Constrained regulation of linear continuous-time dynamical systems

Vassilaki, Marina; Bitsoris, George

doi:10.1016/0167-6911(89)90071-6

Cited by 99 publications

(26 citation statements)

References 6 publications

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“…• The problems related to positively invariant sets and control holdability of sets (see, e.g., [1], [2], and [29]) are essentially different from what is studied in this paper. Indeed (see theorem 1 below) trajectories of (1) remain in for all and all because the dynamics is modified on the boundary of .…”

Section: Introductionmentioning

confidence: 82%

Stability and Instability Matrices for Linear Evolution Variational Inequalities

Goeleven

Brogliato

2004

IEEE Trans. Automat. Contr.

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Abstract-This paper deals with the characterization of the stability and instability matrices for a class of unilaterally constrained dynamical systems, represented as linear evolution variational inequalities (LEVI). Such systems can also be seen as a sort of differential inclusion, or (in special cases) as linear complementarity systems, which in turn are a class of hybrid dynamical systems. Examples show that the stability of the unconstrained system and that of the constrained system, may drastically differ. Various criteria are proposed to characterize the stability or the instability of LEVI.

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Section: Introductionmentioning

confidence: 82%

Stability and Instability Matrices for Linear Evolution Variational Inequalities

Goeleven

Brogliato

2004

IEEE Trans. Automat. Contr.

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“…Such PI sets are easily speci"ed as the level surfaces of a Lyapunov function. It is well known that in the presence of state constraints the commonly used quadratic Lyapunov functions (and the associated ellipsoidal sets) o!er conservative results and thus the more #exible polyhedral PI sets and PL Lyapunov functions have been considered [6,4,10]. Such functions require, in general, a more complex representation (which increases the computational burden that is necessary for their construction) but they have proved to be suitable for the controllable region estimation and constrained stabilization problems.…”

Section: Preliminariesmentioning

confidence: 97%

“…However, the RIP algorithm can now be used to yield initial invariant polytopes only for an LTI approximation of system (10). These are preferred to random initial choices, because they can help in reducing the number of cycles required to complete the BIP procedure.…”

Section: Extension To Pl Uncertain Systems~planar Casementioning

confidence: 98%

A new approach for estimating controllable and recoverable regions for systems with state and control constraints

Yfoulis¹,

Muir²,

Wellstead³

2002

Intl J Robust & Nonlinear

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SUMMARYIn this paper the problem of estimating controllable and recoverable regions for classes of nonlinear systems in the presence of uncertainties, state and control constraints is considered. A new computational technique is proposed based upon a ray-gridding idea in contrast to the usual gridding techniques. The new technique is also based on the positive invariance principle and the use of piecewise linear (PL) Lyapunov functions to generate polytopic approximations to the controllable/recoverable region with arbitrary accuracy. Various types of stabilizing controllers achieving certain trade-o!s between robustness, performance and safety, while respecting state and control constraints, can be easily generated. The technique allows the approximation of nonlinear systems via piecewise linear uncertain models which reduces the conservatism associated with linear uncertain models.

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“…For instance, Lee and Arapostathis [10] investigated global controllability of piecewise-linear affine hypersurface systems, while Veliov and Krastanov [17] studied local controllability of a system which is linear on two half-spaces. Other related work on invariant polyhedral sets of linear systems have been studied by Vassilaki and Bitsoris [16] and Castelan and Hennet [6]. The survey paper by Blanchini [5] on set invariance in control provides many other related references.…”

Section: Introductionmentioning

confidence: 99%

Necessary and sufficient conditions for reachability on a simplex

Roszak

Broucke

2006

Automatica

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Abstract-The reachability problem has received significant attention in the hybrid control literature with many questions still left unanswered. In this paper we solve the general problem of reaching a set of facets of an n-dimensional simplex in finite time, for a system evolving with linear affine dynamics. Necessary and sufficient conditions are presented in the form of inequalities on the vertices of the simplex, and a linear affine controller is constructed that solves the reachability problem.

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Constrained regulation of linear continuous-time dynamical systems

Cited by 99 publications

References 6 publications

Stability and Instability Matrices for Linear Evolution Variational Inequalities

Stability and Instability Matrices for Linear Evolution Variational Inequalities

A new approach for estimating controllable and recoverable regions for systems with state and control constraints

Necessary and sufficient conditions for reachability on a simplex

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