APPROXIMATING REACHABLE SETS FOR A CLASS OF LINEAR SYSTEMS SUBJECT TO BOUNDED CONTROL.
AuthorGAYEK, JONATHAN EDWARD.
AdvisorVincent, Thomas L.
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PublisherThe University of Arizona.
RightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
AbstractA method is proposed for approximating the reachable set from the origin for a class of n first order linear ordinary differential equations subject to bounded control. The technique involves decoupling the system equations into 1- and 2-dimensional linear subsystems, and then finding the reachable set of each of the subsystems. Having obtained bounds on each of the decoupled state variables, a n-dimensional parallelpiped is constructed which contains the reachable set from the origin for the original system. Several illustrative examples are presented for the case where the control is a scalar. The technique is also compared to a Lyapunov approach of approximating the reachable set in a simple 2-dimensional example.
Degree ProgramApplied Mathematics