Electric Vehicle Model Predictive Control Energy Management Strategy: Theory, Applications, Perspectives and Challenges

Abstract

Model predictive control (MPC) has become one of the most promising control strategies in the field of electric vehicle energy management due to its rolling optimization and explicit constraint processing capabilities. This study analyzes the modeling mechanism and implementation path of MPC in power allocation, regenerative braking and energy collaborative control, which elaborates on the improvement principle of energy efficiency and system stability through predictive modeling and dynamic optimization. The evolution of MPC application in hybrid power systems, vehicle dynamic stability control, and hierarchical optimization control is discussed. The synergistic effect of multi-objective optimization and health-conscious control in energy efficiency improvement and service life extension is analyzed. With the development of artificial intelligence technology, MPC is expanding from model-based deterministic control to the directions of intelligent learning and distributed adaptation. Model uncertainty, computational complexity, and real-time solving efficiency are the main challenges faced by MPC. Future research will focus on the deep integration of model simplification, rapid solving, and intelligent learning to achieve a more efficient and reliable intelligent energy management system.

1. Theory of Electric Vehicle MPC Energy Management Strategy

MPC has become one of the key technologies in the energy management system of electric vehicles due to its ability to achieve dynamic optimization and rolling decision-making in muti-constraint systems. It uses a system model to predict future states within a finite prediction time domain to solve for optimal control inputs [1]. MPC can explicitly handle complex constraints such as power limits, battery State of Charge (SOC) and thermal safety thresholds to strike a comprehensive balance among energy efficiency, response performance, and lifespan protection [2], which is different from traditional rule-based or fuzzy logic strategies. Previous research mainly focused on linear systems and single-objective optimization problems. It relied on quadratic programming to achieve real-time solutions for linearized dynamic system models [3].

The linear model predictive control gradually faces limitations in terms of prediction accuracy and robustness as electric vehicle structures grow more complex and the nonlinearity of energy systems increases. Nonlinear model predictive control can achieve high-fidelity prediction and control of energy flow, which introduced more accurate coupled models of motors, batteries, and thermal systems to maintain stable energy efficiency under different driving conditions [4]. The hierarchical MPC structure with multiple layers and timescales is widely adopted. The upper layer is responsible for energy planning and SOC trajectory optimization, while the lower layer ensures the rapid response of current and torque to balance real-time performance and control accuracy [5]. The distributed and collaborative MPC control framework accomplishes fleet-level energy sharing and global energy optimization through information exchange and collaborative optimization among multiple control nodes. MPC can improve the overall energy efficiency with communication costs reduction, which demonstrates the potential of group collaborative control in intelligent transportation systems [6].

The economic-MPC incorporates energy consumption and lifespan factors into the cost function, which enables the system to realize an optimal trade-off between fuel economy and battery health status [7]. The introduction of learning-enhanced methods has further expanded the application boundaries of MPC. The deep learning-assisted MPC framework proposed by Ma et al. utilized neural networks to optimize system prediction accuracy [8], which allowed the controller to adjust to variations in operating conditions. Huang et al. achieved health-conscious through reinforcement learning-guided MPC to lay the foundation for the intelligence of MPC [9]. This type of integrated approach transformed MPC from a deterministic optimizer reliant on models into an intelligent control framework, which was equipped with self-learning and environmental adaptability capabilities. The MPC has evolved from traditional linear single-objective optimization to a comprehensive control system that integrated nonlinear modeling, learning enhancement, and distributed collaboration. In the future, MPC will provide theoretical support and engineering foundation for efficient, robust and sustainable electric transportation systems through the integration of artificial intelligence technology [10].

The MPC strategy inherits traditional rule-based and static optimization ideas with forward-looking prediction and coordination for future environments, vehicle states and system constraints. Amini et al. proposed a two-level MPC architecture for autonomous electric vehicles [11], which achieved collaborative optimization of energy and thermal management. The system consisted of an upper long-term scheduling layer and a lower short-term execution layer. The upper layer organized the future battery temperature and SOC trajectory through a long-term plan based on the traffic flow prediction. The lower layer adopted short-term nonlinear MPC to perform rolling optimization for power distribution between the motor and cooling system, which took into account real-time driving conditions. The two layers interacted through reference trajectories and feedback signals to form a cross-time-domain prediction–optimization–feedback closed loop, which provided a structural foundation for subsequent multi-time-domain energy management of electric vehicles.

