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We investigate the control of constrained stochastic linear systems when faced with limited information regarding the disturbance process, i.e., when only the first two moments of the disturbance distribution are known. We consider two types of distributionally robust constraints. In the first case, we require that the constraints hold with a given probability for all disturbance distributions sharing the known moments. These constraints are commonly referred to as distributionally robust chance constraints. In the second case, we impose conditional value-at-risk (CVaR) constraints to bound the expected constraint violation for all disturbance distributions consistent with the given moment information. Such constraints are referred to as distributionally robust CVaR constraints with second-order moment specifications. We propose a method for designing linear controllers for systems with such constraints that is both computationally tractable and practically meaningful for both finite and infinite horizon problems. We prove in the infinite horizon case that our design procedure produces the globally optimal linear output feedback controller for distributionally robust CVaR and chance constrained problems. The proposed methods are illustrated for a wind blade control design case study for which distributionally robust constraints constitute sensible design objectives. [ABSTRACT FROM PUBLISHER]

We consider robust feedback control of time-varying, linear discrete-time systems operating over a finite horizon. For such systems, we consider the problem of designing robust causal controllers that minimize the expected value of a convex quadratic cost function, subject to mixed linear state and input constraints. Determination of an optimal control policy for such problems is generally computationally intractable, but suboptimal policies can be computed by restricting the class of admissible policies to be affine on the observation. By using a suitable re-parameterization and robust optimization techniques, these approximations can be solved efficiently as convex optimization problems. We investigate the loss of optimality due to the use of such affine policies. Using duality arguments and by imposing an affine structure on the dual variables, we provide an efficient method to estimate a lower bound on the value of the optimal cost function for any causal policy, by solving a cone program whose size is a polynomial function of the problem data. This lower bound can then be used to quantify the loss of optimality incurred by the affine policy. [ABSTRACT FROM AUTHOR]