A small‐gain approach for adaptive output‐feedback NN control of switched pure‐feedback nonlinear systems

This paper investigates the problem of adaptive output‐feedback neural network (NN) control for a class of switched pure‐feedback uncertain nonlinear systems. A switched observer is first constructed to estimate the unmeasurable states. Next, with the help of an NN to approximate the unknown nonlinear terms, a switched small‐gain technique‐based adaptive output‐feedback NN control scheme is developed by exploiting the backstepping recursive design scheme, input‐to‐state stability analysis, the common Lyapunov function method, and the average dwell time (ADT) method. In the recursive design, the difficulty of constructing an overall Lyapunov function for the switched closed‐loop system is dealt with by decomposing the switched closed‐loop system into two interconnected switched systems and constructing two Lyapunov functions for two interconnected switched systems, respectively. The proposed controllers for individual subsystems guarantee that all signals in the closed‐loop system are semiglobally, uniformly, and ultimately bounded under a class of switching signals with ADT, and finally, two examples illustrate the effectiveness of theoretical results, which include a switched RLC circuit system.     

Fixed time synchronization of delayed chaotic neural networks by using active adaptive control

This article aims to investigate the fixed time synchronization of a class of chaotic neural systems by way of adaptive control method. Using Lyapunov stability theory, a new fixed time stability theorem which plays an important role on the synchronization scheme is presented at first. Then, combining the fixed time stability theorem and adaptive control technique, an adaptive control scheme has been developed to achieve the fixed time synchronization of chaotic neural systems. The proposed controllers assure the global convergence of the error dynamics in fixed-time based on the Lyapunov stability theory. Furthermore, the proposed control strategy cannot only provide a fast convergence rate, but also afford a bounded convergence time which is unrelated to the initial values and easy to work out by using the simple time calculation formula. Finally, numerical simulations are presented by taking a typical two-order chaotic neural system as an example to verify and demonstrate the effectiveness of the proposed scheme.     

Fixed-time adaptive neural tracking control for a class of uncertain multi-input and multi-output nonlinear pure-feedback systems

This study examines the fixed-time adaptive neural network tracking control problem for a class of unknown multi-input and multi-output (MIMO) nonlinear pure-feedback systems. The introduction of the radial basis function resolves uncertain problems of unknown MIMO systems. The mean value theorem is introduced to overcome the controller design problem attributed to the nonaffine structure in pure-feedback systems. Moreover, a novel fixed-time virtual controller and an actual controller are designed to solve the issue of previous single-input and single-output and MIMO systems that have no solution in the negative domain and at the origin in finite- and fixed-time controls. Furthermore, a design method is proposed. The final designed controller ensures that all signals in the system are bounded. Simulation experiments show that the designed fixed-time controller facilitates smaller tracking error of the system compared with other finite- or fixed-time controllers. Furthermore, the selection of appropriate design parameters allows the tracking error to converge on a small neighborhood of the origin in a fixed time.     

Precise position control of an ultrasonic motor using the PID controller combined with NN

The input‐output characteristic of an ultrasonic motor (USM) has nonlinear elements and changes with a temperature rise or fluctuation of load‐mass. Therefore, it is difficult to accomplish satisfactory control performance by using conventional PID controllers. In this paper, we propose a PID controller combined with a neural network (NN‐PID controller). In this design method, the controller gains consist of constant gains of the PID controller and variable gains of the NN controller. The weights of the NN are adjusted by the backpropagation method so that the control error can be minimized. This method does not require long learning time of the NN. The effectiveness of the proposed design method is confirmed by experiments using an existing USM. © 2003 Wiley Periodicals, Inc. Electr Eng Jpn, 146(3): 46–54, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10199     

Active fault tolerant control of piecewise affine systems with reference tracking and input constraints

An active fault tolerant control (AFTC) method is proposed for discrete‐time piecewise affine (PWA) systems. Only actuator faults are considered. The AFTC framework contains a supervisory scheme, which selects a suitable controller in a set of controllers such that the stability and an acceptable performance of the faulty system are held. The design of the supervisory scheme is not considered here. The set of controllers is composed of a normal controller for the fault‐free case, an active fault detection and isolation controller for isolation and identification of the faults, and a set of passive fault tolerant controllers (PFTCs) modules designed to be robust against a set of actuator faults. In this research, the piecewise nonlinear model is approximated by a PWA system. The PFTCs are state feedback laws. Each one is robust against a fixed set of actuator faults and is able to track the reference signal while the control inputs are bounded. The PFTC problem is transformed into a feasibility problem of a set of LMIs. The method is applied on a large‐scale live‐stock ventilation model. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive set‐point regulation of discrete‐time nonlinear systems

In this paper, adaptive set‐point regulation controllers for discrete‐time nonlinear systems are constructed. The system to be controlled is assumed to have a parametric uncertainty, and an excitation signal is used in order to obtain the parameter estimate. The proposed controller belongs to the category of indirect adaptive controllers, and its construction is based on the policy of calculating the control input rather than that of obtaining a control law. The proposed method solves the adaptive set‐point regulation problem under the assumption that the target state is reachable for each fixed parameter value. Additional feature of the proposed method is that Lyapunov‐like functions have not been used in the construction of the controllers. Copyright © 2015 John Wiley & Sons, Ltd.     

