Mixed H2/H∞ Predictive Control

Abstract

This paper derives a two degree of freedom receding horizon control law based on the mixed H2/H∞ minimization. First, the integrand in the frequency domain representation of the generalized predictive control (GPC) performance criterion is decomposed into disturbance and reference spectra. Then the controller is derived whose H∞ part minimizes the peaks of the disturbance spectrum and the H2 part minimizes the integral of the reference spectrum on the unit circle. The resulting two degree of freedom control strategy referred to as the minimax predictive control (MPC) turns out to have stabilizing properties superior to the GPC for identical horizons. The MPC synthesis, based on spectral factorization and Diophantine equations, is much simpler than the standard state space H∞ optimal controller. The two degree of freedom MPC is expected to inherit on the one hand some of the robustness of H∞ design, due to both the minimax prediction and optimization, and on the other hand the ability of predictive receding horizon strategies to directly incorporate input constraints and pre-programmed reference inputs, which are nontrivial tasks in the standard H∞ design.