental results reveal that the superiority of MAPC does not merely stem from a combination of two modeling paradigms, but from a structural complementarity. While the data-driven subspace identification captures transient thermal responses and occupancy-induced non-stationarities that RC models typically oversimplify, the RC-based physical prior acts as a strong regularization mechanism. This explains why MAPC achieves a CVRMSE of 1.1166 even under severe data scarcity, whereas pure data-driven N4SID suffers from higher variance. In essence, the physical loss term constrains the solution space to thermodynamically plausible regions, mitigating overfitting without requiring additional data.

However, the model trained based on the data-driven subspace projection method still shares the mathematical structure of the state space equation with the RC model, which means that the model still cannot capture the nonlinear relationships in the building environment effectively, resulting in poor model performance. Using machine learning methods such as neural networks to learn the model is a good solution. In recent years, gray-box algorithms such as physics-informed neural networks (PINNs) have also provided new ideas for solving these problems [55,56]. Furthermore, while this work proposes a paradigm that integrates data-driven method with physical priors for model construction and control, it does not delve deeply into how to better utilize these priors, such as the design of physics-informed loss functions and the optimization strategies for the regularization coefficient $\lambda$ across diverse scenarios. Additionally, our focus is primarily on short-term predictive horizons, leaving the efficacy of longer-term forecasts an open question. Correspondingly, Chen et al. [56] employ an adaptively regularized loss function to investigate how physical priors can be more effectively fused into data-driven models under varying data availability, and they show that the resulting framework maintains robust predictive performance even over extended horizons of 1–15 days. Furthermore, these hybrid paradigms extend beyond building thermal environment control and also demonstrate significant potential in domains like fault detection and diagnosis (FDD), the establishment of PMV fields, and demand response (DR) orchestration. By anchoring data-driven insights to physical laws, these applications can yield superior output in the building environment.

Secondly, in terms of control strategies, from a control-theoretic perspective, the observed 56–68% reduction in optimization latency is not incidental. Centralized MPC scales poorly with the number of zones due to the curse of dimensionality, whereas MAPC decomposes the problem into multiple low-order room-level subproblems. Moreover, the generation of adaptive, room-level control strategies enables personalized comfort regulation. This mirrors distributed MPC strategies reported in recent energy-flexibility studies [22,57,58].

However, this study exclusively investigates model construction and control within small-scale environments comprising 4–5 rooms. The scalability and efficacy of the proposed framework in larger, more complex scenarios that are characterized by a greater number of zones, heterogeneous functionalities, and increased equipment diversity remain unverified. Correspondingly, Li et al. implemented a hierarchical and distributed MPC framework to conduct demand response control for an entire airport terminal, focusing on the joint optimization of occupant comfort and energy load [57]. Their work explored the optimal allocation of resources within such large-scale, complex building environments.

Finally, beyond the above issues, this research still has several problems and limitations that could be solved in future studies like the absence of real-world deployment and validation. Particularly for experiments conducted on the CN-OBEE dataset, the absence of ground-truth physical states or simulated states from platforms like EnergyPlus induces a progressive accumulation of model mismatch during open-loop execution. This inevitably leads to a drift in control authority and eventual instability, thereby constraining the viable experimental window to approximately 8 h. Furthermore, an inevitable gap exists between model-based predictions and real-world dynamics. Consequently, control methodologies capable of direct interaction with the environment are required to bridge this gap, such as Reinforcement Learning (RL). Moreover, the passive impacts of occupants on buildings are considered in this study, but the subjective impacts of occupants on buildings have not been fully explored, such as the feedback of occupants regarding the environment and their active energy-related behaviors.

As a result, the following three aspects could be interesting for future research: (a) Enhancing the integration of physical priors into data-driven algorithms; (b) Improving control efficacy in increasingly complex environments with heterogeneous equipment configurations; (c) Facilitating direct interaction with physical environments for adaptive learning; (d) Incorporating richer occupant-related information into the control loop.

6. Conclusions

In this paper, we propose a model-aware predictive control framework named MAPC, aiming to advance the field of sustainable indoor environments. MAPC is able to enhance occupant comfort and limit energy consumption within buildings. Our technical contributions can be summarized as follows. First, we proposed a model construction and fine-tuning structure combining data-driven methods with physical priors. Based on the subspace projection method and fine-tuned by utilizing RC models, MAPC can identify credible state space models for each room with limited data, which can be used for MPC as predictive models.

Second, to balance the potential conflicts associated with multi-zone distributed control, we propose a hierarchical framework and an adaptive decision-making mechanism based on dynamic rules to ensure that the system can achieve a balance between conflicting objectives and enable adaptive multi-objective room-level control considering both occupant comfort requirements and energy consumption.

Third, we conducted experiments on MAPC in different rooms and under various environmental conditions of a typical duplex apartment, and compared them with conventional methods and baseline control. The results showed that MAPC can effectively balance energy conservation and meet the dynamic needs of occupants while implementing differentiated control schemes for different rooms. Compared with conventional methods, MAPC is able to provide room-level control strategies based on dynamic occupant requirements and user preferences, achieving the effect of improving occupant comfort and energy efficiency. The ablation experiments also demonstrated the superiority of MAPC in constructing reliable models on limited datasets. However, this method has deficiencies in occupant behavior simulation and precise building modeling scenarios. To further overcome these issues, in the future, we will attempt to more accurately model occupant behaviors, and we also expect to integrate data-driven methods such as machine learning and RL to achieve more precise and efficient occupant-driven control for building environments. We position MAPC as a crucial first step toward realizing occupant-centric dynamic environmental control in buildings, thereby facilitating the attainment of sustainable indoor environments.