Backstepping control modification for nonlinear systems based on compensation function observer and barrier Lyapunov function

This paper investigates the improvement for the backstepping tracking control for nonlinear systems with output constraints and unknown functions. A barrier Lyapunov function (BLF) in backstepping design procedure is employed and corresponding backstepping controller is presented to prevent output constraints violation. Unlike the traditional literature on fuzzy logic system or neural networks, a compensation function observer (CFO) is used to observe unknown functions in this paper. A CFO-based BLF backstepping control is proposed. A single inverted pendulum simulation example is provided to illustrate the advantage of the proposed CFO-based BLF backstepping control over the traditional backstepping control algorithm.