Generalized predictive control algorithms with guaranteed frozen-time stability and bounded tracking error

In its present form, for a fixed plant model GPC (generalized predictive control) guarantees stability only for two specific choices of horizons in the cost function. In one instance, GPC has been shown to result in a deadbeat control law while in the other, the control law has been shown to converge to that given by the solution of the corresponding algebraic Riccati equation. However a lower bound on the costing horizon that results in a stabilizing controller is not known a priori. This paper presents sufficient conditions for stability of closed loop systems that result from implementing solutions of the finite horizon LQ problem for arbitrary fixed costing horizons. On this basis, a class of predictive control laws that ensures frozen-time stability of the closed loop system is proposed. When the plant is required to track a known reference signal that is bounded, the sufficient conditions for frozen-time stability of the closed loop are used to derive a controller structure that guarantees the tracking error to be bounded.