The Maximum Principle for Optimal Control Problems with Time Delays**This work was co-funded by the EPSRC grant Control For Energy and Sustainability, grant reference EP/G066477/1 and by the European Union under the 7th Framework Programme 'FP7-PEOPLE-2010-ITN', grant agreement number 264735-SADCO
| Autor: | Andrea Boccia, Richard B. Vinter |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
0209 industrial biotechnology
Mathematical optimization State variable Differential equation 010102 general mathematics Control variable 02 engineering and technology Delay differential equation Optimal control 01 natural sciences Constraint (information theory) 020901 industrial engineering & automation Maximum principle Differential inclusion Control and Systems Engineering Control theory 0101 mathematics Mathematics |
| Zdroj: | IFAC-PapersOnLine. 49:951-955 |
| ISSN: | 2405-8963 |
| DOI: | 10.1016/j.ifacol.2016.10.290 |
| Popis: | In this paper we present necessary conditions for optimal control problems with time delays. The dynamic constraint is formulated as a control delay differential equation, with time delays occuring in both state and control variables. We allow the dependence of the data on the state variables to be nonsmooth, and the necessary conditions are expressed in terms of set-valued subgradients, in place of conventional derivatives. In the problems considered, the end-time is included in the decision variables. The fact that the end-time is a choice variable is accommodated by a new kind of transversality condition. While nonsmooth necessary conditions have earlier been derived for optimal control problems with time delays, for the most part this has been in the framework of controlled differential inclusions with time delays. By contrast, the necessary conditions of this paper cover general problems involving general, nonsmooth, controlled delay differential equations. |
| Databáze: | OpenAIRE |
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