Sufficient Conditions for Complexity Reduction in Min-Max Control of Constrained Uncertain Linear Systems

In this paper we consider finite-time min-max optimization problems for linear systems with additive disturbances subject to hard input constraints and soft state constraints. We present a set of state-dependent sufficient conditions which allow for the efficient solution of the min-max optimization problem. The set of initial states for which the proposed conditions are satisfied is computed by solving a sequence of linear programs. We compare the proposed method to open-loop, vertex enumeration, and affine disturbance feedback techniques in terms of computational complexity and optimal cost using a simple example. We also demonstrate the efficacy of the approach in predictive control design for radiant-slab cooling systems.