A game theoretic approach to nonlinear robust receding horizon control of constrained systems

Chen, H.; Scherer, Carsten W.; Allgöwer, Frank

doi:10.1109/acc.1997.612023

Cited by 94 publications

(53 citation statements)

References 7 publications

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“…Note that di!erently than with the scheme proposed in Chen et al (1997) it is easily shown that 0&(¸).…”

Section: Proof the Proof Of This Theorem Follows By Theorem 1 By Shomentioning

confidence: 99%

“…For further details on the computation of the set see Chen et al (1997) and Michalska and Mayne (1993) where a numerical procedure is given for a similar problem.…”

Section: Inverse Optimality Via a Fake Hji Equationmentioning

confidence: 99%

“…This condition is essential to guarantee that hM (x) is well de"ned. One way to achieve the monotonicity property, with a particular class of uncertainties, can be derived by Chen, Scherer, and AllgoK wer (1997), where a quadratic terminal penalty and a terminal region de"ne as the interior of a suitable level set of such a quadratic function is used. In Chen et al (1997) an open-loop optimization problem is solved to derive the RH control law.…”

Section: Inverse Optimality Via a Fake Hji Equationmentioning

confidence: 99%

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A receding–horizon approach to the nonlinear H∞ control problem

2001

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CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. AbstractThe receding}horizon (RH) methodology is extended to the design of a robust controller of H type for nonlinear systems. Using the nonlinear analogue of the Fake H algebraic Riccati equation, we derive an inverse optimality result for the RH schemes for which increasing the horizon causes a decrease of the optimal cost function. This inverse optimality result shows that the input}output map of the closed-loop system obtained with the RH control law has a bounded¸-gain. Robustness properties of the nonlinear H control law in face of dynamic input uncertainty are considered.

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“…Note that di!erently than with the scheme proposed in Chen et al (1997) it is easily shown that 0&(¸).…”

Section: Proof the Proof Of This Theorem Follows By Theorem 1 By Shomentioning

confidence: 99%

“…For further details on the computation of the set see Chen et al (1997) and Michalska and Mayne (1993) where a numerical procedure is given for a similar problem.…”

Section: Inverse Optimality Via a Fake Hji Equationmentioning

confidence: 99%

Section: Inverse Optimality Via a Fake Hji Equationmentioning

confidence: 99%

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A receding–horizon approach to the nonlinear H∞ control problem

2001

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“…Variations of this type of design are given in Chen et al (1997); Lee & Yu (1997); Mayne (1995); ; Ramirez et al (2002), differing predominantly in the manner by which they select W(·) and X f . If one interprets the word "optimal" in Definition 3.1 in terms of the worst-case trajectory in the optimal cone {x p [t, t+T] } * D , then at time τ ∈ [t, t+T] there are only two possibilities:…”

Section: Explicit Robust Mpc Using Open-loop Modelsmentioning

confidence: 99%

Robust Adaptive Model Predictive Control of Nonlinear Systems

DeHaan¹,

Guay²

2010

Model Predictive Control

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“…Several approaches are proposed using Nash strategy to design robust controls for linear systems [14,8]. A way to treat uncertainty is to interpret perturbation as an exogenous input (a fictitious player) [7,19]. In [19], the definition of equilibria is ex-⋆ This paper was not presented at any IFAC meeting.…”

Section: Introductionmentioning

confidence: 99%

Bounded Nash type controls for uncertain linear systems

et al. 2008

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This paper deals with multicriteria controls for systems coping with polytopic uncertainties. The proposed controls are inspired by a Nash strategy for exactly known systems, reformulated as a nonconvex coupling between Semi-Definite Programming problems. The extension to the uncertain case duplicates the Linear Matrix Inequalities for all vertices of the polytope. A new iterative algorithm using Semi-Definite Programming is provided to design bounded Nash type controls for uncertain systems. A numerical example is given to illustrate the design method.

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A game theoretic approach to nonlinear robust receding horizon control of constrained systems

Cited by 94 publications

References 7 publications

A receding–horizon approach to the nonlinear H∞ control problem

A receding–horizon approach to the nonlinear H∞ control problem

Robust Adaptive Model Predictive Control of Nonlinear Systems

Bounded Nash type controls for uncertain linear systems

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