Robust reference shaping of periodic trajectories for systems with state/input constraints using impulse and step responses

This paper is concerned with off-line reference shaping for uncertain closed loop systems with state/input constraints. First, the upper and lower bounds of the constrained variables of uncertain systems are described in a non-conservative way by using appropriate slack variables. Then, for given periodic trajectories, we propose a method to shape reference signals which achieve the sub-optimal tracking performance at the nominal subject to the condition that the system constraints are satisfied in the presence of uncertainties. Furthermore, we propose an exploitation of step response information to enhance the method. Finally, several simulation results are given to demonstrate its effectiveness.