Reference tracking using H_∞ predictive control based on a minimax predictor

This paper presents a reference tracking controller which utilizes a particular form of the internal model principle to achieve asymptotic tracking. The use of the internal model (a) permits cancellation of the effects on the output error of any reference signal satisfying the specified difference equation and (b) allows formulation of the control problem amenable to rigorous solution by the optimal control methods. The internal model takes the form of a non-Schur weighting filter which is stabilized by inclusion in the closed loop. After the conditions which provide the necessary tracking properties have been met by the internal model filter, the filter is combined with the plant yielding a modified plant, with the controller being designed for the modified plant using the polynomial-based H_∞ predictive control scheme. The predictor is unique in that it minimizes the cost function of the prediction error in a minimax sense, yielding minimization of the peaks of the prediction error spectrum, rather than its integral on the unit circle. This predictor is then used for the derivation of the H_∞ predictive control law. This control law minimizes the peaks of a generalized cost function in the frequency domain. The predictor and control algorithms are derived via embedding of the minimax problem within an LQ problem using polynomial methods. The minimax predictor is shown to yield a flat magnitude graph of a transfer function between noise and prediction error, with a peak lower than that produced by the least squares predictor. When applied to the plant, the minimax predictor based H_∞ controller is combined with the internal model to simultaneously provide robust disturbance rejection and asymptotic tracking. The novel feature of this controller is that the minimax predictor induces a trade-off between stability robustness and tracking performance through the choice of the prediction horizon as follows: the larger prediction horizon yields less aggressive control actions and hence lower performance but a much bigger robustness margin, while the smaller prediction horizon yields much more aggressive control actions and hence provides better performance, but has a lower robustness margin. Thus, the algorithm offers a very nice tuning knob in the form of a prediction horizon which can be used to select the performance/robustness trade-off.