Optimal Control for a Class of Infinite Dimensional Systems Involving an L∞-term in the Cost Functional
| Autor: | Karl Kunisch, Sébastien Court, Laurent Pfeiffer |
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| Rok vydání: | 2017 |
| Předmět: |
0209 industrial biotechnology
State variable Partial differential equation Applied Mathematics 010102 general mathematics Computational Mechanics 02 engineering and technology Function (mathematics) 16. Peace & justice Optimal control 01 natural sciences Control function symbols.namesake 020901 industrial engineering & automation Ordinary differential equation symbols Applied mathematics 0101 mathematics Newton's method Mathematics Free parameter |
| Zdroj: | ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik. 98:569-588 |
| ISSN: | 0044-2267 |
| DOI: | 10.1002/zamm.201600199 |
| Popis: | An optimal control problem with a time-parameter is considered. The functional to be optimized includes the maximum over time-horizon reached by a function of the state variable, and so an L∞-term. In addition to the classical control function, the time at which this maximum is reached is considered as a free parameter. The problem couples the behavior of the state and the control, with this time-parameter. A change of variable is introduced to derive first and second-order optimality conditions. This allows the implementation of a Newton method. Numerical simulations are developed, for selected ordinary differential equations and a partial differential equation, which illustrate the influence of the additional parameter and the original motivation. |
| Databáze: | OpenAIRE |
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