Robust model predictive control of input-constrained stable systems with unstructured uncertainty

For open-loop stable systems having input constraints and unstructured model uncertainty, we present a new closed-loop stability test applicable to typical output-feedback model predictive control (MPC) policies. The new stability test is less conservative than a previous proposal, and it enables both analysis and synthesis of input-constrained MPC policies. In particular, we propose a robust output-feedback MPC design which, at each time step, minimizes a quadratic upper bound on a nominal cost function. We determine the upper bound off-line subject to the new stability test using convex optimization techniques. Simulation results show that the proposed MPC design can be much less conservative than robustly stable MPC designs based on conventional cost functions.