H_∞ prediction and unconstrained H_∞ predictive control: Multi-input-multi-output case

Through the combination of the sequential spectral factorization and the coprime factorization, a k-step ahead MIMO H_∞ (cumulative minimax) predictor is derived which is stable for the unstable noise model. This predictor and the modified internal model of the reference signal are embedded into the H_∞ optimization framework, yielding a single degree of freedom multi-input-multi-output H_∞ predictive controller that provides stochastic disturbance rejection and asymptotic tracking of the reference signals described by the internal model. It is shown that for a plant/disturbance model, that represents a large class of systems, the inclusion of the H_∞ predictor into the H_∞ control algorithm introduces a performance/robustness tuning knob: an increase of the prediction horizon enforces a more conservative control effort and, correspondingly, results in deterioration of the transient and the steady-state (tracking error variance) performance, but guarantees large robustness margin, while the decrease of the prediction horizon results in a more aggressive control signal and better transient and steady-state performance, but smaller robustness margin.