Robust stabilization of uncertain time-varying discrete systems and comments on “an improved approach for constrained robust model predictive control”

Mao, Weijie

doi:10.1016/s0005-1098(03)00069-4

Cited by 150 publications

(116 citation statements)

References 3 publications

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Section: Resultsmentioning

confidence: 95%

“…In [13] and [10], the method of parameter-dependent Lyapunov function has been adopted. Especially, in [10] the results have been improved further compared to the results in [13].…”

Section: Resultsmentioning

confidence: 99%

“…Especially, in [10] the results have been improved further compared to the results in [13]. But, the it can not be proved that the resulting closed-loop system is robustly stable based on the algorithm proposed in [13] and [10], which was neglected in paper [13] and [10]. Firstly, at sampling k, the control feedback is designed such that the upper bound on V (x(k|k)) is minimized, which is little different to Theorem 1 in [13] and Theorem 2 in [10].…”

Section: Resultsmentioning

confidence: 99%

“…Then, the uncertain discrete-time system (1) is time-varying. So the robust stability conditions for system (1) will be more strict than the case that unknown parameter are constant [10].…”

Section: Problem Statementmentioning

confidence: 99%

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Robust Constrained Model Predictive Control Based on Parameter-Dependent Lyapunov Functions

Xia

Liu

Shi

et al. 2008

Circuits Syst Signal Process

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The problem of robust constrained model predictive control (MPC) of systems with polytopic uncertainty is considered in this paper. New sufficient conditions for the existence of parameter-dependent Lyapunov functions are proposed in terms of linear matrix inequalities (LMIs), which will reduce the conservativeness resulting from using a single Lyapunov function. At each sampling instant, the corresponding parameter-dependent Lyapunov function is an upper bound for a worst-case objective function, which can be minimized using the LMI convex optimization approach. Based on the solution of optimization at each sampling instant, the corresponding state feedback controller is designed, which can guarantee that the resulting closed-loop system is robustly asymptotically stable. In addition, the feedback controller will meet the specifications for systems with input or output constraints, for all admissible time-varying parameter uncertainties. Numerical examples are presented to demonstrate the effectiveness of the proposed techniques.

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Section: Resultsmentioning

confidence: 95%

“…In [13] and [10], the method of parameter-dependent Lyapunov function has been adopted. Especially, in [10] the results have been improved further compared to the results in [13].…”

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

“…Then, the uncertain discrete-time system (1) is time-varying. So the robust stability conditions for system (1) will be more strict than the case that unknown parameter are constant [10].…”

Section: Problem Statementmentioning

confidence: 99%

See 2 more Smart Citations

Robust Constrained Model Predictive Control Based on Parameter-Dependent Lyapunov Functions

Xia

Liu

Shi

et al. 2008

Circuits Syst Signal Process

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“…An LMI-based robust MPC first appeared in [3] where a linear state feedback controller with infinite control horizon was proposed for polytopic uncertain models and for the case where the system can be represented by a linear model with a feedback uncertainty. The approach has been extended to improve the feasibility and to reduce conservatism in several works, by defining a parameter-dependent Lyapunov function [8,9], by introducing relaxation matrices in the robust control problem formulation [10] or by introducing linear matrix inequalities as approximations to the robust system constraints [11]. The computer effort was also reduced through the offline solution of a sequence of explicit control laws corresponding to a sequence of asymptotically stable invariant ellipsoids [12].…”

Section: Introductionmentioning

confidence: 99%

Linear matrix inequality-based robust model predictive control for time-delayed systems

Capron

Uchiyama

Odloak

2012

IET Control Theory Appl.

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This work addresses the solution to the problem of robust model predictive control (MPC) of systems with model uncertainty. The case of zone control of multi-variable stable systems with multiple time delays is considered. The usual approach of dealing with this kind of problem is through the inclusion of non-linear cost constraint in the control problem. The control action is then obtained at each sampling time as the solution to a non-linear programming (NLP) problem that for high-order systems can be computationally expensive. Here, the robust MPC problem is formulated as a linear matrix inequality problem that can be solved in real time with a fraction of the computer effort. The proposed approach is compared with the conventional robust MPC and tested through the simulation of a reactor system of the process industry.

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Synthesis of Robust Model Predictive Control

2019

Predictive Control

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Robust stabilization of uncertain time-varying discrete systems and comments on “an improved approach for constrained robust model predictive control”

Cited by 150 publications

References 3 publications

Robust Constrained Model Predictive Control Based on Parameter-Dependent Lyapunov Functions

Robust Constrained Model Predictive Control Based on Parameter-Dependent Lyapunov Functions

Linear matrix inequality-based robust model predictive control for time-delayed systems

Synthesis of Robust Model Predictive Control

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