L(1)-Optimal Control Using State Space, Controlled Invariance Based Methods
Aubrecht, Johannes Aumack Schmidt
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https://hdl.handle.net/2142/83953
Description
Title
L(1)-Optimal Control Using State Space, Controlled Invariance Based Methods
Author(s)
Aubrecht, Johannes Aumack Schmidt
Issue Date
1997
Doctoral Committee Chair(s)
Petros Voulgaris
Department of Study
Mechanical Engineering
Discipline
Mechanical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Electronics and Electrical
Language
eng
Abstract
The application of this controlled invariance based solution method to linear time-invariant systems (LTI) is presented first. Also included is a discussion of a related estimation technique which utilizes a set-valued estimation approach to produce an estimate which is optimal in an $\ell\sp{\infty}$-induced norm sense. The controlled invariance based solution method is then generalized to linear periodically time varying (LPTV) systems. The resulting control law construction method can be used to produce a memoryless periodically varying nonlinear controller, which achieves near-optimal performance. The controlled invariance based solution method is also generalized to linear multirate systems (LMR) systems. As the structure of multirate systems inherently precludes access to the entire state at every time step, the aforementioned set-valued estimation technique is utilized in this solution method. It is shown that this control law construction method can be used to produce a memoryless nonlinear multirate controller, which achieves near-optimal performance.
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