Robust Control Design for Linear Systems via Multiplicative Noise

Abstract¶

Robust stability and stochastic stability have separately seen intense study in control theory for many decades. In this work we establish relations between these properties for discrete-time systems and employ them for robust control design. Specifically, we examine a multiplicative noise framework which models the inherent uncertainty and variation in the system dynamics which arise in model-based learning control methods such as adaptive control and reinforcement learning. We provide results which guarantee robustness margins in terms of perturbations on the nominal dynamics as well as algorithms which generate maximally robust controllers.

Summary¶

Algorithms for synthesizing robust controllers for linear systems using multiplicative noise as a design-time device. Leverages theoretical results on the equivalence of robustness to structured determinstic and stochastic uncertainties.

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