Special Issue "New Directions on Model Predictive Control"

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: closed (31 July 2018)

Special Issue Editors

Guest Editor
Prof. Dr. Jinfeng Liu

Department of Chemical & Materials Engineering, 13-269 Donadeo Innovation Center for Engineering, University of Alberta, 9211-116 Street, Edmonton, AB, T6G 1H9, Canada
Website | E-Mail
Interests: networked process control systems; distributed predictive control of nonlinear systems; distributed state estimation; networked plant-wide monitoring and fault-tolerant control; optimal operation of energy systems
Guest Editor
Prof. Dr. Helen E Durand

Department of Chemical Engineering & Materials Science, 5050 Anthony Wayne Drive, Room 1115, College of Engineering, Wayne State University, Detroit, MI 48202, USA
Website | E-Mail
Interests: plant-wide control of nonlinear systems; centralized and distributed economic model predictive control; operational safety of closed-loop processes; reduced-order modeling in predictive control

Special Issue Information

Dear Colleagues,

Model predictive control (MPC) has been an important and successful advanced control technology in process industries, mainly due to its ability to handle effectively complex systems with hard control constraints. At each sampling time, MPC solves a constrained optimal control problem online, based on the most recent state or output feedback to obtain a finite sequence of control actions and only applies the first portion. MPC presents a very flexible optimal control framework that is capable of handling a wide range of industrial issues while incorporating state or output feedback to aid in robustness of the design.

Traditionally, centralized MPC with quadratic cost functions had dominated the focus of MPC research. Advances in computing, communication and sensing technologies in the last decades have enabled us to look beyond the traditional MPC and brought new challenges and opportunities in MPC research. Two important examples of this technology-driven development are distributed MPC (in which multiple local MPC controllers carry out their calculations in separate processors collaboratively) and economic MPC (in which a general economic cost function that typically is not quadratic is optimized). There are already many results on distributed MPC and economic MPC. However, there are still many important problems that need investigation within and beyond distributed and economic MPC. Along with the theoretical development in MPC, we are also witnessing the application of MPC to many non-traditional control or scheduling problems. Some examples are the use of MPC in the treatment of diabetes, management of hemoglobin in anemia, irrigation scheduling in agriculture, and coordination of distributed energy generation systems.

The purpose of this Special Issue is to assemble a collection of current research in MPC that handles practically-motivated theoretical issues, as well as recent MPC applications to highlight the significant potential benefits of new MPC theory and design.

Prof. Dr. Jinfeng Liu
Prof. Dr. Helen E Durand
Guest Editors

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 350 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Optimal control
  • Predictive control
  • Receding horizon control
  • Moving horizon estimation
  • Nonlinear programming
  • Dissipativity
  • Distributed estimation

Published Papers (9 papers)

