A convex parameterization for solving constrained min-max problems with a quadratic cost

This paper is concerned with the application of a recent result in the literature on robust optimization to the control of linear discrete-time systems, which are subject to unknown, persistent state disturbances and mixed constraints on the state and input. By parameterizing the control input sequence as an affine function of the disturbance sequence, it is shown that a certain class of finite horizon min-max control problems is convex and that the number of variables and constraints grows polynomially with the problem size. It is assumed that the constraint and the disturbance sets are polyhedral and that the cost is a suitably-chosen quadratic, where the disturbance is negatively weighted as in H/sub /spl infin// control.