Continuity of the Value Function for Stochastic Sparse Optimal Control. Issue 2 (2020)

• Record Type: Journal Article
• Authors: Ito, Kaito; Ikeda, Takuya; Kashima, Kenji
• Is Part Of: IFAC-PapersOnLine. Volume 53:Issue 2(2020)
• Page Start: 7179
• Page End: 7184
• Publication Date: 2020
• Subjects: sparsity -- optimal control -- stochastic systems -- value function -- continuity; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2020.12.537
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: In this paper, we investigate the continuity of the value function for a stochastic sparse optimal control. The most common method to solve stochastic optimal control problems is the dynamic programming. Specifically, if the value function is smooth, it satisfies the associated Hamilton-Jacobi-Bellman (HJB) equation. However, in general, the value function for our problem is not differentiable because of the nonsmoothness of the L 0 cost functional. Instead, we can expect that the value function is a viscosity solution to the HJB equation. This paper shows the continuity of our value function as a first step for showing that the value function is a viscosity solution.