A new robust MPC for uncertain linear systems

An improved method of synthesizing constrained robust model predictive controller for systems with polytopic description is proposed. A continuum of terminal constraint sets depending on an external variable is constructed offline, and the robust stability is achieved online with a variable control horizon and a time varying terminal constraint set by solving the minmax optimization problem, which can be formulated as an linear matrix inequality (LMI) problem. This algorithm not only dramatically reduces the on-line computation but also significantly enlarges the size of the allowable set of initial conditions and obtains better performance by introducing extra degrees of freedom through the use of perturbations on a time varying state-feedback law. The effectiveness of the proposed approach is verified by a simulation example.