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Research

Open AccessFeature PaperArticle A Nonlinear Systems Framework for Cyberattack Prevention for Chemical Process Control Systems
Mathematics 2018, 6(9), 169; https://doi.org/10.3390/math6090169
Received: 13 August 2018 / Revised: 11 September 2018 / Accepted: 12 September 2018 / Published: 14 September 2018
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Abstract
Recent cyberattacks against industrial control systems highlight the criticality of preventing future attacks from disrupting plants economically or, more critically, from impacting plant safety. This work develops a nonlinear systems framework for understanding cyberattack-resilience of process and control designs and indicates through an
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Recent cyberattacks against industrial control systems highlight the criticality of preventing future attacks from disrupting plants economically or, more critically, from impacting plant safety. This work develops a nonlinear systems framework for understanding cyberattack-resilience of process and control designs and indicates through an analysis of three control designs how control laws can be inspected for this property. A chemical process example illustrates that control approaches intended for cyberattack prevention which seem intuitive are not cyberattack-resilient unless they meet the requirements of a nonlinear systems description of this property. Full article
(This article belongs to the Special Issue New Directions on Model Predictive Control)
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Open AccessArticle Approximate Dynamic Programming Based Control of Proppant Concentration in Hydraulic Fracturing
Mathematics 2018, 6(8), 132; https://doi.org/10.3390/math6080132
Received: 16 June 2018 / Revised: 26 July 2018 / Accepted: 27 July 2018 / Published: 1 August 2018
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Abstract
Hydraulic fracturing has played a crucial role in enhancing the extraction of oil and gas from deep underground sources. The two main objectives of hydraulic fracturing are to produce fractures with a desired fracture geometry and to achieve the target proppant concentration inside
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Hydraulic fracturing has played a crucial role in enhancing the extraction of oil and gas from deep underground sources. The two main objectives of hydraulic fracturing are to produce fractures with a desired fracture geometry and to achieve the target proppant concentration inside the fracture. Recently, some efforts have been made to accomplish these objectives by the model predictive control (MPC) theory based on the assumption that the rock mechanical properties such as the Young’s modulus are known and spatially homogenous. However, this approach may not be optimal if there is an uncertainty in the rock mechanical properties. Furthermore, the computational requirements associated with the MPC approach to calculate the control moves at each sampling time can be significantly high when the underlying process dynamics is described by a nonlinear large-scale system. To address these issues, the current work proposes an approximate dynamic programming (ADP) based approach for the closed-loop control of hydraulic fracturing to achieve the target proppant concentration at the end of pumping. ADP is a model-based control technique which combines a high-fidelity simulation and function approximator to alleviate the “curse-of-dimensionality” associated with the traditional dynamic programming (DP) approach. A series of simulations results is provided to demonstrate the performance of the ADP-based controller in achieving the target proppant concentration at the end of pumping at a fraction of the computational cost required by MPC while handling the uncertainty in the Young’s modulus of the rock formation. Full article
(This article belongs to the Special Issue New Directions on Model Predictive Control)
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Open AccessFeature PaperArticle Forecast-Triggered Model Predictive Control of Constrained Nonlinear Processes with Control Actuator Faults
Mathematics 2018, 6(6), 104; https://doi.org/10.3390/math6060104
Received: 21 May 2018 / Revised: 11 June 2018 / Accepted: 12 June 2018 / Published: 19 June 2018
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Abstract
This paper addresses the problem of fault-tolerant stabilization of nonlinear processes subject to input constraints, control actuator faults and limited sensor–controller communication. A fault-tolerant Lyapunov-based model predictive control (MPC) formulation that enforces the fault-tolerant stabilization objective with reduced sensor–controller communication needs is developed.
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This paper addresses the problem of fault-tolerant stabilization of nonlinear processes subject to input constraints, control actuator faults and limited sensor–controller communication. A fault-tolerant Lyapunov-based model predictive control (MPC) formulation that enforces the fault-tolerant stabilization objective with reduced sensor–controller communication needs is developed. In the proposed formulation, the control action is obtained through the online solution of a finite-horizon optimal control problem based on an uncertain model of the plant. The optimization problem is solved in a receding horizon fashion subject to appropriate Lyapunov-based stability constraints which are designed to ensure that the desired stability and performance properties of the closed-loop system are met in the presence of faults. The state-space region where fault-tolerant stabilization is guaranteed is explicitly characterized in terms of the fault magnitude, the size of the plant-model mismatch and the choice of controller design parameters. To achieve the control objective with minimal sensor–controller communication, a forecast-triggered communication strategy is developed to determine when sensor–controller communication can be suspended and when it should be restored. In this strategy, transmission of the sensor measurement at a given sampling time over the sensor–controller communication channel to update the model state in the predictive controller is triggered only when the Lyapunov function or its time-derivative are forecasted to breach certain thresholds over the next sampling interval. The communication-triggering thresholds are derived from a Lyapunov stability analysis and are explicitly parameterized in terms of the fault size and a suitable fault accommodation parameter. Based on this characterization, fault accommodation strategies that guarantee closed-loop stability while simultaneously optimizing control and communication system resources are devised. Finally, a simulation case study involving a chemical process example is presented to illustrate the implementation and evaluate the efficacy of the developed fault-tolerant MPC formulation. Full article
