Wavelet Based Adaptive Tracking Control for Uncertain Nonlinear Systems with Input Constraints

Synthesis of smoother robust control for nonlinear uncertain dynamical systems is considered. The existing saturation-type robust controller guarantees asymptotic stability or stability of uniform ultimate boundedness. It is shown that, mainly due to the part of uncertainties that is bounded by a constant, the controller may potentially have a very large rate of change in order to achieve a small ultimate bound for the state. This study, on its gain or the property of its partial derivative, reveals the need for designing smoother nonlinear robust controller along two directions. First, in a recursive design of robust control, fictitious robust control must be designed to be as smooth as possible so that the actual robust control will not have too large of a magnitude for implementation purposes. Second, if the uncertainties are known to have bounded rate of change, it is both practically and theoretically important to design a robust controller which rate of change is limited by that of the uncertainties. The objective of this paper is to design smoother robust controls by providing results on those two topics. >

Robust tracking control of uncertain nonlinear systems with adaptive dynamic programming

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.

This paper deals with the problem of robust control for Uncertain Nonlinear System via fuzzy control approach. First, a fuzzy controller with robust control capability is proposed. For avoiding complex controller parameters adjustment, Multi-objective particle swarm Optimization (PSO) algorithm is adopted during the controller design. Secondly, the multi-model is employed to represent the nonlinear system with norm-bounded parameter uncertainties. Finally, a simulation example illustrates the effectiveness and the feasibility of the proposed approach.

This paper develops a L1 adaptive output-feedback fault-tolerant controller for uncertain nonlinear systems in the presence of unmodeled actuator dynamics and actuator faults. The proposed controller consists of the output predictor, adaptive laws, and the control law. The output predictor is a dynamic system expressed as a linear system with adaptive parameters which mean the matched uncertainties and the unmatched uncertainties. Piecewise-constant adaptive laws are designed to update the adaptive parameters so that the estimation error is driven to zero at each integration time step. The control law with low-pass filters is introduced to compensate for the performance degradation because of system uncertainties, unmodeled actuator dynamics and faults, and to guarantee the uniform boundedness of the input and output signals of the system. Two simulation examples verify the effectiveness of the proposed controller.

Decentralized neural identification and control for uncertain nonlinear systems: Application to planar robot

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.

Adaptive control of uncertain nonlinear systems using mixed backstepping and Lyapunov redesign techniques

This article focuses on the asymptotic tracking control problem for uncertain nonlinear systems subject to both multiple disturbances and parametric uncertainties. To address this issue, a parameter adaptation law is synthesized to deal with the parametric uncertainties, and an adaptive-gain disturbance estimator (ADE) is constructed to estimate the mismatched and matched disturbances, and compensate them in feedforward channels, which eliminates the impact of disturbances on tracking performance. Meanwhile, an updated law for estimator gain driven by the estimation errors is utilized in the ADE when facing unknown upper bounds of disturbances, which reduces the conservatism of estimator gain selection and is beneficial to practical implementation. Based on the parameter adaption technique and the presented ADE approach, a composite controller is proposed to ensure an excellent asymptotic output tracking performance. The stability analysis shows the proposed controller can attain asymptotic tracking performance in the presence of both time-variant disturbances and parametric uncertainties. Comparative simulation results of the application to a robot manipulator reveal the validity of the developed approach.

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.

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

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

This paper describes a hybrid approach to the problem of controlling a class of nonlinear systems in the face of both unknown nonlinearities and unmodeled dynamics. In the proposed methodology, neural networks and direct adaptive control compensate for unknown nonlinear mappings while dynamic nonlinear damping provides robustness to unmodeled dynamics. To illustrate the theoretical development, the authors design a longitudinal autopilot for a simplified nonlinear missile aerodynamic model with input unmodeled dynamics. Simulation results demonstrate robustness in the face of this type of uncertainty.

In this paper,the problem of adaptive control based on memoryless state observer is considered for uncertain nonlinear systems with multiple time delays. The upper bound of the time-delay state disturbance is unknown. And an adaptive law is proposed to estimate the unknown parameter of the disturbance,and the estimated value is used to design a memoryless state observer and controller,which are both independent of time-delay. Based on the Lyapunov-Krasovskii function,it is shown that the observation error can converge asymtotically to zero. Simulation results illustrate the applicability of this method.

This article addresses the optimal tracking control problem with prescribed performance for uncertain nonlinear systems subject to input constraint and unknown disturbances. First, a fixed‐time monotonic convergence function is introduced to restrain tracking error, and a nonlinear mapping technique is employed to transform the constrained error into an unconstrained variable, then the fixed‐time output tracking issue is boiled down to the boundedness problem of the transformed variable. With the aid of a nonquadratic cost function, the input constraint is encoded into the optimization problem. To solve the unknown disturbances, an auxiliary system and an auxiliary disturbance policy are constructed, and the optimal control problem is formulated as a two‐player zero‐sum game. Moreover, a Hamilton–Jacobi–Isaacs (HJI) equation associated with this nonquadratic zero‐sum game is established to give the optimal control and the worst‐case disturbance policy solution. Subsequently, to avoid using knowledge of the system dynamics, three neural network approximators, namely, actor, critic, and disturbance, which are tuned online and simultaneously for approximating the solution of HJI, are constructed based on the integral reinforcement learning algorithm. Theoretical analysis shows that the reconstructed error system states and the weight estimation errors are semi‐globally uniformly ultimately bounded. Finally, the simulation study further tests the availability of the proposed control strategy.