The structure of the electric vehicle is displayed in Figure 1. With the advancement of computing hardware performance, the maturity of vehicle-to-everything and environmental perception technologies, research on MPC has gradually shifted from static optimization to predictive and adaptive dynamic control. Wang et al. proposed an adaptive model predictive control energy management system [12]. The system acquired dynamic load information of the operation scenario through on-board sensors or environmental models and fed it as input to the nonlinear auto-regressive neural network predictor. The predictor inferred load changes and power demands at several future time points based on the historical operating data, which introduced future-oriented condition awareness into the model predictive control framework. The changes in the state of the vehicle after operation were fed back to the upper level prediction and optimization module, which formed a dynamic self-correcting closed loop.

Optimization solving is the core component of the system structure in MPC for energy management. MPC achieved dynamic constraint and energy allocation coordination at multiple time scales by rolling the prediction model to solve the optimal control sequence at each sampling moment. Compared with traditional PID feedback regulation, MPC reached coordination between dynamic constraints and energy allocation across multiple time scales by iteratively solving the optimal control sequence at each sampling time with a predictive model. The MPC architecture introduced hierarchical optimization logic based on the traditional control. The upper layer performed global and local steady-state optimization, while the lower layer achieved real-time adjustment through the dynamic constraint control [13]. The hierarchical structure determined that MPC must be supported by the optimization algorithms. When the system model was linear, the energy management problem could be transformed into a convex quadratic programming problem, which can be quickly solved to use active set or interior-point methods to achieve real-time rolling optimization. The linear MPC structure was computationally efficient, which was easy to deploy and suitable for power distribution control in electric vehicles. In the scenarios involving nonlinear or strongly coupled constraints, the sequential quadratic programming or nonlinear MPC was required for iterative approximation and solution, which aimed to balance computational complexity and control accuracy [14]. MPC can achieve predictive and adaptive control of energy systems across different time scales through the collaborative mechanism of structural hierarchy-optimization solution. In terms of tool implementation, the MPC optimization for vehicle energy management has gradually shifted from simulation verification to the direction of embedded real-time solving. In order to meet the stringent requirements for computing resources and response time of the on-board controller, the solver optimized specifically for embedded systems was selected for deployment [15]. The modeling assumptions and effect on prediction accuracy of different MPC methodologies are given in

Table 1. The modeling assumptions and effect on prediction accuracy of different MPC methodologies.

Methodology	Modeling Assumptions	Effect on Prediction Accuracy
Linear MPC	System dynamics are linearized around operating points Neglects strong nonlinear couplings Ignores degradation and time-varying parameters	The advantage is that it can obtain high computational efficiency for real-time rolling optimization. The limitation is that prediction accuracy degrades significantly with increased system complexity or operating point deviations. Errors accumulate in dynamic driving conditions which leads to suboptimal energy allocation [3,14].
Low-order MPC	Reduces state dimensions Omits high-order nonlinear terms Focuses on key state variables while neglecting secondary factors	The advantage is that it can lower computational burden to enable faster solver convergence for embedded deployment. The limitation is that it sacrifices fidelity in complex scenarios of extreme maneuvering and rapid load changes. The reduced-order battery models may underestimate transient power surges to cause prediction errors in energy demand [16].
Degradation-aware MPC	Integrates aging models Assumes degradation is predictable via empirical or data-driven models Couples degradation costs with energy efficiency in the cost function	The advantage is that it can improve the long-term prediction accuracy for lifespan-related objectives (reducing fuel cell degradation by 13.29% [17]). Prediction errors increase if degradation models fail to capture parameter drift to bring suboptimal trade-offs between energy use and lifespan [18].

