When the nonlinear mechanical system has mismatched uncertainties, it is difficult to design control algorithm to achieve high precision trajectory tracking control. Traditional backstepping control is an effective control method for uncertain, mismatched nonlinear systems, but there is inherent problem of "complexity due to the explosion of terms". In this paper, based on the backstepping method, only one fuzzy system is used to approximate the unknown nonlinear functions, the unknown control gain and the differential of virtual control law of each subsystem. In order to reduce the influence of fuzzy approximation error and external interference, the above control scheme is further improved by designing special adjustable control parameters and first order low pass filter. The improved control scheme not only improves the control precision of the system obviously, but also solves the problem of "explosion of terms", and greatly reduces the initial control input, and provides the conditions for the practical application. The simulation results show the effectiveness of the proposed methods.

As we all know, it is very difficult to design the controller and prove the stability for switched nonlinear systems. Therefore, the engineering application of switching system and the development of switching control theory are limited. In order to solve the control problem for constrained switched system, an adaptive output feedback control scheme based on backstepping technology is studied in this paper for switched non-strict feedback nonlinear systems with asymmetric time-varying full state constraints and unknown external disturbances. A switched state observer based on fuzzy logic system is designed to estimate the unmeasurable states of the uncertain switched system. Asymmetric time-varying barrier Lyapunov functions are adopted to keep the full states of the system satisfying their asymmetric timevarying constraints. A variable separation approach is used to address the algebraic loop problem of nonstrict feedback structure. The stability of the closed-loop system and the semi-globally uniformly ultimately bounds of the signals are proved by the Lyapunov method and average dwell time theory. Finally, simulation results are given to show the effectiveness of the proposed control scheme. Different from the existing results, this paper is the first to investigate adaptive control for switched non-strict feedback systems with full state time-varying constraints, unmeasurable states and unknown disturbances, which is a more general case in real systems.

In this paper, a new fuzzy dynamic surface control approach based on a state observer is proposed for uncertain nonlinear systems with time-varying output constraints and external disturbances. An adaptive fuzzy state observer is used to estimate the states that cannot be measured in the systems. In our method, a time-varying Barrier Lyapunov Function (BLF) is used to ensure that the output does not violate time-varying constraints. In addition, dynamic surface control (DSC) technology is applied to overcome the problem of “explosion of complexity” in a backstepping control. Finally, the stability and signal boundedness of the system are confirmed by the Lyapunov method. The simulation results show the effectiveness and correctness of the proposed method.

This article deals with the design of adaptive fuzzy backstepping control for uncertain nonlinear systems in strictfeedback form with tracking error constraints. In this article, a fuzzy system is used to approximate the unknown nonlinear functions and the differential of virtual control law of each subsystem. In order to satisfy the limitation of tracking error constraints, the barrier Lyapunov function is introduced. Moreover, by applying the minimal learning parameters technique, the number of online parameters update for each subsystem is reduced to only 1. The control scheme not only ensures the tracking error is not to transgress the constraint bounds but also solves the problem of ''explosion of complexity'' and greatly reduces the initial control input and the number of the adaptive parameters; this provides the conditions for the practical application. The simulation results show the effectiveness of the proposed method.

In order to solve the control problem of uncertain nonlinear systems with state constraints, a dynamic surface output feedback control technology based on Radial Basis Function (RBF) neural networks state observer is proposed. The state observer is designed to estimate the unknown state of the systems by using the approximation characteristics of RBF neural networks, and to constrain the system state by using the Barrier Lyapunov Function (BLF). Based on the backstepping control, a first-order low-pass filter is introduced to design a dynamic surface control (DCS), which solves the "differential explosion" phenomenon that can easily occur in backstepping control. Finally, the stability of the closed-loop system which is confirmed by the Lyapunov method guarantees the semi-globally uniformly ultimately boundedness (SGUUB) of all the signals. The effectiveness of the methods that the boundedness of the tracking errors, the observer states and the controllers can be guaranteed, and good control performance could be achieved is shown by simulation results. INDEX TERMSDynamic surface control, full state constraints, nonlinear constrained systems, RBF neural networks, state observer.