The Maximum Principle for Optimal Control Problems with Time Delays
Autor: | Richard B. Vinter, Andrea Boccia |
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Rok vydání: | 2017 |
Předmět: |
0209 industrial biotechnology
Mathematical optimization Time delays Control and Optimization Transversality Applied Mathematics 010102 general mathematics Control (management) Control variable 02 engineering and technology Optimal control 01 natural sciences 020901 industrial engineering & automation Maximum principle Cover (topology) Control theory State (computer science) 0101 mathematics Mathematics |
Zdroj: | SIAM Journal on Control and Optimization. 55:2905-2935 |
ISSN: | 1095-7138 0363-0129 |
DOI: | 10.1137/16m1085474 |
Popis: | This paper provides necessary conditions of optimality for optimal control problems with time delays in both state and control variables. Different versions of the necessary conditions cover fixed end-time problems and, under additional hypotheses, free end-time problems. The conditions improve on previous available conditions in a number of respects. They can be regarded as the first maximum principle for fully nonsmooth optimal control problems, involving delays in state and control variables, only special cases of which have previously been derived. Even when the data is smooth, the conditions advance the existing theory. For example, we provide a new “two-sided” generalized transversality condition, associated with the optimal end-time, which gives more information about the optimal end-time than the “one-sided” condition in the earlier literature. But there are improvements in other respects, relating to the treatment of initial data, specifying past histories of the state and control, the nature of ... |
Databáze: | OpenAIRE |
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