Integration of model predictive control and backstepping approach and its stability analysis

Backstepping controller (BS) and model predictive controller (MPC) have been widely used for many applications by virtue of their own merits. BS works even with non-minimum phase and finite-time escape and MPC can handle state and input constraints explicitly. Nevertheless, BS requires repeated differentiations of the virtual control, whereas high computational loads of MPC are obstacles to practical implementation. This study proposes a control strategy that combines BS and MPC for nonlinear systems in strict-feedback form. It is proven that the controller renders the closed-loop system asymptotically stable. The proposed MPC-BS requires less computational load than that of MPC, since it only optimizes the virtual input of the first step and computes the input by backstepping approach. The explosion of terms caused by the consecutive differentiation in BS approach is also addressed.