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Register a new userSparse optimal stochastic control
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Added by
Kaito Ito
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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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.
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In power distribution systems, the growing penetration of renewable energy resources brings new challenges to maintaining voltage safety, which is further complicated by the limited model information of distribution systems. To address these challenges, we develop a model-free optimal voltage control algorithm based on projected primal-dual gradient dynamics and continuous-time zeroth-order method (extreme seeking control). This proposed algorithm i) operates purely based on voltage measurements and does not require any other model information, ii) can drive the voltage magnitudes back to the acceptable range, iii) satisfies the power capacity constraints all the time, iv) minimizes the total operating cost, and v) is implemented in a decentralized fashion where the privacy of controllable devices is preserved and plug-and-play operation is enabled. We prove that the proposed algorithm is semi-globally practically asymptotically stable and is structurally robust to measurement noises. Lastly, the performance of the proposed algorithm is further demonstrated via numerical simulations.
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