Simplified adaptive backstepping control for uncertain nonlinear systems with unknown input saturation and its application

This paper deals with an adaptive robust tracking control using a multilayer neural network (NN) for a class of nonlinear dynamic systems with unknown time varying state delays. Typical adaptive NN backstepping controllers for uncertain nonlinear systems with time-delay give rise to computation complexity caused by the the repeated derivatives of virtual controllers and nonlinear functions. Moreover, the combined techniques usually result in only uniformly ultimately bounded (UUB) stability caused by the inherent NN approximation error. This paper presents a control scheme that uses an integral sliding mode control as a feedback term and an adaptive neural controller as a feedforward term based on the desired compensation adaptive law (DCAL) technique. First, we develop a new DCAL formulation which avoids the explosion of complexity caused by the general NN backstepping scheme to compensate for nonlinear system uncertainties, bounded system disturbances, and unknown state time delays. Then, using a Lyapunov-Krasovskii (LK) functional, it is shown that the proposed controller renders the class of uncertain nonlinear time-delay systems asymptotically stable.

In this paper, we present a new scheme to design adaptive fuzzy output-feedback controller for uncertain nonlinear systems in the presence of input saturation. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a state filter is designed to estimate unmeasured states. Combining the backstepping recursive design with modular design techniques, a new adaptive fuzzy output control scheme is synthesized. Unlike some existing control schemes for systems with input saturation, the developed controller dose not require assumptions on the states available and nonlinear systems satisfying the matching condition. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin. A simulation is included to illustrate the effectiveness of the proposed approach.

A novel adaptive control method is designed for the uncertain nonlinear systems with quantized states under the condition that system nonlinearities do not satisfy the Lipschitz condition. In this paper, the global control for an uncertain nonlinear system with quantized states in the case that the system nonlinearities do not satisfy the Lipschitz condition is first achieved. Separation theorem is used to model the uncertainties appropriately and then an adaptive term is designed to help attenuate the effects of system uncertainties. Furthermore, the global boundedness of all signals of the closed-loop system is proved based on the Lyapunov stability theorem. Finally, simulation results are given to demonstrate the effectiveness of the proposed methods.

In this paper, an adaptive fuzzy output feedback control approach is presented for a class of single-input single-output uncertain nonlinear systems with unknown backlash-like hysteresis and unmeasured states. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a state filter observer is designed to estimate unmeasured states. Combining the backstepping recursive design with modular design techniques, a new adaptive fuzzy output control scheme is developed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semiglobally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin. A simulation is included to illustrate the effectiveness of the proposed approach. The important feature of the proposed control approach is that it can solve the states immeasurable problem of nonlinear systems with unknown backlash-like hysteresis and the problem of unknown virtual control coefficients.

Event-triggered adaptive optimal tracking control for nonlinear stochastic systems with dynamic state constraints

SummaryThis paper investigates the issue of adaptive reliable tracking control for a class of uncertain nonlinear parametric strict‐feedback systems under actuator faults. To guarantee better transient performance of adaptive systems especially when actuator faults occur, a novel prescribed performance bounds (PPBs) method based on exponent‐dependent barrier Lyapunov function is developed. Differing from the existing results where the control schemes have introduced the strictly monotone smooth function to achieve constrained error transformation, the proposed PPBs scheme is designed by using the time‐varying barriers to constrain the error trajectories, which accurately characterizes the convergence rates and convergence bounds of errors. Finally, under the framework of backstepping technique and Lyapunov stability theorem, an adaptive reliable controller is designed to ensure that all the closed‐loop signals are semiglobally uniformly ultimately bounded with the tracking errors converging to the specified PPBs. Simulation results demonstrate the effectiveness of the proposed approach.

