Approximations of closed-loop minimax MPC

Minimax or worst-case approaches have been used frequently recently in model predictive control (MPC) to obtain control laws that are less sensitive to uncertainty. The problem with minimax MPC is that the controller can become overly conservative. An extension to minimax MPC that can resolve this problem is closed-loop minimax MPC. Unfortunately, closed-loop minimax MPC is essentially an intractable problem. In this paper, we introduce a novel approach to approximate the solution to a number of closed-loop minimax MPC problems. The result is convex optimization problems with size growing polynomially in system dimension and prediction horizon.