Gonçalves, José Agostinho Basto, 1952- (1981) Nonlinear controllability and observability with applications to gradient systems. PhD thesis, University of Warwick.

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Abstract

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.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Nonlinear control theory, Hamiltonian systems, Riemannian manifolds, Lie algebras, Differential equations
Date:	May 1981
Institution:	University of Warwick
Theses Department:	School of Engineering
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Crouch, Peter
Sponsors:	Fundaýao Calouste Gulbenkian
Extent:	iii, 69 leaves
Language:	eng
URI:	http://wrap.warwick.ac.uk/id/eprint/3496

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