Constrained model predictive control: Stability and optimality

Mayne, D. Q.; Rawlings, James B.; Rao, Christopher V.; Scokaert, P.O.M.

doi:10.1016/s0005-1098(99)00214-9

Cited by 7,283 publications

(4,717 citation statements)

References 89 publications

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“…In what follows we sketch an approximation method for the solution of (2.1)-(2.2), based on model predictive control (MPC), which furnishes a suboptimal control by an iterative solution over a sequence of finite time steps, but, nonetheless, it allows an explicit representation of the control strategy [6,35,81,80].…”

Section: Model Predictive Control Of the Microscopic Dynamicsmentioning

confidence: 99%

Recent Advances in Opinion Modeling: Control and Social Influence

Albi

Pareschi

Toscani

et al. 2017

Modeling and Simulation in Science, Engineering and Technology

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We survey some recent developments on the mathematical modeling of opinion dynamics. After an introduction on opinion modeling through interacting multi-agent systems described by partial differential equations of kinetic type, we focus our attention on two major advancements: optimal control of opinion formation and influence of additional social aspects, like conviction and number of connections in social networks, which modify the agents' role in the opinion exchange process. PreliminariesWe introduce some of the essential literature on the opinion formation, by emphasizing the role of the kinetic description. New problems recently treated in the scientific community are outlined. Then, the mathematical description of the core ideas of kinetic models for opinion formation are presented in details.

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Section: Model Predictive Control Of the Microscopic Dynamicsmentioning

confidence: 99%

Recent Advances in Opinion Modeling: Control and Social Influence

Albi

Pareschi

Toscani

et al. 2017

Modeling and Simulation in Science, Engineering and Technology

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“…In contrast to standard NMPC approaches (see e.g. [6], [8], [9]) the cost functional to be minimized at all sampling instances t k = kδ is given by…”

Section: Model Predictive Path-followingmentioning

confidence: 99%

“…The assumptions follow well-known stability results, see e.g. [6], [8], [9]: A1 The state constraint set X ⊆ R n is closed and connected and contains the origin in its interior. A2 U ⊆ R m is compact and the origin is contained in the interior of U.…”

Section: Stability Of Mpfcmentioning

confidence: 99%

“…In this contribution we propose a solution to the path-following problem for nonlinear systems subject to constraints on inputs and states. In order to consider constraints the proposed control scheme relies on nonlinear model predictive control (NMPC) [6], [8], [9]. Since NMPC can be applied to tracking problems (see [10] for early results) we point out the difference between tracking and path-following in detail in Section II.…”

Section: Introductionmentioning

confidence: 99%

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Model predictive path-following for constrained nonlinear systems

Faulwasser

Kern

Findeisen

2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

100

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Abstract-We propose a model predictive control approach to path-following problems of constrained nonlinear systems. We directly consider input and state constraints. Furthermore, we introduce an extended corridor path-following problem, which allows to add spatial degrees of freedom to the path formulation. We give sufficient stability conditions for predictive solutions to 1d and corridor path-following problems. To illustrate the performance of our approach we discuss the example of an autonomous vehicle subject to input constraints.Index Terms-Nonlinear model predictive control, corridor path-following, input and state constraints, stability.

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“…Linear MPC (LMPC) is a control scheme for linear systems, which has been studied extensively [1] . However, most of the practical systems have nonlinearities.…”

Section: Introductionmentioning

confidence: 99%

A Contractive Sliding- mode MPC Algorithm for Nonlinear Discrete- time Systems

Zhao

Ding

2013

Int. J. Autom. Comput.

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This paper investigates a sliding-mode model predictive control (MPC) algorithm with auxiliary contractive sliding vector constraint for constrained nonlinear discrete-time systems. By adding contractive constraint into the optimization problem in regular sliding-mode MPC algorithm, the value of the sliding vector is decreased to zero asymptotically, which means that the system state is driven into a vicinity of sliding surface with a certain width. Then, the system state moves along the sliding surface to the equilibrium point within the vicinity. By applying the proposed algorithm, the stability of the closed-loop system is guaranteed. A numerical example of a continuous stirred tank reactor (CSTR) system is given to verify the feasibility and effectiveness of the proposed method.

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Constrained model predictive control: Stability and optimality

Cited by 7,283 publications

References 89 publications

Recent Advances in Opinion Modeling: Control and Social Influence

Recent Advances in Opinion Modeling: Control and Social Influence

Model predictive path-following for constrained nonlinear systems

A Contractive Sliding- mode MPC Algorithm for Nonlinear Discrete- time Systems

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