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Optimal control of a stochastic dynamical system usually requires a good dynamical model with probability distributions, which is difficult to obtain due to limited measurements and/or complicated dynamics. To solve it, this work proposes a data-driven distributionally robust control framework with the Wasserstein metric via a constrained two-player zero-sum Markov game, where the adversarial player selects the probability distribution from a Wasserstein ball centered at an empirical distribution. Then, the game is approached by its penalized version, an optimal stabilizing solution of which is derived explicitly in a linear structure under the Riccati-type iterations. Moreover, we design a model-free Q-learning algorithm with global convergence to learn the optimal controller. Finally, we verify the effectiveness of the proposed learning algorithm and demonstrate its robustness to the probability distribution errors via numerical examples.
We study safe, data-driven control of (Markov) jump linear systems with unknown transition probabilities, where both the discrete mode and the continuous state are to be inferred from output measurements. To this end, we develop a receding horizon es
Stochastic model predictive control (SMPC) has been a promising solution to complex control problems under uncertain disturbances. However, traditional SMPC approaches either require exact knowledge of probabilistic distributions, or rely on massive
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
Chance constrained optimal power flow (OPF) has been recognized as a promising framework to manage the risk from variable renewable energy (VRE). In presence of VRE uncertainties, this paper discusses a distributionally robust chance constrained appr
Inverse multiobjective optimization provides a general framework for the unsupervised learning task of inferring parameters of a multiobjective decision making problem (DMP), based on a set of observed decisions from the human expert. However, the pe