Continuity of the Value Function in Sparse Optimal Control

Takuya Ikeda; Masaaki Nagahara

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arXiv · 1412.5707

Continuity of the Value Function in Sparse Optimal Control

Takuya Ikeda·Masaaki Nagahara

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Abstract

We prove the continuity of the value function of the sparse optimal control problem. The sparse optimal control is a control whose support is minimum among all admissible controls. Under the normality assumption, it is known that a sparse optimal control is given by L^1 optimal control. Furthermore, the value function of the sparse optimal control problem is identical with that of the L1-optimal control problem. From these properties, we prove the continuity of the value function of the sparse optimal control problem by verifying that of the L1-optimal control problem.

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Takuya Ikeda, Masaaki Nagahara. 2014-12-18. Continuity of the Value Function in Sparse Optimal Control. https://arxiv.org/abs/1412.5707

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