Minimax predictive control

The authors derive a receding horizon control law based on the minimization of the H_∞ norm of the integrand in the frequency domain representation of the generalized predictive control (GPC) performance criterion. The resulting control strategy, referred to as minimax predictive control (MPC), minimizes the peaks of the error spectrum, rather than its integral on the unit circle. The MPC turns out to have stabilizing properties superior to the GPC for identical horizons. An example is presented, where the MPC stabilizes a plant with an unstable zero between two unstable poles, for which the standard GPC is not capable of achieving stability. The MPC synthesis, based on spectral factorization and Diophantine equations, is much simpler than that of the standard state spaces H_∞ optimal controller. The MPC is expected to inherit some of the robustness of H_∞ design, due to both the minimax prediction and optimization, and the ability of receding horizons strategies to directly incorporate input constraints, which is a nontrivial task in the standard H_∞ design