Receding horizon H_∞ predictive control for systems with input saturation

A receding horizon H_∞ predictive control method is derived by solving a min-max problem in nonrecursive form. The min-max cost index is converted to a quadratic form which, for systems with input saturation, can be minimised using QP. Stability conditions and H_∞ norm bounds on disturbance rejection are obtained. Without input saturation, stabilising terminal weights guaranteeing finite H_∞ norm bounds always exist, but the guaranteed H_∞ norm bound may be conservative; this is remedied through the use of closed-loop prediction. Feasible sets for state and disturbances are derived, for which stability can be guaranteed. The algorithm and weight selection procedures are given in terms of LMIs.