In this thesis we study the stabilization of closed sets for passive nonlinear control systems, developing necessary and sufficient conditions under which a passivity-based feedback stabilizes a given goal set. The development of this result takes us to a journey through the so-called reduction problem: given two nested invariant sets G1 subset of G2, and assuming that G1 enjoys certain stability properties relative to G2, under what conditions does G1 enjoy the same stability properties with respect to the whole state space? We develop reduction principles for stability, asymptotic stability, and attractivity which are
applicable to arbitrary closed sets. When applied to the passivity-based set stabilization problem, the reduction theory suggests a new definition of detectability which is geometrically appealing and captures precisely the property that the control system must possess in order for the stabilization problem to be solvable.
The reduction theory and set stabilization results developed in this thesis are used to
solve a distributed coordination problem for a group of unicycles, whereby the vehicles
are required to converge to a circular formation of desired radius, with a specific ordering and spacing on the circle.
| Identifer | oai:union.ndltd.org:TORONTO/oai:tspace.library.utoronto.ca:1807/29714 |
| Date | 30 August 2011 |
| Creators | El-Hawwary, Mohamed |
| Contributors | Maggiore, Manfredi |
| Source Sets | University of Toronto |
| Language | en_ca |
| Detected Language | English |
| Type | Thesis |
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