. On the whole, MPC achieves coordinated control of energy flow, lifespan, and thermal safety through model prediction and optimization solving, which strikes a balance between energy efficiency and dynamic performance. The combination of explicit control, rapid optimization, and distributed computing continuously enhances the real-time performance and stability, while hardware co-implementation propels MPC from theory to engineering applications.

This paper introduces the MPC of the energy management strategy technology of an electric vehicle which can be applied to various types of electric vehicles. In this context, this paper also introduces some research hot-spots in MPC, which are expected to have practical applications in the future. Some applications and related solutions are the academic research of researchers. It focuses on exploring the challenges faced in implementing MPC technology.

The structure of this paper consists of five parts with the first part being the overview. The second part describes the application of MPC. The third part describes perspectives and the fourth part focuses on exploring the key challenges faced by MPC. Finally, the conclusion of this paper is presented in the fifth part.

2. Application of MPC in Energy Management and Optimization Strategies

2.1. Vehicle Dynamics and Stability Control Strategy

Vehicle dynamics and stability control have always been the core of research in electric vehicle control systems. The complexities mainly come from the highly nonlinear characteristics of longitudinal, transverse, and coupled dynamics. With the development of electrification and intelligence, MPC stranded out due to the explicit constraint handling and rolling optimization characteristics, which became a key method for high-precision dynamic control and multi-objective coordination. MPC can realize predictive decision-making in environments with strong coupling, time-varying, and nonlinear constraints, which can enhance the stability and response speed of the system. Further learning enhanced the two-layer MPC framework by compensating for the vehicle mismatch model with the sparse variational Gaussian processes. The average lateral error was reduced by at least 43% under varying curvature trajectories. When there was a 2% mismatch in friction coefficient, the average lateral error decreased by 72% after learning [19]. Trajectory tracking and obstacle avoidance control was another crucial application of MPC in vehicle longitudinal and lateral coordinated control. He et al. adopted a decoupling structure of upper-level prediction and lower-level adaptive feedback with hierarchical lateral control [20], which utilized the foresight and multi-constraint handling capabilities of MPC to ensure global feasibility and stability. The structure relied on the feedback correction and low-pass characteristics of PID to suppress high-frequency disturbances. The steady-state error can be reduced and the continuity and executability of the steering command can be maintained under curved roads and complex working conditions. Yang et al. [21] conducted a comparison of the performance of model predictive control and robust state feedback control in trajectory tracking for autonomous vehicles. The results demonstrated that the robust controller can maintain a stable vehicle speed of 14 m/s. A small lateral deviation under low adhesion conditions had the strong robustness to model uncertainties and external disturbances. However, MPC was limited by the constraints of the model feasible region and the prediction horizon, which had a maximum maintainable speed of approximately 10 m/s. MPC exhibited faster dynamic response and higher trajectory tracking accuracy.

In terms of extreme maneuvering and drift motion control, MPC demonstrates superior dynamic response capabilities. Xu et al. utilized nonlinear dynamics and the Uni-Tire model to construct a drift controller [22]. All state variables converged to the same steady-state drift trajectory after a brief transition despite initial condition differences. The drift angle and yaw rate errors remained within a repeatable and stable range, which verified the robustness and consistency of the proposed MPC controller under nonlinear drift conditions. Meijer et al. suggested a nonlinear MPC strategy for automatic drift control based on a single-track vehicle model and simplified tire mechanics [23]. The control structure included two modes of stability constraints and without stability constraints. Nonlinear MPC can achieve stable closed-loop control on a circular drift trajectory with a maximum lateral deviation of approximately 1 m, which can enhance the dynamic response performance of the vehicle under extreme maneuvering. The MPC has achieved full coverage in the field of vehicle dynamics and stability control, linear yaw control to nonlinear trajectory tracking, obstacle avoidance, drift and longitudinal cruising. By integrating hybrid system modeling, learning enhancement and hierarchical optimization structure, MPC exhibited robustness, real-time performance, and high accuracy under complex operating conditions, which provided a systematic solution for the multi-objective balance among safety, energy efficiency, and handling stability [24].

