Nonlinear controllability and observability with applications to gradient systems
Gonçalves, José Agostinho Basto, 1952- (1981) Nonlinear controllability and observability with applications to gradient systems. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b1753329~S15
We extend the theory of nonlinear observability due to Hermann- Krener  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 , 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|
|Institution:||University of Warwick|
|Theses Department:||School of Engineering|
|Sponsors:||Fundaýao Calouste Gulbenkian|
|Extent:||iii, 69 leaves|
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