Adaptive Bounding Technique Research Articles

Global fuzzy adaptive asymptotic tracking control for nonlinear reaction-diffusion equations with time-varying coefficients

This study focuses on the research of the globally asymptotic tracking problem of unknown nonlinear reaction-diffusion equations with time-varying coefficients and uncertain external disturbance. Firstly, fuzzy logic systems and adaptive bounding technique are used to deal with nonlinear reaction-diffusion equations with time-varying coefficients and uncertain external disturbance. Secondly, a novel global state feedback adaptive fuzzy control algorithm is proposed to make the nonlinear reaction-diffusion equations track the target systems globally and asymptotically. In addition, the globally asymptotic tracking condition can be obtained, which overcomes the semi-global results in the existing literatures. Finally, three simulation examples are given to illustrate the feasibility and effectiveness of the proposed control protocols.

Repetitive Learning Control for Control-Affine Systems With Time Delays

This article presents a repetitive learning control method, which deals with both parametric and nonparametric uncertainties involved in the control-affine systems with time delays. The desired control is taken as a time-varying parameter, and a learning algorithm is applied for estimation. The time-delay nonlinearity and the state-dependent input gain are handled as the nonparametric uncertainties, for which the adaptive bounding technique is adopted such that the requirement for the knowledge about the system undertaken can be reduced, and the troublesome time delays are effectively treated. The presented control method only needs the lower bound of the input gain is to be known as a priori. Furthermore, it is shown applicable to systems with multiple time delays. The fully saturated learning algorithms are utilized to solve the positive accumulation of estimates so that the possible divergence phenomenon can be avoided. The convergence of the tracking error is established, while the boundedness of the variables in the closed-loop system is assured. The numerical results are presented to verify the effectiveness of the proposed learning control method.

A Robust Adaptive Model Reference Impedance Control of a Robotic Manipulator With Actuator Saturation

This paper develops a robust adaptive model reference impedance controller for an n-link robotic manipulator with parameter uncertainties, actuator saturation, and imprecise force sensor measurement. In order to handle the system uncertainties, the adaptive technique and prediction error are used. To reduce calculation complexity, the adaptation law for robot parameters estimation is designed in the joint space. Actuator saturation is also overcome by an auxiliary system, and imprecise force sensor measurement is compensated with utilization of adaptive bounding technique. Moreover, the joint acceleration vector problem, which is nonmeasurable, is covered by the filtered regressor matrix. Using Lyapunov's direct method, as long as two conditions are satisfied the proposed controller ensures the exponential stability of all the signals of the closed loop system; otherwise, the closed loop system is globally stable. Finally, simulations are performed on prototyped robots to analyze and evaluate the established controller as well as to demonstrate the effectiveness of the proposed scheme.

A robust adaptive observer for a class of singular nonlinear uncertain systems

ABSTRACTThis paper proposes a robust adaptive observer for a class of singular nonlinear non-autonomous uncertain systems with unstructured unknown system and derivative matrices, and unknown bounded nonlinearities. Unlike many existing observers, no strong assumption such as Lipschitz condition is imposed on the recommended system. An augmented system is constructed, and the unknown bounds are calculated online using adaptive bounding technique. Considering the continuous nonlinear gain removes the chattering which may appear in practical applications such as analysis of electrical circuits and estimation of interaction force in beating heart robotic-assisted surgery. Moreover, a simple yet precise structure is attained which is easy to implement in many systems with significant uncertainties. The existence conditions of the standard form observer are obtained in terms of linear matrix inequality and the constrained generalised Sylvester's equations, and global stability is ensured. Finally, simulation results are obtained to evaluate the performance of the proposed estimator and demonstrate the effectiveness of the developed scheme.

Adaptive critic design-based robust neural network control for nonlinear distributed parameter systems with unknown dynamics

Abstract In this paper, an adaptive critic design (ACD)-based robust on-line neural network control design is developed for a class of parabolic partial differential equation (PDE) systems with unknown nonlinear dynamics. First, the Galerkin method is applied to the parabolic PDE system to derive a finite-dimensional slow one and an infinite-dimensional stable fast subsystem. The obtained slow system is an ordinary differential equation (ODE) system with unknown nonlinearities, which accurately describes the dynamics of the slow modes of the PDE system. Then, a novel ACD-based robust optimal control scheme is proposed for the resulting nonlinear slow system with unknown dynamics. An action neural network (NN) is employed to approximate all the derived unknown nonlinear terms and a robust control term is further developed to attenuate the NN reconstruction errors and disturbances. Especially, by developing novel critic signals and Lyapunov function candidate, together with the adaptive bounding technique, no a prior knowledge for the bounds of the disturbance term, the NN ideal weights of action NN and critic NN and the NN reconstruction errors is required. Finally, simulation results demonstrate the effectiveness of the proposed robust optimal control scheme.

