Asymptotics of the optimal time in a time-optimal control problem with a small parameter |
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Authors: | A R Danilin O O Kovrizhnykh |
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Institution: | 1.Krasovskii Institute of Mathematics and Mechanics,Ural Branch of the Russian Academy of Sciences,Yekaterinburg,Russia;2.Ural Federal University,Yekaterinburg,Russia |
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Abstract: | A time-optimal control problem for a singularly perturbed linear autonomous system is considered. The main difference between this case and the case of systems with fast and slow variables studied earlier is that the eigenvalues of the matrix at the fast variables do not satisfy the standard requirement of negativity of the real part. We obtain and justify a complete power asymptotic expansion in the sense of Erdélyi of the optimal time and optimal control in a small parameter at the derivatives in the equations of the system. |
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