Robust model predictive control schemes for tracking setpoints

This paper briefly reviews the development of nontracking robust model predictive control (RMPC) schemes for uncertain systems using linear matrix inequalities (LMIs) subject to input saturated and softened state constraints. Then we develop two new tracking setpoint RMPC schemes with common Lyapunov function and with zero terminal equality subject to input saturated and softened state constraints. The novel tracking setpoint RMPC schemes are able to stabilize uncertain systems once the output setpoints lead to the violation of the state constraints. The state violation can be regulated by changing the value of the weighting factor. A brief comparative simulation study of the two tracking setpoint RMPC schemes is done via simple examples to demonstrate the ability of the softened state constraint schemes. Finally, some features of future research from this study are discussed.