Electrical Engineering and Systems Science > Systems and Control
[Submitted on 6 Mar 2023 (v1), last revised 7 Jun 2023 (this version, v2)]
Title:Generalized Filippov solutions for systems with prescribed-time convergence
View PDFAbstract:Dynamical systems with prescribed-time convergence sometimes feature a right-hand side exhibiting a singularity at the prescribed convergence time instant. In an open neighborhood of this singularity, classical absolutely continuous Filippov solutions may fail to exist, preventing indefinite continuation of such solutions. This note introduces a generalized Filippov solution definition based on the notion of generalized absolute continuity in the restricted sense. Conditions for the continuability of such generalized solutions are presented and it is shown, in particular, that generalized Filippov solutions of systems with an equilibrium that is attractive, in prescribed time or otherwise, can always be continued indefinitely. The results are demonstrated by applying them to a prescribed-time controller for a perturbed second-order integrator chain.
Submission history
From: Richard Seeber [view email][v1] Mon, 6 Mar 2023 13:51:36 UTC (366 KB)
[v2] Wed, 7 Jun 2023 11:59:58 UTC (184 KB)
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