Full-state time-varying asymmetric constraint control for non-strict feedback nonlinear systems based on dynamic surface method

We investigate the tracking control problem for a non-strict feedback nonlinear system with external disturbance and time-varying asymmetric full state constraints. Firstly, the unknown nonlinear term with external disturbance in the system are estimated by fuzzy logic system. The backstepping method is applied to the design of adaptive fuzzy controller. However, to prevent that the constraints are overstepped by introducing an improved log-type time-varying asymmetric barrier Lyapunov function (TABLF) in each step of backstepping design. Secondly, the dynamic surface control (DSC) is introduced in the designed algorithm to solve the computational explosion problem of controller caused by the derivative of control law. The proposed control scheme can speed up the tracking speed of the system. Compared with the previous work, it is verified that the combination of DSC and TABLF can obtain good performance within the constraint range, and can ensure fast and stable tracking convergence under external disturbance. Finally, two simulation examples verify the performance of the adaptive controller.