Gonçalves, José Agostinho Basto (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 (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Nonlinear control theory, Hamiltonian systems, Riemannian manifolds, Lie algebras, Differential equations
Official Date:	May 1981
Dates:	Date Event May 1981 Submitted
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Publication Status:	Unpublished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

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