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Preprints, Working Papers, ... Year : 2023

Feedback Classification and Optimal Control with Applications to the Controlled Lotka-Volterra Model

Abstract

Let M be a σ-compact C^∞ manifold of dimension n ≥ 2 and consider a single-input control system: ẋ(t) = X (x(t)) + u(t) Y (x(t)), where X , Y are C^∞ vector fields on M. We prove that there exist an open set of pairs (X , Y ) for the C^∞ –Whitney topology such that they admit singular abnormal rays so that the spectrum of the projective singular Hamiltonian dynamics is feedback invariant. It is applied to controlled Lotka–Volterra dynamics where such rays are related to shifted equilibria of the free dynamics.
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Dates and versions

hal-03917363 , version 1 (01-01-2023)

Identifiers

  • HAL Id : hal-03917363 , version 1

Cite

Bernard Bonnard, Jérémy Rouot. Feedback Classification and Optimal Control with Applications to the Controlled Lotka-Volterra Model. 2023. ⟨hal-03917363⟩
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