Economic Model Predictive Control

Ellis, Matthew J.; Liu, Jinfeng; Christofides, Panagiotis D.

doi:10.1007/978-3-319-41108-8

Cited by 58 publications

(42 citation statements)

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Section: F Proof Of Theoremmentioning

confidence: 99%

“…We now solve (38) analytically. By considering the constraint (38c), we have that at all feasible points of (38) Our argument proceeds by demonstrating that the sequence of controls realized by the proposed EMPC method induce the desired decay property. Principally, the proof relies on an induction, and an application of the tower property of conditional expectations [64,Proposition 13.2.7].…”

Section: F Proof Of Theoremmentioning

confidence: 99%

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Robust Economic Model Predictive Control of Continuous-Time Epidemic Processes

Watkins

Nowzari

Pappas

2020

IEEE Trans. Automat. Contr.

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In this paper, we develop a robust economic model predictive controller for the containment of stochastic Susceptible-Exposed-Infected-Vigilant pSEIV q epidemic processes which drives the process to extinction quickly, while minimizing the rate at which control resources are used. The work we present here is significant in that it addresses the problem of efficiently controlling general stochastic epidemic systems without relying on mean-field approximation, which is an important issue in the theory of stochastic epidemic processes. This enables us to provide rigorous convergence guarantees on the stochastic epidemic model itself, improving over the mean-field type convergence results of most prior work. There are two primary technical difficulties addressed in treating this problem: (i) constructing a means of tractably approximating the evolution of the process, so that the designed approximation is robust to the modeling error introduced by the applied moment closure, and (ii) guaranteeing that the designed controller causes the closed-loop system to drive the SEIV process to extinction quickly. As an application, we use the developed framework for optimizing the use of quarantines in containing an SEIV epidemic outbreak.

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Section: F Proof Of Theoremmentioning

confidence: 99%

Section: F Proof Of Theoremmentioning

confidence: 99%

Robust Economic Model Predictive Control of Continuous-Time Epidemic Processes

Watkins

Nowzari

Pappas

2020

IEEE Trans. Automat. Contr.

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“…Ellis and Christofides propose a two‐layer EMPC formulation in which Lyapunov‐based controllers are used at both the upper economic and lower tracking levels, with a longer prediction horizon used at the upper level. A similar structure is applied in Ellis and Christofides, but with the upper level controller stability mechanism involving a bound on the rate of change of the states.…”

Section: Literature Reviewmentioning

confidence: 99%

The utilization of closed‐loop prediction for dynamic real‐time optimization

Jamaludin

Swartz

2017

Can J Chem Eng

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Real‐time optimization (RTO) is a layer within the hierarchical process automation architecture in which economically optimal set‐points are computed for the underlying plant control system. RTO calculations are traditionally based on steady‐state models, but an increasingly global and dynamic marketplace has led to the development of dynamic RTO (DRTO) strategies. Typical DRTO approaches optimize process input trajectories based on the open‐loop response dynamics of the process, with controller set‐point trajectories constructed from the resulting output response. This paper describes recent developments that utilize closed‐loop prediction in the DRTO calculations for MPC regulated processes. A rigorous closed‐loop DRTO problem is formulated as a multilevel dynamic optimization problem due to the inclusion of a sequence of MPC quadratic programming subproblems to generate the closed‐loop response dynamics. A simultaneous solution strategy is applied in which the MPC subproblems are replaced by their equivalent Karush‐Kuhn‐Tucker (KKT) optimality conditions, permitting reformulation of the original problem as a single‐level mathematical program with complementarity constraints (MPCC). Closed‐loop approximation techniques are proposed to reduce the dimension of the DRTO problem while maintaining good closed‐loop prediction accuracy. The performance of the proposed approaches is illustrated using case studies. Conclusions are drawn, and further research directions identified.

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“…Distributed model predictive control (DMPC), which controls each subsystem by an individual local model predictive control (MPC), has been one of the most important distributed control and optimization methods . It is because that DMPC not only inherits MPC's abilities to obtain good optimization performance, explicitly accommodating constraints, but also has the advantages of a distributed framework mentioned above .…”

Section: Introductionmentioning

confidence: 99%

Enhanced information reconfiguration for distributed model predictive control for cyber‐physical networked systems

Wei

Zheng

2019

Intl J Robust & Nonlinear

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Summary This paper considers a class of cyber‐physical networked systems, which are composed of many interacted subsystems, and are controlled in a distributed framework. The operating point of each subsystem changes with the varying of working conditions or productions, which may cause the change of the interactions among subsystems correspondingly. How to adapt to this change with good closed‐loop optimization performance and appropriate information connections is a problem. To solve this problem, the impaction of a subsystem's control action on the performance of related closed‐loop subsystems is first deduced for measuring the coupling among subsystems. Then, a distributed model predictive control (MPC) for tracking, whose subsystems online reconfigure their information structures, is proposed based on this impaction index. When the operating points changed, each local MPC calculates the impaction indices related to its structural downstream subsystems. If and only if the impaction index exceeds a defined bound, its behavior is considered by its downstream subsystem's MPC. The aim is to improve the optimization performance of entire closed‐loop systems and avoid the unnecessary information connections among local MPCs. Besides, contraction constraints are designed to guarantee that the overall system converges to the set points. The stability analysis is also provided. Simulation results show that the proposed impaction index is reasonable along with the efficiency of the proposed distributed MPC.

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Economic Model Predictive Control

Cited by 58 publications

References 0 publications

Robust Economic Model Predictive Control of Continuous-Time Epidemic Processes

Robust Economic Model Predictive Control of Continuous-Time Epidemic Processes

The utilization of closed‐loop prediction for dynamic real‐time optimization

Enhanced information reconfiguration for distributed model predictive control for cyber‐physical networked systems

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