Exact Solutions to Minmax Optimal Control Problems for Constrained Noisy Linear Systems

We present a numerically tractable technique for exact solutions to a class of robust minmax optimal control problems (OCPs) under constraints. The underlying dynamical system is assumed to be linear and subjected to bounded disturbances, and the objective function is a sum of quadratic stage and quadratic terminal costs. We impose convex constraints on the states and the control; the control minimizes and the disturbance maximizes the objective. The resulting constrained minmax OCP admits a reformulation in the language of convex semi-infinite programs (CSIPs), and we employ recently developed numerical tools in CSIP to solve the ensuing optimization problem. A simple benchmark numerical example is provided to illustrate our results.