Event-triggered low-computation adaptive output-feedback fuzzy tracking control of uncertain nonlinear systems

The problem of command-filter-based adaptive fixed-time tracking control is investigated for nonlinear systems with time-varying uncertain parameters and disturbances in this article. Existing fixed-time control strategies via an adaptive approach are primarily bounded-error, trajectory tracking-oriented. Different from previous results, we propose a new fixed-time stability lemma utilizing an exponential decay function. Then, by leveraging the proposed lemma and command filtered backstepping technique, a novel adaptive fixed-time control scheme is constructed, which can reduce the computational complexity and completely counteract uncertain parameters. We demonstrate that the tracking error enters a neighborhood near zero within a fixed-time and ultimately converges to zero. Furthermore, through the incorporation of a piecewise function into both the filter error compensation system and virtual control laws, the second-order derivability of virtual control laws is guaranteed, thereby ensuring the validity of the command filter. Finally, the proposed strategy's effectiveness is confirmed through simulation results.

The problem of adaptive robust control for uncertain nonlinear systems with time-varying delay is considered in this paper. The upper bound of the uncertainty is assumed to be nonlinear functions with unknown coefficients. By using adaptive control method, a class of adaptive robust state feedback controller is proposed. Based on Lyapunov-Krasovskii method and Lyapunov stability theory, it is shown that the controller designed can render the uniform asymptotic stability of the system. Finally, a numerical example is given to show the controller is valid.

Event-triggered adaptive fixed-time fuzzy control for uncertain nonlinear systems with unknown actuator faults

In this work, the tracking control problem of nonlinear system which contains unknown parameters, multiple state delays, external disturbances and the dead-zone input is studied. By introducing a dynamic gain-based adaptive control strategy and employing a new Lyapunov–Krasovskii (L–K) functional, we construct an adaptive tracking controller to ensure the boundedness of all the states and guarantee the tracking error small enough. Two examples are given to verify the correctness of the control theory.

SUMMARYThe paper considers the discrete‐time implementation of a class of backstepping adaptive controllers for uncertain nonlinear systems in the parametric strict‐feedback form. The stability of the resultant sampled‐data system cannot be guaranteed when the direct discretization of the continuous‐time backstepping controller is applied to the same system via a sampling and hold device. Therefore, the paper has presented a sampled‐data control scheme which involves first modifying the existing continuous‐time controller and then discretizing it using the forward Euler method. It has been shown that the proposed control guarantees in a semi‐global sense the boundedness of all the variables of the overall sampled‐data system under some conditions. Particularly, the state of the nonlinear system to be controlled can converge to any arbitrarily small neighbourhood of the origin. Copyright © 2011 John Wiley & Sons, Ltd.

Adaptive actuator failure compensation control of uncertain nonlinear systems with guaranteed transient performance

This paper addresses the problem of state estimation and the tracking control scheme combining fuzzy control technique for a class of MIMO nonlinear systems, in which some variables are not measurable, with plant uncertainties and external disturbances First, the nonlinearities are approximated using neural networks, and then are modeled based on linear difference inclusions(LDI), which makes the structure of the desired filter simpler and parameter turning easier. A unified framework is established to solve the addressed H ∞ filtering problem by exploiting linear matrix inequality (LMI) approach. The proposed control law is based on indirect adaptive fuzzy control and uses two on-line estimations. The adaptive fuzzy tracking control using Variable Structure (VS) control technique is derived based on Lyapunov criterion to resolve system uncertainties and external disturbances. This is done in such a way that all states of the system are bounded and the H ∞ tracking performance is achieved. Finally, A numerical example is investigated to demonstrate the feasibility and the effectiveness of the proposed methodology.

The robust neural adaptive control scheme is developed for a class of nonlinear MIMO uncertain systems. Two types of uncertainties are considered: parametric uncertainty and unknown nonlinearities. In the control procedure, neural networks are implemented to estimate the uncertain system owing to parametric uncertainty and robust compensating controllers are designed in H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> sense for attenuating the unmatched nonlinearities, in which no property of uncertainties is assumed and needed for design, only its possible bound which may not unique, is used for analytical purposes. And also relaxes some of restrictive assumptions that are usually made in neural adaptive control schemes, one such assumption is the requirement of a known bound on the network reconstruction error. It is shown that the proposed control is continuous, guarantees global stability and the H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> performance index. Extensive simulations on the tracking control of a two-link rigid robotic manipulator verify the effectiveness of the design methodology and controller.