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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.
We propose a reachability approach for infinite and finite horizon multi-objective optimization problems for low-thrust spacecraft trajectory design. The main advantage of the proposed method is that the Pareto front can be efficiently constructed fr
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
We consider the minimization of an $L_0$-Lipschitz continuous and expectation-valued function, denoted by $f$ and defined as $f(x)triangleq mathbb{E}[tilde{f}(x,omega)]$, over a Cartesian product of closed and convex sets with a view towards obtainin
In this effort, a novel operator theoretic framework is developed for data-driven solution of optimal control problems. The developed methods focus on the use of trajectories (i.e., time-series) as the fundamental unit of data for the resolution of o
This paper studies an optimal consensus problem for a group of heterogeneous high-order agents with unknown control directions. Compared with existing consensus results, the consensus point is further required to an optimal solution to some distribut