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Time-Optimal Control Problem for <i>n</i>× <i>n</i> Co-Operative Parabolic Systems with Control in Initial Conditions
Department of Mathematics, Faculty of Science, Jazan University, Jazan, KSA
- 1 Department of Mathematics, Faculty of Science, Jazan University, Jazan, KSA
Advances in Pure Mathematics·Volume 03 (2013)·Pages 38–43·Published 29 November 2013·DOI10.4236/apm.2013.39A1006
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Abstract
In this paper, time-optimal control problem for a liner n × n co-operative parabolic system involving Laplace operator is considered. This problem is, steering an initial state y(0)=u , with control u so that an observation y(t) hitting a given target set in minimum time. First, the existence and uniqueness of solutions of such system under conditions on the coefficients are proved. Afterwards necessary and sufficient conditions of optimality are obtained. Finally a scaler case is given.
KeywordsTime-Optimal Control ProblemsBang-Bang ControlsParabolic SystemCo-Operative Systems
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