State estimation of linear dynamical systems under bounded control

Summers, Danny; Wu, Zong Y.; Sabin, G. C. W.

doi:10.1007/bf00940520

Cited by 10 publications

(2 citation statements)

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“…The problem of computing the set of all states reachable from a given initial state has been an active topic of research for several decades. Here the emphasis is typically on efficient and scalable methods to over-and under-approximate the reachable set [8,11,12,21,33]. By contrast, relatively little attention has been paid to the decidability of the reachable set-the focus of the present paper.…”

Section: Introductionmentioning

confidence: 99%

On the decidability of reachability in linear time-invariant systems

Fijalkow

Ouaknine

Pouly

et al. 2019

Proceedings of the 22nd ACM International Conference on Hybrid Systems: Computation and Control

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We consider the decidability of state-to-state reachability in linear time-invariant control systems over discrete time. We analyse this problem with respect to the allowable control sets, which in general are assumed to be defined by boolean combinations of linear inequalities. Decidability of the version of the reachability problem in which control sets are affine subspaces of R n is a fundamental result in control theory. Our first result is that reachability is undecidable if the set of controls is a finite union of affine subspaces. We also consider versions of the reachability problem in which (i) the set of controls consists of a single affine subspace together with the origin and (ii) the set of controls is a convex polytope. In these two cases we respectively show that the reachability problem is as hard as Skolem's Problem and the Positivity Problem for linear recurrence sequences (whose decidability has been open for several decades). Our main contribution is to show decidability of a version of the reachability problem in which control sets are convex polytopes, under certain spectral assumptions on the transition matrix.

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Section: Introductionmentioning

confidence: 99%

On the decidability of reachability in linear time-invariant systems

Fijalkow

Ouaknine

Pouly

et al. 2019

Proceedings of the 22nd ACM International Conference on Hybrid Systems: Computation and Control

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“…We note that the constraint Kξ ≥ 1 is not active. For our case, let the Lagrangian function be defined by (20) . Recall that the level for the level set found inside the linear unsaturated region given by Lee and Hedrick [9] is .…”

Section: Maximize the Level Set Under The Lyapunov Descent Critementioning

confidence: 99%

Stability of Linear Time‐invariant Open‐loop Unstable Systems With Input Saturation

Wang

Mukai

2004

Asian Journal of Control

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This paper analyzes the stability of a linear time-invariant open-loop unstable system subject to input saturation. First, we extend the idea of approximating the locally asymptotically stable region (controllable set) of the system for the case where the control is small enough to be unsaturated (inside the linear region), to the case when the control is allowed to saturate. It is shown that, when the Lyapunov descent criterion and the Kuhn-Tucker Theorem is applied, a superior locally asymptotically stable region is found. A technique for approximating the locally asymptotically stable region is presented.

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