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We present a data-driven method for solving the linear quadratic regulator problem for systems with multiplicative disturbances, the distribution of which is only known through sample estimates. We adopt a distributionally robust approach to cast the controller synthesis problem as semidefinite programs. Using results from high dimensional statistics, the proposed methodology ensures that their solution provides mean-square stabilizing controllers with high probability even for low sample sizes. As sample size increases the closed-loop cost approaches that of the optimal controller produced when the distribution is known. We demonstrate the practical applicability and performance of the method through a numerical experiment.
With the large-scale integration of renewable power generation, frequency regulation resources (FRRs) are required to have larger capacities and faster ramp rates, which increases the cost of the frequency regulation ancillary service. Therefore, it
We study identification of linear systems with multiplicative noise from multiple trajectory data. A least-squares algorithm, based on exploratory inputs, is proposed to simultaneously estimate the parameters of the nominal system and the covariance
The study of multiplicative noise models has a long history in control theory but is re-emerging in the context of complex networked systems and systems with learning-based control. We consider linear system identification with multiplicative noise f
Appropriate greenhouse temperature should be maintained to ensure crop production while minimizing energy consumption. Even though weather forecasts could provide a certain amount of information to improve control performance, it is not perfect and f
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