Optimal sliding mode output tracking control for linear systems with uncertainties

The problem of designing optimal sliding mode output tracking controllers for uncertain linear systems with the reference signals given by exosystem outputs is considered in this paper. Firstly, an augmented system, composed of the original system and the exosystem, is constructed to transform the optimal output tracking issue into the design problem of linear quadratic regulators (LQRs). And then the optimal tracking control problem for the nominal augmented system is studied. Secondly, the integral sliding mode control is used to robustify the optimal LQR so that the augmented system is completely robust to uncertainties which satisfy the matching conditions. As a result, the tracking error converges to zero asymptotically and the original system output can follow the exosystem output trajectory effectively even the uncertainties exist. Finally, a simulation example is taken. The simulation results show that the proposed optimal tracking controller based on sliding mode control gives good tracking performance and robustness.