6533b855fe1ef96bd12b1990
RESEARCH PRODUCT
Feedback Classification and Optimal Control with Applications to the Controlled Lotka-Volterra Model
Bernard BonnardJérémy Rouotsubject
Feedback classificationLotka-Volterra modelFeedback classification Nonlinear systems Lotka-Volterra model Optimal control Direct numerical methodsDirect numerical methodsNonlinear systems[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC][MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]Optimal controldescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2023-01-01 |