Constrained discrete-time state-dependent Riccati equation technique: A model predictive control approach

The continuous time state-dependent Riccati equation (SDRE) technique is extended to discrete-time under input and state constraints, yielding constrained (C) discrete-time (D) SDRE, referred to as CD-SDRE. For the latter, stability analysis and calculation of a region of attraction are carried out. The derivation of the D-SDRE under state-dependent weights is provided, and the result is compared with that of D-SDRE obtained by using the discrete-time algebraic Riccati equation (DARE) and that of discrete-time linear quadratic regulator (D-LQR). Stability of the D-SDRE feedback system is established using input-to-state stability (ISS) approach. Receding horizon strategy is used to take into account the constraints on D-SDRE controller.