Further results on global state feedback stabilization of high-order nonlinear systems with time-varying delays

Adaptive Fixed-Time Control of Strict-Feedback High-Order Nonlinear Systems

This paper examines the adaptive control of high-order nonlinear systems with strict-feedback form. An adaptive fixed-time control scheme is designed for nonlinear systems with unknown uncertainties. In the design process of a backstepping controller, the Lyapunov function, an effective controller, and adaptive law are constructed. Combined with the fixed-time Lyapunov stability criterion, it is proved that the proposed control scheme can ensure the stability of the error system in finite time, and the convergence time is independent of the initial condition. Finally, simulation results verify the effectiveness of the proposed control strategy.

Output Tracking Control for High-Order Nonlinear Systems with Time Delay via Output Feedback Design

Design approach of an output feedback tracking controller is proposed for a class of high-order nonlinear systems with time delay. To deal with the time delays, an appropriate Lyapunov–Krasovskii the tracking analysis is ingeniously constructed, and an output feedback tracking controller is designed by using a homogeneous domination method. It is shown that the proposed output controller independent of time delay can make the tracking error be adjusted to be sufficiently small and render all the trajectory of the closed-loop system as bounded. An example is given to illustrate the effectiveness of the proposed method.

A Novel Error-Compensation Control for a Class of High-Order Nonlinear Systems With Input Delay

A novel tracking error-compensation-based adaptive neural control scheme is proposed for a class of high-order nonlinear systems with completely unknown nonlinearities and input delay. In the tracking errors of existing papers, there exist the following difficulties: first, output curve always lags behind the desired trajectory, second, some big peak errors cause a decrease in tracking precision, and third, a big initial value of the modified tracking error can make the closed-loop system unstable. To tackle them, three corresponding error-compensation terms are constructed, including a prediction and compensation term, an auxiliary signal produced by the constructed auxiliary system, and a damping term. However, inequality amplification caused by high order will weaken the effectiveness of the proposed error-compensation scheme, and the control precision will decrease under an assumption that the lower bounds of the unknown control coefficients should be exactly known. To overcome aforementioned difficulties, in the derivation of the first virtual control law, the radial basis function neural network is used to approximate a hybrid term online constructed by unknown nonlinearities, a lumped control coefficient achieved by state transformation, and the dynamic of the proposed error-compensation terms and desired signal. Meanwhile, input delay is coped with a robust compensation signal constructed based on a finite integral of the past control values. Finally, it is proven that all the closed-loop signals are semiglobally uniformly ultimately bounded. Simulation results demonstrate the effectiveness of the proposed method.

Adaptive fuzzy predictive sliding control of uncertain nonlinear systems with bound-known input delay

In this paper, a new Adaptive Fuzzy Predictive Sliding Mode Control (AFP-SMC) is presented for nonlinear systems with uncertain dynamics and unknown input delay. The control unit consists of a fuzzy inference system to approximate the ideal linearization control, together with a switching strategy to compensate for the estimation errors. Also, an adaptive fuzzy predictor is used to estimate the future values of the system states to compensate for the time delay. The adaptation laws are used to tune the controller and predictor parameters, which guarantee the stability based on a Lyapunov-Krasovskii functional. To evaluate the method effectiveness, the simulation and experiment on an overhead crane system are presented. According to the obtained results, AFP-SMC can effectively control the uncertain nonlinear systems, subject to input delays of known bound.