2.2. Traditional and Multi-Objective Optimization MPC

The research on MPC in electric vehicle energy management has evolved from single-objective optimization to health-aware control. Previous research primarily focused on energy allocation to enhance the fuel economy. The linear MPC can effectively coordinate the energy flow between batteries and super-capacitors equipped with hybrid energy storage systems, which results in a maximum improvement of 21.88% in fuel economy under typical cycles [25]. The MPC longitudinal control strategy of the dual-motor drive system improves the vehicle’s speed tracking performance and energy utilization efficiency with energy consumption consideration. Experiments have indicated that this method can improve the speed tracking accuracy by 58.93%, which expands the efficient operating range of the power system by 40.93% with a 9.29% reduction in equivalent power consumption [26]. In the energy management study based on deep neural networks speed prediction and energy demand prediction system adaptive constraints, the fuel economy improved by 6.48% compared to the baseline scheme whose results approached the optimal solution obtained through dynamic programming [27]. The achievements have laid the theoretical and practical foundation for MPC in power allocation and energy coordination. The prediction accuracy and robustness of traditional linear MPC were limited with the increasing complexity of systems and the enhancement of nonlinear characteristics. Nonlinear MPC achieved more efficient energy scheduling by means of adding dynamic constraints and time-varying optimization. In the fuel cell hybrid power system, the combination of variable-horizon nonlinear MPC and Pontryagin’s minimum principle can decrease hydrogen consumption by 8.9% to ensure the lifespan of the fuel cell stack [28].

The integrated thermal management MPC model attained multi-level coordination among the motor, battery and cabin systems, which led to an energy consumption reduction of approximately 10.3% [29]. The battery power and torque predictive control used reduced-order MPC to decrease the computational dimension from two dimensions to one, which can improve the real-time performance [16]. The control framework for a dual-motor fuel cell system, which integrated the BiLSTM prediction and dynamic programming to obtain an overall energy efficiency improvement of 17.25% [30]. Nonlinear MPC has advantages in dealing with nonlinear and multi-coupled systems. Multi-objective MPC maintained a comprehensive balance among energy consumption, response, and lifespan with hierarchical and multi-time-domain structure as listed in Figure 2. Xiong et al. proposed the multi-input MPC structure [31], which assigned multi-objective weights by a coordination controller at the upper level. The framework employed a multi-input predictive optimizer at the lower level to perform coordinated control over states of combustion, air flow and speed, which achieved dynamic adaptive adjustment across different time scales.

MPC was gradually evolving towards fast solution methods to overcome the bottleneck of real-time performance and computational load issues. The stochastic MPC model declined fuel consumption by 3.9% under uncertain driving cycles [32], which combined Markov chain prediction with dynamic weight adjustment. The neural network prediction performed the best in energy allocation accuracy and fuel economy by comparing the different prediction algorithms [33]. Explicit MPC offline solving for multi-parameter quadratic programming can reduce the computational load by 97.46% and ascend fuel economy by 23.37% [34]. The multi-mode MPC framework controlled the fuel performance deviation within 2% through integrating the transmission engagement loss model [35]. The research findings offered an efficient and feasible implementation path for embedded real-time optimization.

Health perception and lifespan-driven control have emerged as notable new directions for the development of MPC. Quan et al. [36] proposed a health-aware learning model predictive control framework which combined reinforcement learning mechanisms with the health state modeling of fuel cell stacks. As given in Figure 3, it accomplished an expansion from single energy optimization to health–energy collaborative optimization with the predictive control process. The health-aware linear MPC system constituted a closed-loop control architecture including health estimation, predictive optimization, and energy execution. The learning-based predictive optimizer comprehensively considered energy demand, health indicators, and historical operating experience within the prediction time horizon. It utilized reinforcement learning mechanisms to generate optimal control sequences for the future to achieve adaptive energy management decisions under multi-objective constraints. The energy allocation execution layer coordinated the power and issues commands to the fuel cell. The energy storage system based on the prediction optimization results can ensure the vehicle’s driving demand which considered the system’s health and stable operation.