(This article belongs to the Special Issue New Directions on Model Predictive Control)
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Open AccessArticle Model Predictive Control of Mineral Column Flotation Process
Mathematics 2018, 6(6), 100; https://doi.org/10.3390/math6060100
Received: 28 April 2018 / Revised: 1 June 2018 / Accepted: 4 June 2018 / Published: 13 June 2018
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Abstract
Column flotation is an efficient method commonly used in the mineral industry to separate useful minerals from ores of low grade and complex mineral composition. Its main purpose is to achieve maximum recovery while ensuring desired product grade. This work addresses a model
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Column flotation is an efficient method commonly used in the mineral industry to separate useful minerals from ores of low grade and complex mineral composition. Its main purpose is to achieve maximum recovery while ensuring desired product grade. This work addresses a model predictive control design for a mineral column flotation process modeled by a set of nonlinear coupled heterodirectional hyperbolic partial differential equations (PDEs) and ordinary differential equations (ODEs), which accounts for the interconnection of well-stirred regions represented by continuous stirred tank reactors (CSTRs) and transport systems given by heterodirectional hyperbolic PDEs, with these two regions combined through the PDEs’ boundaries. The model predictive control considers both optimality of the process operations and naturally present input and state/output constraints. For the discrete controller design, spatially varying steady-state profiles are obtained by linearizing the coupled ODE–PDE model, and then the discrete system is obtained by using the Cayley–Tustin time discretization transformation without any spatial discretization and/or without model reduction. The model predictive controller is designed by solving an optimization problem with input and state/output constraints as well as input disturbance to minimize the objective function, which leads to an online-solvable finite constrained quadratic regulator problem. Finally, the controller performance to keep the output at the steady state within the constraint range is demonstrated by simulation studies, and it is concluded that the optimal control scheme presented in this work makes this flotation process more efficient. Full article
(This article belongs to the Special Issue New Directions on Model Predictive Control)
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Open AccessArticle Enhancing Strong Neighbor-Based Optimization for Distributed Model Predictive Control Systems
Mathematics 2018, 6(5), 86; https://doi.org/10.3390/math6050086
Received: 1 April 2018 / Revised: 7 May 2018 / Accepted: 8 May 2018 / Published: 22 May 2018
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Abstract
This paper considers a class of large-scale systems which is composed of many interacting subsystems, and each of them is controlled by an individual controller. For this type of system, to improve the optimization performance of the entire closed-loop system in a distributed
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This paper considers a class of large-scale systems which is composed of many interacting subsystems, and each of them is controlled by an individual controller. For this type of system, to improve the optimization performance of the entire closed-loop system in a distributed framework without the entire system’s information or too-complicated network information, connectivity is always an important topic. To achieve this purpose, a distributed model predictive control (DMPC) design method is proposed in this paper, where each local model predictive control (MPC) considers the optimization performance of its strong coupling subsystems and communicates with them. A method to determine the strength of the coupling relationship based on the closed-loop system’s performance and subsystem network connectivity is proposed for the selection of each subsystem’s neighbors. Finally, through integrating the steady-state calculation, the designed DMPC is able to guarantee the recursive feasibility and asymptotic stability of the closed-loop system in the cases of both tracking set point and stabilizing system to zeroes. Simulation results show the efficiency of the proposed DMPC. Full article
(This article belongs to the Special Issue New Directions on Model Predictive Control)
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Open AccessArticle Safeness Index-Based Economic Model Predictive Control of Stochastic Nonlinear Systems
Mathematics 2018, 6(5), 69; https://doi.org/10.3390/math6050069
Received: 28 March 2018 / Revised: 26 April 2018 / Accepted: 27 April 2018 / Published: 3 May 2018
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Abstract
Process operational safety plays an important role in designing control systems for chemical processes. Motivated by this, in this work, we develop a process Safeness Index-based economic model predictive control system for a broad class of stochastic nonlinear systems with input constraints. A
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Process operational safety plays an important role in designing control systems for chemical processes. Motivated by this, in this work, we develop a process Safeness Index-based economic model predictive control system for a broad class of stochastic nonlinear systems with input constraints. A stochastic Lyapunov-based controller is first utilized to characterize a region of the state-space surrounding the origin, starting from which the origin is rendered asymptotically stable in probability. Using this stability region characterization and a process Safeness Index function that characterizes the region in state-space in which it is safe to operate the process, an economic model predictive control system is then developed using Lyapunov-based constraints to ensure economic optimality, as well as process operational safety and closed-loop stability in probability. A chemical process example is used to demonstrate the applicability and effectiveness of the proposed approach. Full article
