Parabolic set simulation for reachability analysis of linear time-invariant systems with integral quadratic constraint

This paper describes the computation of reachable sets and tubes for linear time-invariant systems with an unknown input bounded by integral quadratic constraints, modeling e.g. delay, rate limiter, or energy bounds. We define a family of paraboloidal overapproximations. These paraboloids are suppor...

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Bibliographic Details
Published inEuropean journal of control Vol. 58; pp. 152 - 167
Main Authors Rousse, Paul, Garoche, Pierre-Loïc, Henrion, Didier
Format Journal Article
LanguageEnglish
Published Philadelphia Elsevier Ltd 01.03.2021
Elsevier Limited
Elsevier
Subjects
Boundary value problems
Computer Science
Constraint modelling
Control theory
Dynamical systems
Game theory
Integral quadratic constraints
Linear quadratic regulator
Mathematics
Methods
Optimization and Control
Parabolic bodies
Reachability analysis
Set-based simulation
Systems and Control
Time invariant systems
Tubes
Uncertain systems
Integral quadratic constraints
Uncertain systems
Reachability analysis
Set-based simulation
Integral Quadratic Constraints
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Summary:This paper describes the computation of reachable sets and tubes for linear time-invariant systems with an unknown input bounded by integral quadratic constraints, modeling e.g. delay, rate limiter, or energy bounds. We define a family of paraboloidal overapproximations. These paraboloids are supported by the reachable tube on touching trajectories. Parameters of each paraboloid are expressed as a solution to an initial value problem. Compared to previous methods based on the classical linear quadratic regulator, our approach can be applied to unstable systems as well. We tested our approach on large scale systems.
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content type line 14
ISSN:0947-3580
1435-5671
DOI:10.1016/j.ejcon.2020.08.002