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Mathematical Control and Related Fields (MCRF)
 

Time optimal control problems for some non-smooth systems

Pages: 289 - 314, Volume 4, Issue 3, September 2014      doi:10.3934/mcrf.2014.4.289

 
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Hongwei Lou - School of Mathematical Sciences and LMNS, Fudan University, Shanghai 200433, China (email)
Junjie Wen - School of Mathematical Sciences, Fudan University, Shanghai 200433, China (email)
Yashan Xu - School of Mathematical Sciences, Fudan University, KLMNS, Shanghai, 200433, China (email)

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.

Keywords:  Optimal blowup time, optimal quenching time, maximum principle, existence, monotonicity.
Mathematics Subject Classification:  Primary: 49J15; Secondary: 49K15, 34A34.

Received: September 2013;      Revised: November 2013;      Available Online: April 2014.

 References