Computation of Maximal Safe Sets for Switching Systems

Santis, Elena De; Benedetto, Maria Domenica Di; Berardi, Luca

doi:10.1109/tac.2003.822860

Cited by 89 publications

(34 citation statements)

References 30 publications

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“…We base our contribution on invariant set results for linear and general PWA systems (Blanchini, 1999;Kolmanovsky and Gilbert, 1998;Kerrigan, 2000;Raković et al, 2004;Saint-Pierre, 1994) and on recent results for linear switched systems (Julius and van der Schaft, 2002;De Santis et al, 2004). Our results agree with the general and abstract viability theory framework elaborated in (Aubin, 1991).…”

Section: Introductionsupporting

confidence: 65%

Invariant Sets for Switched Discrete Time Systems Subject to Bounded Disturbances

Grieder

Raković

Morari

et al. 2005

IFAC Proceedings Volumes

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This paper addresses invariant set computation for discrete-time switched systems subject to bounded disturbances. Specifically, we show how to compute the maximal robust switched invariant setC S ∞ , which we define to be the set of states which can be made robust invariant by an appropriate switching law. Furthermore it is demonstrated how the maximal robust reachable setK S ∞ (Ω) can be computed, i.e., all states which can be robustly steered into the target set Ω by an appropriate switching law. We also show how these sets may be used to obtain a minimum time controller for switched systems, i.e., a controller which robustly steers the state into a given target set in minimal time. Copyright

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Section: Introductionsupporting

confidence: 65%

Invariant Sets for Switched Discrete Time Systems Subject to Bounded Disturbances

Grieder

Raković

Morari

et al. 2005

IFAC Proceedings Volumes

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“…We remark that the procedure outlined, contrary to De Santis et al [2004], does not require CV to be a C-set (a convex compact set with a nonempty interior containing the origin) and it appears simpler to implement. When X, U, V, are specified as convex polyhedra, Algorithm 1 reduces to a sequence of linear programs and elementary operations on convex sets.…”

Section: Algorithmmentioning

confidence: 99%

“…The drawback however is that an initial control invariant set S -with respect to a given P and given V -must be found. This is easy to do in absence of disturbances, for in that case the equilibrium state x e is evidently invariant under u e such that x e = Ax e + Bu e , and it can be assumed Gutman, Cwikel [1987], De Santis et al [2004] S = {x e } as a starting point for the internal algorithm. However, we know of no general procedure to determine S in presence of disturbances.…”

Section: Introductionmentioning

confidence: 99%

On the Approximation of Invariant Sets for Constrained LDT Systems

Caravani

2005

IFAC Proceedings Volumes

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“…This equation implicitly determines the maximal controlled invariant set and the least restrictive feedback control map. Due to the complexity of exactly solving the HJB equation, researchers have been investigating approximate algorithms for computing inner-approximations of the maximal controlled invariant set [30,31,44,50]. Termination of the algorithm that computes the maximal controlled invariant set is often an issue and work has been investigating special classes of systems that allow to prove termination [46][47][48].…”

Section: Introductionmentioning

confidence: 99%

Safety Control of Hidden Mode Hybrid Systems

Verma

Vecchio

2012

IEEE Trans. Automat. Contr.

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Abstract-In this paper, we consider the safety control problem for Hidden Mode Hybrid Systems (HMHSs), which are a special class of hybrid automata in which the mode is not available for control. For these systems, safety control is a problem with imperfect state information. We tackle this problem by introducing the notion of non-deterministic discrete information state and by translating the problem to one with perfect state information. The perfect state information control problem is obtained by constructing a new hybrid automaton, whose discrete state is an estimate of the HMHS mode and is, as such, available for control. This problem is solved by computing the capture set and the least restrictive control map for the new hybrid automaton. Sufficient conditions for the termination of the algorithm that computes the capture set are provided. Finally, we show that the solved perfect state information control problem is equivalent to the original problem with imperfect state information under suitable assumptions. We illustrate the application of the proposed technique to a collision avoidance problem between an autonomous vehicle and a human driven vehicle at a traffic intersection.Index Terms-Mode estimation, dynamic feedback, multiagent systems.

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Computation of Maximal Safe Sets for Switching Systems

Cited by 89 publications

References 30 publications

Invariant Sets for Switched Discrete Time Systems Subject to Bounded Disturbances

Invariant Sets for Switched Discrete Time Systems Subject to Bounded Disturbances

On the Approximation of Invariant Sets for Constrained LDT Systems

Safety Control of Hidden Mode Hybrid Systems

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