Unconstrained \(H_{\infty}\) predictive control with \(H_\infty\) prediction: Single-input single-output case (Q2708059)

An \(H_\infty\)-optimal \(k\)-step ahead (cumulative minimax) predictor for an unstable single-input single-output controlled autoregressive moving average (CARMA) model is derived. On the basis of this predictor, a two-degrees of freedom (2DOF) multistep robust predictive control algorithm is derived. A rigorous proof on the predictor optimality and boundedness of the prediction error is given. In the derivation of the control law, a nested embedding procedure is used: first, the embedding is utilized to derive the minimax predictor, then the controller cost function is decomposed into two parts, one induced by the disturbance and the other by the reference input. The embedding procedure is repeated to minimize the first part in the \(H_\infty\)-norm, and the second part in the \(H_2\)-norm. The resulting 2DOF control law is computed via spectral factorizations and the solution to Diophantine equations. The properties of the control law (stability/robustness relation, transient tracking performance, steady-state performance/robustness trade-off) are evaluated on three CARMA models.