Converging Approximations of Attractors via Almost Lyapunov Functions and Semidefinite Programming

In this letter we combine two existing approaches for approximating global attractors. One of them approximates the global attractors arbitrarily well by sublevel sets related to solutions of infinite dimensional linear programming problems. A downside there is that these sets are not necessarily po...

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Bibliographic Details
Published in:IEEE control systems letters Vol. 6; pp. 2912 - 2917
Main Author: Schlosser, C.
Format: Journal Article
Language:English
Published: IEEE 01.01.2022
Subjects:
Convergence
Costs
Dynamical systems
Linear programming
LMIs
Lyapunov methods
Mathematics
Optimization
Optimization and Control
Programming
semidefinite programming
outer approximations
dynamical systems
sum-of-squares
infinite-dimensional linear programming
Global attractor
Lyapunov function
ISSN:2475-1456, 2475-1456
Online Access:Get full text
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Summary:In this letter we combine two existing approaches for approximating global attractors. One of them approximates the global attractors arbitrarily well by sublevel sets related to solutions of infinite dimensional linear programming problems. A downside there is that these sets are not necessarily positively invariant. On the contrary, the second method provides supersets of the global attractor which are positively invariant. Their method on the other hand has the disadvantage that the underlying optimization problem is not computationally tractable without the use of heuristics - and incorporating them comes at the price of losing guaranteed convergence. In this letter we marry both approaches by combining their techniques and we get converging outer approximations of the global attractor consisting of positively invariant sets based on convex optimization via sum-of-squares techniques. The method is easy to use and illustrated by numerical examples.
ISSN:2475-1456
2475-1456
DOI:10.1109/LCSYS.2022.3180110