Backstepping design for nonlinear control system with uncertainties

Accounting for the stabilization and tracking of general nonlinear strict-feedback system with uncertainties, some recursive formulas for direct design of backstepping control laws were proposed and proved. To deal with the problem of extreme expanded operation quantity of backstepping method, a method of simplifying design by using high-gain feedback to dominate differential items of virtual inputs was introduced. And some recursive formulas based on high-gain backstepping design were proposed. The simulation results show the effectiveness of these methods.