Backstepping control integrated with Lyapunov-based model predictive control. (January 2019) - Kim, Yeonsoo; Oh, Tae Hoon; Park, Taekyoon; Lee, Jong Min
Highlights: A new control design, backstepping control integrated with Lyapunov-model predictive control (BS-MPC) are proposed, and its stability and robustness are proven. The desired virtual input for the subsystem is determined by solving the finite-time horizon optimal control problem (FHOCP) with the consideration of an objective function and input constraints explicitly. With the optimal solution of FHOCP, the real BS-MPC input is calculated using the backstepping method. BS-MPC provides a better desired value of the virtual input for the subsystem, and stabilizes the system faster than the backstepping control. The computational load of BS-MPC is less than that of MPC. Abstract: In this study, backstepping control integrated with Lyapunov-based model predictive control (BS-MPC) is proposed for nonlinear systems in a strict-feedback form. The virtual input of the first step is designed by solving the finite-horizon optimal control problem (FHOCP), and the real input is designed by the backstepping method. BS-MPC guarantees (semiglobal) ultimate boundedness of the closed-loop system when the control is implemented in a zero-order hold manner. When the robustness of BS-MPC is analyzed for uniformly bounded disturbances, the ultimate boundedness of the solution of perturbed system is guaranteed. BS-MPC can provide a better desired value of the virtual input of the first step by solving the FHOCP, resulting in a faster stabilization of the system compared with the backstepping control. In addition, BS-MPC requires less computational load compared with MPC because the dimension of the states considered in the on-line optimization problem of BS-MPC is lower than that of MPC.