Feedback classification and optimal control with applications to the controlled Lotka–Volterra model
Year: 2024
Type: article
Abstract: Let M be a σ-compact C∞ manifold of dimension n≥2 and consider a single-input control system: x˙(t)=X(x(t))+u(t)Y(x(t)), where X, Y are C∞ vector fields on M. We prove that there exists an open set of pairs (X,Y) for the C∞-Whitney topology is such that they admit singular abnormal rays so that the spectrum of the projective singular Hamiltonian dynamics is feedback invariant. This result is applied to the controlled Lotka–Volterra dynamics, where such rays are related to shifted equilibria of the free dynamics.
Source: Optimization
Authors: Bernard Bonnard, Jérémy Rouot
Institutions: Institut national de recherche en sciences et technologies du numérique, Institut de Mathématiques de Bourgogne, MCTAO: Mathématiques pour le Contrôle, le Transport et leurs Applications, Centre National de la Recherche Scientifique, Université de Bretagne Occidentale, Laboratoire de Mathématiques de Bretagne Atlantique
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4313459720