Nonlinear controllability and observability with applications to gradient systems

• Main Author: Gonçalves, José Agostinho Basto
• Published: University of Warwick 1981
• Subjects: 510; QA Mathematics
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.238031

We extend the theory of nonlinear observability due to Hermann- Krener [5] to the non-regular case, in which the observability codistribution is not constant dimensional, and we obtain results in some sense dual of the ones already known for accessibility. We discuss a conjecture of P. Varaya [15], namely that the isomorphism of two locally controllable gradient systems is an isometry for the underlying pseudo Riemannian manifolds, proving it to be false without further, or different, assumptions; we also prove some positive results, and the analogue of the above for Hamiltonian systems, with weaker conditions: an isomorphism of reachable Hamiltonian systems is a symplectomorphism. Finally we prove that a Hamiltonian system with finite-dimensional Lie algebra, satisfying standard conditions, has an accessible Hamiltonian realization, constructed in a canonical way.