Constrained tracking control by continuous resets of the state of a gain-scheduled controller

In this paper, a tracking control problem for discrete-time linear systems with actuator saturation is addressed. Firstly, a design condition of a controller parameterized by a single scheduling parameter is introduced. The proposed controller includes an integrator to achieve the zero steady-state error in the case where a step reference signal is applied. Then a gain-scheduled control algorithm that guarantees closed-loop stability and makes the tracking error converge to zero in the case of a step reference signal is proposed. In the proposed control algorithm, the scheduling parameter and the state of the controller are determined on-line so that the tracking control performance is improved. The scheduling parameter and the state of the controller are computed simultaneously by solving a convex optimization problem with a linear matrix inequality constraint. Two numerical examples are provided to illustrate effectiveness of the proposed control algorithm.