Hou et al. [37] put forward a multi-time-domain predictive energy management strategy which was compared with dynamic programming methods to evaluate the optimality and real-time feasibility. The hydrogen consumption was 4.96% in multiple typical driving cycles, which indicated that this strategy can achieve near-optimal energy allocation to reduce computational complexity. The degradation cost of the fuel cell was incorporated into the control objective function, which ensured that the optimization process can prioritize energy efficiency and consider the battery’s state of health. The power output curve of the fuel cell under hierarchical MPC was smoother and the fluctuation amplitude was reduced compared to dynamic programming. This method can effectively suppress transient power surges and slow down the degradation of reactor performance, which achieves a balance between energy utilization and lifespan extension. The findings verified real-time feasibility and health perception advantages of hierarchical MPC in energy management. The learning MPC strategy combined the reinforcement learning and health sensing mechanisms to incorporate the degradation state of fuel cells into the energy optimization process. The method can decrease hydrogen consumption and total operating costs by approximately 8.61% and 13.29% with energy efficiency maintenance [17]. The real-time cost minimization MPC strategy proposed by Zhou et al. [38] integrated hydrogen consumption cost, energy allocation, and fuel cell degradation cost into an optimization model.

The MPC transitioned from short-term energy consumption control to a phase of life cycle and health awareness optimization. MPC has developed from a single linear optimization approach to a comprehensive framework, which integrates nonlinear modeling, multi-objective trade-offs and health-aware control. MPC attained system-level optimization in terms of energy efficiency, response speed, and lifetime balance through a hierarchical structure, variable time-domain prediction, and a data-driven mechanism.

2.3. Energy Management Strategy for Hybrid Power System

The core characteristic of a hybrid power-train system is the coexistence of multiple energy sources of internal combustion engines, electric motors, batteries, fuel cells, or super capacitors. The energy sources are highly coupled in power distribution and energy recovery to necessitate a balance among fuel economy, power performance, and battery SOC maintenance. Compared with the traditional rule-based or static optimization methods, MPC can gain an important development direction for energy management strategies in hybrid systems. Borhan et al. demonstrated the coupled structure of the four subsystems of engine, generator, motor, and battery, which pointed out that power flow paths and system constraints [39]. SOC boundaries and maximum motor power were key prerequisites for MPC design. The trend and state variables can be incorporated into the prediction model and rolling optimization can be achieved through the system topology diagram. Sampathnarayanan et al. transformed the energy management problem of hybrid electric vehicles into an optimal control problem [40], which constructed a solution framework based on MPC. In order to achieve a balance among fuel economy, power performance, and SOC, the core idea was to utilize the dynamic model of the system and future operating condition prediction to solve for the optimal power distribution scheme in real-time for several future steps. In energy coupled systems, hierarchical and multi-objective structures were key to enhance the control performance and computational efficiency. Wei et al. proposed a driving mode recognition module founded on variational mode decomposition and extreme learning machine [41]. This module planned the battery SOC reference trajectory and combined an adaptive equivalent consumption minimization strategy to achieve coordinated power allocation between the motor/generator and the battery. Real-car testing showed that it reduced the average transient change of battery power by more than 11.61% compared with traditional energy management strategies. Feng et al. [42] proposed an optimization strategy that considered both fuel economy and battery life degradation costs, which can result in a reduction in total operating costs by 3.1–15.9% on hybrid mining trucks. The achieved superior control effects in battery and fuel cell degradation can enhance potential system lifespan.

The hierarchical multi-objective MPC possessed advantages in energy economy and component degradation suppression. The hybrid energy management strategy collaborative optimization proposed by Liu et al. [43] gained hierarchical optimal control under traffic constraints and dynamic boundaries by decoupling and coupling vehicle speed planning and energy allocation. The framework depicted in Figure 4 establishes an integrated energy management system encompassing information–decision–execution.

The backward solution and forward optimization processes reflect the rolling energy allocation in the hybrid system under future power forecasting. In this process, the battery and engine torque are optimized in coordination, which enables the system to adapt switch between different operating modes and achieve optimal overall energy efficiency under energy collaboration. The performance comparison among the MPC variants by regarding computational load, solver form, prediction horizon length, and real-time applicability are given in

Table 2. Performance comparison among the MPC variants by regarding computational load, solver form, prediction horizon length, and real-time applicability.

