Barrier Lyapunov functions-based dynamic surface control for pure-feedback systems with full state constraints

This studies an adaptive control problem of pure-feedback non-linear systems with full state constraints. The mean value theorem is employed to deal with unknown non-linearities. A novel backstepping design is constructed via barrier Lyapunov function (BLF) combined with dynamic surface control (DSC). The BLF guarantees the full state constraints are not violated and all the closed-loop signals remain bounded. DSC solves the problems of restrictions on high order differentiability of stabilising functions and avoiding the complexity that arises due to the explosion of terms in backstepping design. It is shown that all the signals in the closed-loop system are ultimately bounded and the tracking error converges to an adjustable neighbourhood of the origin while the full state constraints remain unchanged. The performance of the BLF-based DSC is illustrated with two simulation examples.