Time optimal control problems for some non-smooth systems

Hongwei Lou; Junjie Wen; Yashan Xu

doi:10.3934/mcrf.2014.4.289

Article Contents

2014, Volume 4, Issue 3: 289-314. Doi: 10.3934/mcrf.2014.4.289

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Time optimal control problems for some non-smooth systems

1.
School of Mathematical Sciences and LMNS, Fudan University, Shanghai 200433
2.
School of Mathematical Sciences, Fudan University, Shanghai 200433
3.
School of Mathematical Sciences, Fudan University, KLMNS, Shanghai, 200433

Received: August 31, 2013

Revised: October 31, 2013

Published: August 2014

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Abstract

Time optimal control problems for some non-smooth systems in general form are considered. The non-smoothness is caused by singularity. It is proved that Pontryagin's maximum principle holds for at least one optimal relaxed control. Thus, Pontryagin's maximum principle holds when the optimal classical control is a unique optimal relaxed control. By constructing an auxiliary controlled system which admits the original optimal classical control as its unique optimal relaxed control, one get a chance to get Pontryagin's maximum principle for the original optimal classical control. Existence results are also considered.

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Mathematics Subject Classification: Primary: 49J15; Secondary: 49K15, 34A34.

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