(This article belongs to the Special Issue New Directions on Model Predictive Control)
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Open AccessFeature PaperArticle Economic Model Predictive Control with Zone Tracking
Mathematics 2018, 6(5), 65; https://doi.org/10.3390/math6050065
Received: 1 April 2018 / Revised: 22 April 2018 / Accepted: 23 April 2018 / Published: 25 April 2018
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Abstract
In this work, we propose a framework for economic model predictive control (EMPC) with zone tracking. A zone tracking stage cost is incorporated into the existing EMPC framework to form a multi-objective optimization problem. We provide sufficient conditions for asymptotic stability of the
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In this work, we propose a framework for economic model predictive control (EMPC) with zone tracking. A zone tracking stage cost is incorporated into the existing EMPC framework to form a multi-objective optimization problem. We provide sufficient conditions for asymptotic stability of the optimal steady state and characterize the exact penalty for the zone tracking cost which prioritizes zone tracking objective over economic objective. Moreover, an algorithm to modify the target zone based on the economic performance and reachability of the optimal steady state is proposed. The modified target zone effectively decouples the dynamic zone tracking and economic objectives and simplifies parameter tuning. Full article
(This article belongs to the Special Issue New Directions on Model Predictive Control)
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Open AccessFeature PaperArticle A Novel Distributed Economic Model Predictive Control Approach for Building Air-Conditioning Systems in Microgrids
Mathematics 2018, 6(4), 60; https://doi.org/10.3390/math6040060
Received: 26 March 2018 / Revised: 12 April 2018 / Accepted: 13 April 2018 / Published: 17 April 2018
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Abstract
With the penetration of grid-connected renewable energy generation, microgrids are facing stability and power quality problems caused by renewable intermittency. To alleviate such problems, demand side management (DSM) of responsive loads, such as building air-conditioning system (BACS), has been proposed and studied. In
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With the penetration of grid-connected renewable energy generation, microgrids are facing stability and power quality problems caused by renewable intermittency. To alleviate such problems, demand side management (DSM) of responsive loads, such as building air-conditioning system (BACS), has been proposed and studied. In recent years, numerous control approaches have been published for proper management of single BACS. The majority of these approaches focus on either the control of BACS for attenuating power fluctuations in the grid or the operating cost minimization on behalf of the residents. These two control objectives are paramount for BACS control in microgrids and can be conflicting. As such, they should be considered together in control design. As individual buildings may have different owners/residents, it is natural to control different BACSs in an autonomous and self-interested manner to minimize the operational costs for the owners/residents. Unfortunately, such “selfish” operation can result in abrupt and large power fluctuations at the point of common coupling (PCC) of the microgrid due to lack of coordination. Consequently, the original objective of mitigating power fluctuations generated by renewable intermittency cannot be achieved. To minimize the operating costs of individual BACSs and simultaneously ensure desirable overall power flow at PCC, this paper proposes a novel distributed control framework based on the dissipativity theory. The proposed method achieves the objective of renewable intermittency mitigation through proper coordination of distributed BACS controllers and is scalable and computationally efficient. Simulation studies are carried out to illustrate the efficacy of the proposed control framework. Full article
(This article belongs to the Special Issue New Directions on Model Predictive Control)
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Open AccessFeature PaperArticle Data Driven Economic Model Predictive Control
Mathematics 2018, 6(4), 51; https://doi.org/10.3390/math6040051
Received: 7 March 2018 / Revised: 21 March 2018 / Accepted: 22 March 2018 / Published: 2 April 2018
Cited by 1 | PDF Full-text (3145 KB) | HTML Full-text | XML Full-text
Abstract
This manuscript addresses the problem of data driven model based economic model predictive control (MPC) design. To this end, first, a data-driven Lyapunov-based MPC is designed, and shown to be capable of stabilizing a system at an unstable equilibrium point. The data driven
[...] Read more.
This manuscript addresses the problem of data driven model based economic model predictive control (MPC) design. To this end, first, a data-driven Lyapunov-based MPC is designed, and shown to be capable of stabilizing a system at an unstable equilibrium point. The data driven Lyapunov-based MPC utilizes a linear time invariant (LTI) model cognizant of the fact that the training data, owing to the unstable nature of the equilibrium point, has to be obtained from closed-loop operation or experiments. Simulation results are first presented demonstrating closed-loop stability under the proposed data-driven Lyapunov-based MPC. The underlying data-driven model is then utilized as the basis to design an economic MPC. The economic improvements yielded by the proposed method are illustrated through simulations on a nonlinear chemical process system example. Full article
(This article belongs to the Special Issue New Directions on Model Predictive Control)
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