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Sparse optimal stochastic control
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DOI：10.1016/j.automatica.2020.109438.png)
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Abstract
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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. (C) 2020 Elsevier Ltd. All rights reserved.
Keywords:
Sparsity
Non-smooth optimal control
Bang-off-bang control
Dynamic programming
Viscosity solution
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