Converging to and escaping from the global equilibrium: Isostables and optimal control

Research output: Contribution in Book/Catalog/Report/Conference proceedingConference contribution

Abstract

This paper studies the optimal control of trajectories converging to or escaping from a stable equilibrium. The control duration is assumed to be short. When the control is turned off, the trajectories have not reached the target and they subsequently evolve according to the free motion dynamics. In this context, we show that the problem can be formulated as a finite-horizon optimal control problem which relies on the notion of isostables. For linear and nonlinear systems, we solve this problem using Pontryagin's maximum principle and we study the relationship between the optimal solutions and the geometry of the isostables. Finally, optimal strategies for choosing the magnitude and duration of the control are considered.

Original languageEnglish
Title of host publicationProceedings of the 53rd IEEE Conference on Decision and Control
Pages5888-5893
Number of pages6
Volume2015-February
EditionFebruary
DOIs
Publication statusPublished - 2014
Externally publishedYes

Fingerprint

Optimal Control
Trajectory
Pontryagin Maximum Principle
Finite Horizon
Optimal Strategy
Trajectories
Optimal Control Problem
Nonlinear Systems
Optimal Solution
Linear Systems
Maximum principle
Target
Motion
Linear systems
Nonlinear systems
Geometry
Relationships
Context

Cite this

Mauroy, A. (2014). Converging to and escaping from the global equilibrium: Isostables and optimal control. In Proceedings of the 53rd IEEE Conference on Decision and Control (February ed., Vol. 2015-February, pp. 5888-5893) https://doi.org/10.1109/CDC.2014.7040311
Mauroy, Alexandre. / Converging to and escaping from the global equilibrium : Isostables and optimal control. Proceedings of the 53rd IEEE Conference on Decision and Control. Vol. 2015-February February. ed. 2014. pp. 5888-5893
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Mauroy, A 2014, Converging to and escaping from the global equilibrium: Isostables and optimal control. in Proceedings of the 53rd IEEE Conference on Decision and Control. February edn, vol. 2015-February, pp. 5888-5893. https://doi.org/10.1109/CDC.2014.7040311

Converging to and escaping from the global equilibrium : Isostables and optimal control. / Mauroy, Alexandre.

Proceedings of the 53rd IEEE Conference on Decision and Control. Vol. 2015-February February. ed. 2014. p. 5888-5893.

Research output: Contribution in Book/Catalog/Report/Conference proceedingConference contribution

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Mauroy A. Converging to and escaping from the global equilibrium: Isostables and optimal control. In Proceedings of the 53rd IEEE Conference on Decision and Control. February ed. Vol. 2015-February. 2014. p. 5888-5893 https://doi.org/10.1109/CDC.2014.7040311