Minimax Mpc for Systems with Uncertain Gain

Robust synthesis is one of the remaining challenges in model predictive control (MPC). One way to robustify an MPC controller is to formulate a minimax problem, i.e., optimize a worst-case performance measure. For systems modeled with an uncertain gain, there are many results available. Typically, the minimax formulations have given intractable problems, or unorthodox performance measures have been used to obtain tractable problems. In this paper, we show how the standard quadratic performance measure can be used in a computationally tractable minimax MPC controller. The controller is developed in a linear matrix inequality framework that easily allows extensions and generalizations.