MPC Variant	Computational Load	Solver Form	Prediction Horizon Length	Real-Time Applicability
Linear MPC	Low (O(n2) for quadratic programming)	Active set/interior-point methods [13]	Short to medium (5–20 steps)	High Deployable on standard ECUs; Suitable for power distribution [25,26]
Nonlinear MPC	High (iterative approximation required [14])	Sequential quadratic programming	Medium (10–30 steps)	Moderate Feasible for embedded systems with optimized solvers; Used in thermal management [29]
Explicit MPC	Ultra-Low (97.46% load reduction [34])	Offline multi-parameter quadratic programming	Fixed	Very high No online optimization; Ideal for high-frequency control of torque distribution [34]
Hierarchical MPC	Medium-Low (decoupled upper/lower layers [5])	Upper is global optimization; Lower is fast local solvers	Upper: Long (30–100 steps); Lower: Short (5–15 steps)	High Balances real-time response and global optimality; Used in fleet-level energy sharing [6]
Learning-enhanced MPC	Medium-High (neural network inference [8,9])	Hybrid (model-based data-driven solvers)	Adaptive (10–40 steps)	Moderate Requires hardware acceleration for neural network inference; Suitable for adaptive energy management [36]
Stochastic MPC	High (probabilistic modeling [32])	Stochastic dynamic programming and Markov chain	Medium (15–30 steps)	Low Computational burden limits real-time use; Used in uncertain driving cycles [32]

.

3. Perspectives

3.1. Data-Driven Control Strategy

Traditional MPC relies on precise system models and prior knowledge of disturbances. However, it was susceptible to nonlinear coupling, parameter drift and external uncertainties under complex operating conditions, which lead to prediction biases and performance degradation. To overcome this problem, data-driven MPC emerged as the times required. This method took vehicle operation data as the core, which constructed predictive models, cost or constraint functions. It enhanced the adaptability of the controller to complex operating conditions and unknown disturbances by learning the dynamic laws of the system and the characteristics of energy flow [44]. Data-driven MPC established an input–output mapping through system operation data to reduce modeling dependencies and enhance real-time performance. Berberich et al. proposed a MPC method to construct a predictive model solely based on the historical input–output measurement data [45], which did not require an explicit system model. Guo et al. proposed a three-layer data-driven model to enhance MPC structure [46], which consisted of a state estimation layer, an enhanced predictive model layer, and an MPC solver layer. The structure exhibited estimated the deviation between the classical vehicle dynamics model and the actual state through data learning, which loaded this deviation as a residual model into the prediction model layer. The MPC solver made optimal control decisions based on the enhanced model.

Elokda et al. [47] drew a comparison between the data-driven Data-enabled Predictive Control (DeePC) algorithm and the MPC method. DeePC achieved comparable tracking accuracy to MPC in closed-loop trajectory tracking tasks. Its online computation time remained within an acceptable range to demonstrate the feasibility in complex nonlinear systems. Min et al. [48] further merged supervised learning with MPC to utilize the neural networks to generate a reference trajectory for SOC and guide power optimization. This approach reduced energy consumption by 34.73% compared with traditional charge depleting and charge sustaining strategies, which demonstrated the potential of learning-guided MPC in energy allocation tasks.

3.2. Intelligent Learning Control Strategy

In terms of intelligent learning control strategies, the main approach is to integrate traditional MPC with online/offline intelligent learning modules to form an intelligent structure with model adaptability and future prediction capabilities. Yeom suggested a method which combined the traditional MPC with an online learning module [49]. The traffic status, the behavior of the preceding vehicle, the vehicle dynamics, and the energy consumption model were all input into the prediction domain module along with environmental information. Adaptive predictions were made for future states through a continuously updated learning mechanism and the optimal control strategy was output by the MPC optimizer. Millo et al. applied a dual-layer recurrent neural network to construct an energy management system for hybrid electric vehicles as demonstrated with temporal learning [50]. This structure achieved adaptive optimization of energy allocation strategies by memorizing the dynamic relationship between vehicle operating states and power demands, which maintained consistency between prediction and control under different operating conditions.

