Time optimal control problems for some non-smooth systems. (English) Zbl 1307.49018
Summary: 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 gets a chance to get Pontryagin’s maximum principle for the original optimal classical control problem. Existence results are also considered.
MSC:
49K15 | Optimality conditions for problems involving ordinary differential equations |
49J15 | Existence theories for optimal control problems involving ordinary differential equations |
49J45 | Methods involving semicontinuity and convergence; relaxation |
34A34 | Nonlinear ordinary differential equations and systems |
Keywords:
optimal control problems; Pontryagin’s maximum principle; optimal relaxed control; optimal blowup time; optimal quenching timeReferences:
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