Fixed-time adaptive neural network control for nonstrict-feedback nonlinear systems with deadzone and output constraint

This paper considers fixed-time control problem of nonstrict-feedback nonlinear system subjected to deadzone and output constraint. First, tan-type Barrier Lyapunov function (BLF) is constructed to keep system output within constraint. Next, unknown nonlinear function is approximated by radial basis function neural network (RBFNN). Using the property of Gaussian radial basis function, the upper bound of the term containing the unknown nonlinear function is derived and the updating law is proposed to estimate the square of the norm of the neural network weights. Then, virtual control inputs are developed using backstepping design and their derivatives are obtained by fixed-time differentiator. Finally, the actual control input is designed based on deadzone inverse approach. Lyapunov stability analysis shows that the presented method guarantees fixed-time convergence of the tracking error to a small neighborhood around zero while all the other closed-loop signals keep bounded. The presented control strategy addresses algebraic-loop problem, overcomes explosion of complexity and reduces the number of adaptation parameters, which is easy to be implemented with less computation burden. The presented control scheme is applied to academic system, real electromechanical system and aircraft longitudinal system and simulation results demonstrate its effectiveness.