Zhang et al. proposed a two-layer learning-enhanced MPC structure incorporating Gaussian processes [51]. The upper layer used a Gaussian process model to learn and compensate for the deviation between the vehicle prediction model and actual dynamics, while the lower layer performed rolling optimization and torque distribution based on the corrected model. The MPC prediction component can adapt in real time according to the system state by continuously updating the vehicle model with historical state data, which was highly suitable for the multi-source uncertainty scenarios of electric vehicles. MPC possesses the ability to intelligently adjust through the closed-loop process of learning–compensation–prediction–optimization. Wang et al. put forward a reinforcement learning-based MPC control structure for autonomous vehicle following scenarios and constructed a scenario risk threshold model to classify traffic scenarios based on the characteristics [52]. The reinforcement learning algorithm was designed to adjust the weight coefficients of MPC online. The framework included scene feature extraction, risk level judgment, and MPC execution. The controller was capable of adaptively adjusting the weights among safety distance, comfort, energy efficiency, and other performance factors based on the current scenario. It constituted an intelligent control framework equipped with scene perception, autonomous trade-off, and dynamic optimization capabilities.

Based on the energy and emission collaborative control framework of distributed deep reinforcement learning [53], Tang et al. presented the convergence curves of different deep reinforcement learning algorithms. It achieved the stability within approximately 20 iterations, whereas the traditional deep Q-network required about 80 iterations to converge. It indicated a training efficiency improvement of approximately four times which exhibited a faster convergence rate and more stable policy updates. The overview of the decentralized MPC in the modular powertrain system is given in Figure 5. The decentralized MPC framework for federated reinforcement learning was proposed by Khalatbarisoltani et al. [54]. The training strategies function independent of each vehicle’s local controller through reinforcement learning, without directly sharing sensitive data and only exchanging model parameters, which can help achieve globally optimal collaboration with protecting data privacy. This method enables each sub-controller to continuously absorb global experience to maintain the independence, which can enhance the computational efficiency and inter-module adaptability.

The contrast of real-time performance and complexity trade-offs of the different MPC methodologies is given in

Table 3. Real-time performance and complexity trade-offs contrast.

Metric	Linear MPC	Nonlinear MPC	Explicit MPC	Learning-Enhanced MPC
Energy efficiency gain	Up to 21.88% [25]	Up to 17.25% [30]	23.37% [34]	34.73% [48]
Computational complexity	1× (Baseline)	5–10× [14]	0.025× [34]	8–15× [9]
Prediction error	±10–15% [3]	±5–8% [29]	±8–12% [34]	±3–6% [48]
Lifespan extension	Negligible	10–15% [28]	Negligible	13.29% [17]
Sampling time	10–20 ms	20–50 ms	1–5 ms	50–100 ms
ECU hardware requirement	Standard motor control unit	Mid-range motor control unit	Low-power motor control unit	High-performance motor control unit
Convergence Time	<5 ms [13]	10–20 ms [14]	<1 ms [34]	20–40 ms [36]
Applicability	Electric Vehicle power distribution	Thermal/hybrid systems	Embedded real-time control	Adaptive energy management

. Through the integration of intelligent modules of deep learning, reinforcement learning, and distributed optimization, MPC is able to achieve adaptive modeling and dynamic optimization in complex and dynamic environments.

4. Challenges

Although MPC has demonstrated excellent optimization performance and constraint handling capabilities in energy management for electric vehicles and hybrid power systems, it still faces challenges in various aspects of model accuracy, computational complexity, real-time performance, and verifiability in engineering applications [55]. As the control objective expands from single energy consumption minimization to multi-objective coordination and lifetime optimization, the performance improvement is often constrained by both model errors and hardware computing power. The model accuracy and prediction error are the core factors that affect the control effect of MPC, which relies on system models for state prediction. When there are deviations in vehicle dynamics or battery models, the prediction errors can cause energy allocation to deviate from the optimal trajectory, which lead to a decline in control performance [56,57]. In the nonlinear modeling, considering degradation and thermal effects, uncertainty is further amplified, which makes it difficult for the optimization problem to converge [58]. The main bottleneck for the implementation of MPC lies in the issues of real-time performance and computational complexity. As the controller needs to solve an optimization problem in each sampling period, its computational burden grows exponentially with the prediction horizon and state dimension. Although methods of convex optimization, fast gradient algorithms, and explicit MPC have significantly improved solving speed, they still struggle to meet the real-time requirements of on-board control in high-dimensional nonlinear systems. Computational load can be partially reduced through hierarchical structures or dual explicit strategies. The overly fine division of the state space increases memory consumption, which stills limit long-term operation in embedded hardware [59].

