Stabilizing uncertain nonlinear systems via the constrained discrete-time state-dependent Riccati equation controller

The constrained discrete-time state-dependent Riccati equation technique in the presence of uncertainties in the nonlinear system to be controlled is investigated. The CD-SDRE is divided into two parts - D-SDRE and MPC-based controllers, and the entire system is considered to be a switched system. First, the system stability under each controller is separately established. The stability of the entire switched system (CD-SDRE) is then proven based on the each control system stability. Control of the spacecraft with nonlinear attitude dynamics in the presence of fuel slosh effect under limited actuator performance is used to show the effectiveness of the proposed CD-SDRE controller.