Tracking control with adaptively allocated maximum input amplitudes and enlarged domain of attraction for linear systems

We propose a novel method for designing a fast trajectory tracking controller based on a 2-DOF control structure for linear systems subject to input constraints. Major steps are: First, we derive a required decaying rate of a quadratic Lyapunov function (QLF) that enables an adaptation of the maximum input amplitudes reserved for error compensation. This adaptation is based on the current feedforward signal. Second, we show a saturating control law which ensures the existence of such a QLF. The corresponding domain of attraction is estimated by solving a convex optimization problem. Third, we add a Lyapunov-based command governor in order to further enlarge the controller's domain of attraction. Simulation and experimental results confirm the performance benefit of the proposed method.