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Article Dans Une Revue IEEE Transactions on Automatic Control Année : 2024

From Relaxed Constraint Satisfaction to p-Invariance of Sets

Résumé

The present paper proposes a general framework for the analysis of constraints satisfaction with respect to the trajectories of a dynamical system. The results are presented in a discrete-time framework and pertain to the class of set-theoretic methods. The main objective is to go beyond the state-of-the-art by characterizing the intermittent constraint satisfaction along the evolution of the trajectories of a dynamical system. Two relaxed notions are introduced in this sense, one characterizing the validation of constraints within a given finite window and the other imposing the validation after a fixed number of time-steps following a violation. The constraint satisfaction with respect to a controlled trajectory will then be extended to a set of constraints and then to tubes of trajectories. It is shown that all these notions can be accordingly anchored to the well-known controlled positive set invariance, thus offering a generalized framework for the analysis of dynamical systems in a set-theoretic framework. The technical note is completed with illustrations of the constructions on both linear and nonlinear case.
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Dates et versions

hal-04565096 , version 1 (03-05-2024)

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Citer

Sorin Olaru, Martin Soyer, Zhixin Zhao, Carlos Dórea, Ernesto Kofman, et al.. From Relaxed Constraint Satisfaction to p-Invariance of Sets. IEEE Transactions on Automatic Control, 2024, pp.1-8. ⟨10.1109/TAC.2024.3394544⟩. ⟨hal-04565096⟩
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