Journal Article

A maximum principle for optimal control problems with mixed constraints

M. D. R. De Pinho, R. B. Vinter and H. Zheng

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 18, issue 2, pages 189-205
Published in print June 2001 | ISSN: 0265-0754
Published online June 2001 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/18.2.189
A maximum principle for optimal control problems with mixed constraints

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Necessary conditions in the form of maximum principles are derived for optimal control problems with mixed control and state constraints. Traditionally, necessary condtions for problems with mixed constraints have been proved under hypothesis which include the requirement that the Jacobian of the mixed constraint functional, with respect to the control variable, have full rank. We show that it can be replaced by a weaker ‘interiority’ hypothesis. This refinement broadens the scope of the optimality conditions, to cover some optimal control problems involving differential algebraic constraints, with index greater than unity.

Keywords: optimal control; maximum principle; mixed constraints; differential algebraic equations

Journal Article.  0 words. 

Subjects: Mathematics

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