The uncertainty and disturbances under complex operating conditions impose higher requirements on the robustness of MPC. MPC’s robustness is defined by its ability to maintain performance under model uncertainty, parameter drift, and external disturbances. The mechanism of robustness to model uncertainty is that robust MPC uses worst-case scenario bounds or data-driven correction to mitigate modeling errors. Parameter drift mechanism entails degradation-aware MPC integrating real-time health estimation and adaptive model updates via reinforcement learning [17,36,37], which extends the component lifespan while maintaining energy efficiency. Disturbance rejection uses hierarchical structures to suppress high-frequency disturbances to obtain obstacle avoidance and drift control. Variations in battery parameters, fluctuations in road friction, and frequent external disturbances occur, which can lead to model deviations and control instability during vehicle operation. Although robust MPC can maintain system performance under disturbances, computational complexity increases significantly and makes it difficult to achieve real-time performance. Stochastic MPC improves system stability through probabilistic modeling, but the computational burden brought by long-term optimization remains unresolved. It is difficult to attain a balance between robustness and computational efficiency [60].

The complexity of MPC further increases with the introduction of multi-objective and lifetime constraints into the energy management framework. Energy efficiency, economy, and lifespan often present a competitive relationship, and it is difficult to maintain global optimality for fixed cost weights under different operating conditions [61,62]. Although multi-objective optimization methods can realize performance tradeoffs, the increase in solution dimensions and frequent activation of constraints can easily lead to non-convexity and numerical instability [63]. The uncertainty of battery aging models further accumulates long-term prediction errors to weaken the feasibility of controllers in life-cycle optimization [18]. Future research on MPC in electric vehicle energy management should integrate algorithm structure with hardware collaboration. An intelligent predictive control structure combines real-time performance, stability, and interpretability, which can be constructed by consolidating model reduction, fast convex optimization, explicit control, and adaptive learning.

5. Conclusions

MPC has evolved from linear single-objective optimization to a comprehensive framework integrating nonlinear modeling, learning enhancement, health-aware control, effectively balancing energy efficiency, dynamic performance, and component lifespan in electric and hybrid vehicles. MPC excels in dynamics control (reducing lateral errors by up to 72%), energy optimization (improving fuel economy 8.9—17.25% via nonlinear MPC), and cost reduction (13.29% lower total operating costs with health-aware MPC). Explicit MPC and distributed learning boost computational efficiency to lay an engineering foundation. These efforts will advance MPC’s technical upgrading and support sustainable electric transportation.

(1)

With the prediction–optimization–feedback closed loop as the core, MPC uniformly handles multiple constraints of SOC, thermal safety, and power boundaries to achieve trade-offs among energy efficiency, dynamic performance, and life-cycle economy. Targeted researches yield substantial benefits. The high-precision adaptive modeling cuts prediction errors by over 50% and life-cycle costs by 10–15%.

(2)

Driven by data and intelligent learning, MPC has evolved from model dependency to learning enhancement. MPC incorporates degradation and thermal coupling into cost design to realize full life cycle optimization. The efficient algorithms reduce computational load by 60% for real-time on-board deployment. The robust optimization enhances anti-disturbance capability by 50–60% and lowers maintenance costs.

(3)

MPC necessitates simultaneous advancements in algorithm structure and hardware coordination, verification, and safety compliance. The intelligent multi-objective trade-offs reduce energy consumption by 8–12%. The hardware–software co-design slashes system costs by 25–30%.