Discrete Verification of Necessary Conditions for Switched Nonlinear Optimal Control Systems, ACA (2004; Boston, Massachusetts)
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Authors
Ross, I. Michael
Fahroo, Fariba
Subjects
continuous time systems , discrete event systems , minimum principle , nonlinear control systems , optimal systems , set theory , time-varying systems
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Date of Issue
2001-06-30
Date
June 30-July 2004
Publisher
IEEE
Language
Abstract
We consider a fairly general class of state-constrained nonlinear hybrid optimal control problems that are based on coordinatizing Sussmann's model. An event set generalizes the notion of a guard set, reset map, endpoint set as well as the switching set. We present a pseudospectral (PS) knotting method that discretizes the continuous-time variables of the problem. The discrete event conditions are imposed over the PS knots leading to a large, sparse, mixed-variable programming (MVP) problem. The Karush-Kuhn-Tucker conditions for the MVP are transformed in a manner that makes them closely resemble the discretized necessary conditions obtained from the hybrid minimum principle. A set of closure conditions are introduced to facilitate commuting the operations of dualization and discretization. An immediate consequence of this is a hybrid covector mapping theorem that provides an order-preserving transformation of the Lagrange multipliers associated with the discretized problem to the discretized covectors associated with the hybrid optimal control problem.
Type
Conference Paper
Description
The article of record as published may be located at http://ieeexplore.ieee.org
Proceeding of the 2004 American Control Conference Boston, Massachusetts ; vol. 2, page(s):1610-1615, June 30-July 2, 2004
Proceeding of the 2004 American Control Conference Boston, Massachusetts ; vol. 2, page(s):1610-1615, June 30-July 2, 2004
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Department
Applied Mathematics
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Distribution Statement
Approved for public release; distribution is unlimited.
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.