Sparse optimal stochastic control
Copyright policy )Sparse optimal stochastic control
In this paper, we investigate a sparse optimal control of continuous-time stochastic systems. We adopt the dynamic programming approach and analyze the optimal control via the value function. Due to the non-smoothness of the $L^0$ cost functional, in general, the value function is not differentiable in the domain. Then, we characterize the value function as a viscosity solution to the associated Hamilton-Jacobi-Bellman (HJB) equation. Based on the result, we derive a necessary and sufficient condition for the $L^0$ optimality, which immediately gives the optimal feedback map. Especially for control-affine systems, we consider the relationship with $L^1$ optimal control problem and show an equivalence theorem.
13 pages, 4 figures
- Kyoto University Japan
- The University of Kitakyushu Japan
dynamic programming, viscosity solution, Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games, sparsity, bang-off-bang control, Systems and Control (eess.SY), Electrical Engineering and Systems Science - Systems and Control, Optimization and Control (math.OC), FOS: Mathematics, FOS: Electrical engineering, electronic engineering, information engineering, Optimal stochastic control, Mathematics - Optimization and Control, non-smooth optimal control
dynamic programming, viscosity solution, Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games, sparsity, bang-off-bang control, Systems and Control (eess.SY), Electrical Engineering and Systems Science - Systems and Control, Optimization and Control (math.OC), FOS: Mathematics, FOS: Electrical engineering, electronic engineering, information engineering, Optimal stochastic control, Mathematics - Optimization and Control, non-smooth optimal control
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