A Uniformity Principle for Probabilistic Robustness of the Discrete-Time Linear Quadratic Regulator1

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 Fr 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 uk =−Kkxk is implemented, the uniform distribution for the disturbances turns out to be risk maximizing.