Approximation-based adaptive tracking control of nonlinear pure-feedback systems with time-varying output constraints

An adaptive neural network control problem of completely non-affine pure-feedback systems with a time-varying output constraint and external disturbances is investigated. For the controller design, we presents an appropriate Barrier Lyapunov Function (BLF) considering both the time-varying output constraint and the control direction nonlinearities induced from the implicit function theorem and mean value theorem. From an error transformation, the BLF dependent on the time-varying constraint is transformed into the explicitly time-independent BLF. Based on the explicitly time-independent BLF, an adaptive dynamic surface control scheme using the function approximation technique is designed to ensure both the constraint satisfaction and the desired tracking ability. It is shown that all signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error converges to an adjustable neighborhood of the origin while the time-varying output constraint is never violated.