On the Rate of Convergence for the Pseudospectral Optimal Control of Feedback Linearizable Systems
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Authors
Kang, Wei
Subjects
Advisors
Date of Issue
2009
Date
6 Apr 2009
Publisher
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Abstract
In this paper, we prove a theorem on the rate of convergence for the optimal cost computed using PS methods. It is a first proved convergence rate in the literature of PS optimal control. In addition to the high-order convergence rate, two theorems are proved for the existence and convergence of the approximate solutions. This paper contains several essential differences from existing papers on PS optimal control as well as some other direct computational methods. The proofs do not use necessary conditions of optimal control. Furthermore, we do not make coercivity type of assumptions. As a result, the theory does not require the local uniqueness of optimal solutions. In addition, a restrictive assumption on the cluster points of discrete solutions made in existing convergence theorems are removed.
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Description
Series/Report No
Department
Applied Mathematics