Time Optimal Control for Some Ordinary Differential Equations with Multiple Solutions
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This paper studies a time optimal control problem for a class of ordinary differential equations. The control systems may have multiple solutions. Based on the properties fulfilled by the solutions of the concerned equations, we get both the existence and the Pontryagin maximum principle for optimal controls.
KeywordsNonlinear ordinary differential equations Multiple solution Time optimal control
Mathematics Subject Classification49J15 34A34
This work was partially supported by the National Natural Science Foundation of China under Grant 11471070, 11301472, the Natural Science Foundation of Guangdong Province under Grant 2014A030307011, the Training Program Project for Outstanding Young Teachers of Colleges and Universities in Guangdong Province under Grant Yq2014116 and the Characteristic Innovation Project of Common Colleges and Universities in Guangdong Province under Grant 2014KTSCX158.