A uniformity principle for probabilistic robustness of the discrete-time linear quadratic regulator

This paper concentrates on the use of a recently developed new paradigm for probabilistic robustness in the context of the classical linear quadratic regulator. Distributional robustness of the performance is sought with respect to an entire class ℱ_τ of admissible probability density functions for the disturbance. Disturbances are deemed to be “good” or “tolerable” if the performance index remains below an acceptable level γ>0. The main result of this paper indicates that the so-called uniformity principle holds at the optimum, that is, when the optimal control u_k=-K_kx_k is implemented, the uniform distribution for the disturbances turns out to be risk maximizing