Multivariable H_∞ predictive control based on minimax predictor

This paper presents a multi-input-multi-output H_∞ predictive controller design based on minimax predictor. Through the combination of the sequential spectral factorization and the coprime factorization, a k-step ahead MIMO H_∞ predictor is derived which is stable for the unstable noise model. This predictor minimizes the H_∞ norm of the power spectral density of the prediction error signal (and in fact flattens the spectrum), in contract to the standard quadratic predictor which minimizes the variance of the error signal. It is also shown that the minimax and quadratic predictors are equivalent for one-step ahead predictions. The H_∞ predictor and the internal model principle are embedded into the H_∞ optimization framework to address the disturbance rejection and the tracking problems, respectively. The inclusion of the minimax predictor into the H_∞ control algorithm introduces a tuning knob in the form of the prediction horizon, capable of setting a trade-off between the desired transient performance and the closed loop robustness.