Set-Theoretic Methods in Control

Blanchini, Franco; Miani, Stefano

doi:10.1007/978-3-319-17933-9

Cited by 209 publications

(111 citation statements)

References 266 publications

(487 reference statements)

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“…Observe that every forward invariant set C ⊆ X satisfies the inclusion C ⊆ F ∞ and that the set of admissible states X is, in general, much larger than the viability kernel F ∞ . Methods which can be used in order to compute invariant sets can be found in Blanchini and Miani (2008). The set C is said to be recursively feasible if it is forward invariant with respect to the feedback law µ N , that is µ N (x) ∈ U (x) and f (x, µ N (x)) ∈ C for all x ∈ C.…”

Section: Recursive Feasibility and Asymptotic Stabilitymentioning

confidence: 99%

Stability and feasibility of state constrained MPC without stabilizing terminal constraints

Boccia

Grüne

Worthmann

2014

Systems & Control Letters

142

122

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In this paper we investigate stability and recursive feasibility of a nonlinear receding horizon control scheme without terminal constraints and costs but imposing state and control constraints. Under a local controllability assumption we show that every level set of the infinite horizon optimal value function is contained in the basin of attraction of the asymptotically stable equilibrium for sufficiently large optimization horizon N .For stabilizable linear systems we show the same for any compact subset of the interior of the viability kernel. Moreover, estimates for the necessary horizon length N are given via an analysis of the optimal value function at the boundary of the viability kernel.

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Section: Recursive Feasibility and Asymptotic Stabilitymentioning

confidence: 99%

Stability and feasibility of state constrained MPC without stabilizing terminal constraints

Boccia

Grüne

Worthmann

2014

Systems & Control Letters

142

122

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“…By Blanchini and Miani (2008), Lemma 3 indicates that system (2.1) is asymptotically stable over D κ if and only if there exists a set of polytopes X i with vertex representation matrix X i being, such that ψ i (x) = inf{ p 1 : x = X i p} can serve as a Lyapunov function candidate. Moreover, suppose that F i (full column rank matrix) is the plane representation matrix of X i , then F i x ∞ = inf{ p 1 : x = X i p}.…”

Section: Switched Homogeneous Lyapunov Function For Switched Systemsmentioning

confidence: 99%

“…Definition 5 (Blanchini & Miani, 2008): A set S ∈ R n is called C-set if it is convex and compact and includes the origin as an interior point. A C-set S is 0-symmetric if x ∈ S implies that −x ∈ S .…”

Section: Appendix 1 Proof Of Lemmamentioning

confidence: 99%

Stability analysis of discrete-time switched systems: a switched homogeneous Lyapunov function method

Liu

Zhao

2015

International Journal of Control

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This paper addresses the stability issue of discrete-time switched systems with guaranteed dwelltime. The approach of switched homogeneous Lyapunov function of higher order is formally proposed. By means of this approach, a necessary and sufficient condition is established to check the exponential stability of the considered system. With the observation that switching signal is actually arbitrary if the dwell time is one sample time, a necessary and sufficient condition is also presented to verify the exponential stability of switched systems under arbitrary switching signals. Using the augmented argument, a necessary and sufficient exponential stability criterion is given for discretetime switched systems with delays. A numerical example is provided to show the advantages of the theoretical results.

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“…The prime reasons for academic and practical interest in these set-valued notions stem from their intimate relationships with fundamental aspects of control and systems theory as well as theory of dynamical systems. A selection of comprehensive and influential research monographs (Aubin, 1991;Blanchini and Miani, 2008;Rawlings and Mayne, 2009;Kurzhanski and Varaiya, 2014), together with numerous references therein, provides overwhelming evidence that reachability and set invariance have made a huge impact across a wide spectrum of classical fields of dynamics, controls and systems in general, and deterministic/robust/stochastic optimal and model predictive control syntheses as well as safety and stability analyses in particular. The contemporary, increasingly sophisticated autonomous engineered systems frequently require a prior-to-operation assurances of, at least, safe, resilient, secure and fault tolerant operability.…”

Section: Introductionmentioning

confidence: 99%

“…Interestingly enough, the majority of existing research efforts on the subjects have been focused almost exclusively on either discrete or continuous times formulations. A nonexhaustive list of selected works includes (Bertsekas, 1972;Schweppe, 1973;Gilbert and Tan, 1991;Aubin, 1991;Artstein, 1995;Kolmanovsky and Gilbert, 1998;Raković, 2007;Raković and Kouramas, 2007;Artstein and Raković, 2008;Blanchini and Miani, 2008;Kurzhanski and Varaiya, 2014).…”

Section: Introductionmentioning

confidence: 99%

Reachability and Invariance for Linear Sampled–data Systems

2017

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Abstract:We consider linear sampled-data dynamical systems subject to additive and bounded disturbances, and study properties of their forward and backward reach sets as well as robust positively invariant sets. We propose topologically compatible notions for the sampled-data forward and backward reachability as well as robust positive invariance. We also propose adequate notions for maximality and minimality of related robust positively invariant sets.Keywords: Reachability Analysis, Robust Positive Invariance, Sampled-data Systems.SYSTEC Report 2017-SC2, July 2017. This is a preprint of the article to be published in the Proceedings of the 20th IFAC World Congress, July 9-14, 2017, Toulouse, France. Reachability and Invariance for LinearSampled-data Systems S. V. Raković * ,1 , F. A. C. C. Fontes * , and I. V. Kolmanovsky * * * Universidade do Porto, Porto, Portugal * * The University of Michigan at Ann Arbor, Ann Arbor, U.S. Abstract:We consider linear sampled-data dynamical systems subject to additive and bounded disturbances, and study properties of their forward and backward reach sets as well as robust positively invariant sets. We propose topologically compatible notions for the sampled-data forward and backward reachability as well as robust positive invariance. We also propose adequate notions for maximality and minimality of related robust positively invariant sets.

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Set-Theoretic Methods in Control

Cited by 209 publications

References 266 publications

Stability and feasibility of state constrained MPC without stabilizing terminal constraints

Stability and feasibility of state constrained MPC without stabilizing terminal constraints

Stability analysis of discrete-time switched systems: a switched homogeneous Lyapunov function method

Reachability and Invariance for Linear Sampled–data Systems

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