Lagrangian methods for approximating the viability kernel in high-dimensional systems

Maidens, John; Kaynama, Shahab; Mitchell, Ian M.; Oishi, Meeko; Dumont, Guy A.

doi:10.1016/j.automatica.2013.03.020

Cited by 122 publications

(130 citation statements)

References 18 publications

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“…This is a fair assumption because we are mainly concerned with discrete-time systems that arise from the discretization of continuous time systems. Such systems have a dynamics matrix of the form A = exp(A c ) which is always invertible [3]. Following computation algorithm in [7], we can find this reachable set using zonotopes by…”

Section: Viability Theory Background a Viability Theory Conceptsmentioning

confidence: 99%

“…Viability is a theory that until now has mostly used in safety verification in control systems [3]. Viability theory has also been found useful in areas different from automatic control as e.g.…”

Section: Introductionmentioning

confidence: 99%

“…Nowadays, several algorithms have been proposed that can approximate these sets effectively. Some of these algorithms are surveyed [3]. Finding the viability theory concepts that can be used in fault tolerance evaluation is a major contribution of this paper.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fault tolerance evaluation of nonlinear systems using viability theory

Zarch

Poshtan

Puig

2016

2016 3rd Conference on Control and Fault-Tolerant Systems (SysTol)

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Abstract-This paper presents a computational procedure based on viability theory to evaluate the fault tolerance admissibility of a given fault configuration of a nonlinear system controlled by means of a predictive control law. The admissible solution set for the control problem, including the effect of faults, is determined using viability kernel and capture basin. Finally, water heater part of pasteurization process is provided as benchmark in order to show the usefulness of viability theory for fault tolerance evaluation.

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Section: Viability Theory Background a Viability Theory Conceptsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fault tolerance evaluation of nonlinear systems using viability theory

Zarch

Poshtan

Puig

2016

2016 3rd Conference on Control and Fault-Tolerant Systems (SysTol)

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“…Non-Lyapunov methods also exist for estimating the RA [12]- [14]. Among these approaches, the backward reachable sets approach provides the domain from which the trajectories of a system converge to some selected target set, thus making it useful for estimating the RA of a given…”

Section: Introductionmentioning

confidence: 99%

“…In [20], a Lagrangian method is proposed for computing the viability kernel via ellipsoidal representation. In [14], this method is extended by using polytopic and support vector representations. However, the problem of estimating and enlarging the RA is rarely considered via backward reachable sets.…”

Section: Introductionmentioning

confidence: 99%

On enlarging backward reachable sets via Zonotopic set membership

Han

Rizaldi

El-Guindy

et al. 2016

2016 IEEE International Symposium on Intelligent Control (ISIC)

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Abstract-While a number of efficient methods have been proposed for approximating backward reachable sets, no synthesis method via backward reachable sets has been developed for estimating and enlarging the region of attraction (RA). This paper shows how to use backward reachable sets to enlarge the estimate of the RA of linear discrete-time systems, by using an optimal static feedback controller. Two controller design methods are provided: the first method enlarges the estimate of the RA via invariant sets, whose existence is ensured by zonotope containment; the second method provides the optimal control input by using Lyapunov stability and quadratic stabilization. The backward reachable set is represented by zonotopes which give a good compromise between accuracy and efficiency. The effectiveness of both methods is illustrated by a numerical example.

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Viability Criteria for a Switched System on Bounded Polyhedron

Gao

Zhao

2017

Asian Journal of Control

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The viability of a switched system on a bounded polyhedron set, which is expressed by some linear inequalities, is investigated. Based on nonsmooth analysis and the properties of the tangent cone, a necessary and sufficient condition for viability is proposed. It is shown that the viability of a system is equivalent to the consistency of some systems of linear inequalities. Specifically, a viability condition for a switched system on a bounded polyhedron is presented. According to this condition, determining the viability of a bounded polyhedron can be transformed into verifying certain conditions at vertices of each facet. The method of determining viability, which transforms verifying the condition from infinite points to finite ones, can be implemented easily in practice. An algorithm to determine the viability for the switched system is constructed by using convex analysis. In addition, the approach can be extended to the switched system in which a control input is present. Finally, an example is listed to illustrate the effectiveness of the results.

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Lagrangian methods for approximating the viability kernel in high-dimensional systems

Cited by 122 publications

References 18 publications

Fault tolerance evaluation of nonlinear systems using viability theory

Fault tolerance evaluation of nonlinear systems using viability theory

On enlarging backward reachable sets via Zonotopic set membership

Viability Criteria for a Switched System on Bounded Polyhedron

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