Hybrid function projective synchronization of chaotic systems with uncertain time-varying parameters via Fourier series expansion

In this paper, the hybrid function projective synchronization (HFPS) of different chaotic systems with uncertain periodically time-varying parameters is carried out by Fourier series expansion and adaptive bounding technique. Fourier series expansion is used to deal with uncertain periodically time-varying parameters. Adaptive bounding technique is used to compensate the bound of truncation errors. Using the Lyapunov stability theory, an adaptive control law and six parameter updating laws are constructed to make the states of two different chaotic systems asymptotically synchronized. The control strategy does not need to know the parameters thoroughly if the time-varying parameters are periodical functions. Finally, in order to verify the effectiveness of the proposed scheme, the HFPS between Lorenz system and Chen system is completed successfully by using this scheme.

Adaptive Hybrid Function Projective Synchronization of Chaotic Systems with Time‐Varying Parameters

The adaptive hybrid function projective synchronization (AHFPS) of different chaotic systems with unknown time‐varying parameters is investigated. Based on the Lyapunov stability theory and adaptive bounding technique, the robust adaptive control law and the parameters update law are derived to make the states of two different chaotic systems asymptotically synchronized. In the control strategy, the parameters need not be known throughly if the time‐varying parameters are bounded by the product of a known function of t and an unknown constant. In order to avoid the switching in the control signal, a modified robust adaptive synchronization approach with the leakage‐like adaptation law is also proposed to guarantee the ultimately uni‐formly boundedness (UUB) of synchronization errors. The schemes are successfully applied to the hybrid function projective synchronization between the Chen system and the Lorenz system and between hyperchaotic Chen system and generalized Lorenz system. Moreover, numerical simulation results are presented to verify the effectiveness of the proposed scheme.

Adaptive variable structure state estimation for uncertain systems with persistently bounded disturbances

AbstractThis paper develops an adaptive state estimator design methodology for nonlinear systems with unknown nonlinearities and persistently bounded disturbances. In the proposed estimation scheme, the boundary layer strategy in variable structure techniques is utilized to design a continuous state estimator such that the undesirable chattering phenomenon is avoided; and the adaptive bounding technique is used for online estimation of the unknown bounding parameter. The existence condition of the adaptive estimators is provided in terms of linear matrix inequality (LMI). Since the orthogonal projection of the state estimation error onto the null space of the linear measurement distribution matrix is used in the derivation process, the update law of bounding parameter estimate is represented in terms of the available measurement error. The proposed estimator can ensure that the state estimation error is uniformly ultimately bounded (UUB) with an ultimate bound. Furthermore, using the existing LMI optimization technique, a suboptimal adaptive state estimator can be obtained in the sense of minimizing an upper bound of the peak gains in the ultimate bound. Finally, a simulation example is given to illustrate the effectiveness of the proposed design method. Copyright © 2010 John Wiley & Sons, Ltd.

Asymptotic Tracking of Uncertain Systems With Continuous Control Using Adaptive Bounding

This paper presents a robust adaptive control design method for a class of multiple-input-multiple-output uncertain nonlinear systems in the presence of parametric and nonparametric uncertainties and bounded disturbances. Using the approximation properties of the unknown continuous nonlinearities and the adaptive bounding technique, the developed controller achieves asymptotic convergence of the tracking error to zero, while ensuring boundedness of parameter estimation errors. The algorithm does not assume the knowledge of any bound on the unknown quantities in designing the controller. It is based on an integral technique involving the filtered tracking error and produces a continuous control. Theoretical developments are illustrated via simulation results.

Observação adaptativa neural com convergência assintótica na presença de parâmetros variantes no tempo e distúrbios

Neste artigo é proposto um esquema baseado em redes neurais para estimação adaptativa dos estados de uma classe de sistemas não-lineares contínuos, incertos, variantes no tempo e sujeita a distúrbios. Prova-se, via argumentos usuais de Lyapunov e uma técnica de limitação adaptativa (adaptive bounding technique), que o erro residual de observação converge para zero, inclusive na presença de erros de aproximação e distúrbios, enquanto os erros de estimação (pesos, parâmetros e função limitadora) permanecem limitados. Um exemplo de simulação é apresentado para ilustrar a aplicação e desempenho do esquema proposto.

Robust Adaptive Observer Design for Uncertain Systems With Bounded Disturbances

This paper presents a robust adaptive observer design methodology for a class of uncertain nonlinear systems in the presence of time-varying unknown parameters with absolutely integrable derivatives, and nonvanishing disturbances. Using the universal approximation property of radial basis function (RBF) neural networks and the adaptive bounding technique, the developed observer achieves asymptotic convergence of state estimation error to zero, while ensuring boundedness of parameter errors. A comparative simulation study is presented by the end.

Adaptive output feedback control for nonlinear time-delay systems using neural network

This paper extends the adaptive neural network (NN) control approaches to a class of unknown output feedback nonlinear time-delay systems. An adaptive output feedback NN tracking controller is designed by backstepping technique. NNs are used to approximate unknown functions dependent on time delay. Delay-dependent filters are introduced for state estimation. The domination method is used to deal with the smooth time-delay basis functions. The adaptive bounding technique is employed to estimate the upper bound of the NN approximation errors. Based on Lyapunov-Krasovskii functional, the semi-global uniform ultimate boundedness of all the signals in the closed-loop system is proved. The feasibility is investigated by two illustrative simulation examples.