Indirect adaptive control of nonlinear system via dynamic multilayer neural networks with multi‐time scales

This paper deals with adaptive nonlinear identification and trajectory tracking problem via dynamic multilayer neural network with different time scales. By means of a Lyapunov‐like analysis, we determine stability conditions for the on‐line identification. Then, a sliding mode controller is designed for trajectory tracking with consideration of the modeling error and disturbance. The main contributions of the paper lie in the following aspects. First, we extend our prior identification results of single‐layer dynamic neural networks with multi‐time scales to those of multilayer case. Second, the e‐modification in standard use in adaptive control is introduced in the on‐line update laws to guarantee bounded weights and bounded identification errors. Third, the potential singularity problem in controller design is solved by using new update laws for the NN weights so that the control signal is guaranteed bounded. The stability of proposed controller is proved by using Lyapunov function. Simulation results demonstrate the effectiveness of the proposed algorithm. Copyright © 2014 John Wiley & Sons, Ltd.     

Variable neural adaptive robust controllers for uncertain systems

A class of variable neural adaptive robust controllers is proposed. Essential components of the proposed controllers are raised‐cosine radial basis function (RCRBF) neural networks that can vary their structures dynamically by adding or removing RBFs online. The compact support of the RCRBFs alleviate the problem of determining the parameters of the RBFs and can, together with a simple adding and removing algorithm, significantly reduce the computational effort in the training process of the network. The stability of the overall closed‐loop system is analyzed using the Lypaunov type of arguments. It is guaranteed that the tracking error of the closed‐loop systems driven by the proposed controller is uniformly ultimately bounded. Copyright © 2007 John Wiley & Sons, Ltd.     

Adaptive neural network output feedback stabilization of nonlinear non‐minimum phase systems

This paper presents an adaptive output feedback stabilization method based on neural networks (NNs) for nonlinear non‐minimum phase systems. The proposed controller comprises a linear, a neuro‐adaptive, and an adaptive robustifying parts. The NN is designed to approximate the matched uncertainties of the system. The inputs of the NN are the tapped delays of the system input–output signals. In addition, an appropriate reference signal is proposed to compensate the unmatched uncertainties inherent in the internal system dynamics. The adaptation laws for the NN weights and adaptive gains are obtained using Lyapunov's direct method. These adaptation laws employ a linear observer of system dynamics that is realizable. The ultimate boundedness of the error signals are analytically shown using Lyapunov's method. The effectiveness of the proposed scheme is shown by applying to a translation oscillator rotational actuator model. Copyright © 2009 John Wiley & Sons, Ltd.     

Adaptive neural control for nonstrict‐feedback stochastic nonlinear time‐delay systems with input and output constraints

This paper investigates an adaptive neural tracking control for a class of nonstrict‐feedback stochastic nonlinear time‐delay systems with input saturation and output constraint. First, the Gaussian error function is used to represent a continuous differentiable asymmetric saturation model. Second, the appropriate Lyapunov‐Krasovskii functional and the property of hyperbolic tangent functions are used to compensate the time‐delay effects, the neural network is used to approximate the unknown nonlinearities, and a barrier Lyapunov function is designed to ensure that the output parameters are restricted. At last, based on Lyapunov stability theory, a robust adaptive neural control method is proposed, and the designed controller decreases the number of learning parameters and thus reduces the computational burden. It is shown that the designed neural controller can ensure that all the signals in the closed‐loop system are 4‐Moment (or 2 Moment) semi‐globally uniformly ultimately bounded and the tracking error converges to a small neighborhood of the origin. Two examples are given to further verify the effectiveness of the proposed approach.     

Decentralized adaptive robust stabilization of uncertain interconnected time‐delay systems

This paper considers the problem of decentralized adaptive robust stabilization of a class of interconnected time‐delay systems with arbitrarily bounded matched but limitedly bounded unmatched uncertainties. A new class of decentralized adaptive controllers based on Lyapunov–Krasovskii functional is proposed that guarantees bounded stability of the system and ensures nonfragileness of the controller to perturbations in its nonadaptive gain factor. The existence of such controllers is formulated in the LMI framework besides being presented using the Algebraic Riccati Equations. A numerical example is considered to illustrate the applicability and effectiveness of the proposed controller. Copyright © 2011 John Wiley & Sons, Ltd.     

Adaptive PI secondary control for smart autonomous microgrid systems

In this paper, the authors present a neural‐network‐based distributed secondary control to regulate the output voltage and frequency of a smart autonomous microgrid system. Generally, the secondary controller is implemented in a centralized manner using a fixed‐gain proportional‐plus‐integral controller which may perform well under certain operating conditions only. Also the failure of centralized controller implies no secondary control action for the entire system. The control technique proposed in this paper is a distributed one and makes use of neural network (NN) concept to improve the performance of system. A well‐trained NN supplies the controller with suitable gains according to each operating point. Before training the NN, evolutionary optimization technique, differential evolution, is employed to obtain the optimal gains of controller at each operating load condition which forms the training set for NN. Simulation results show that the proposed controller damps the oscillations caused by load changes, restores the output voltage and frequency of the system to their nominal values, and maintains proper load sharing property of the baseline controller. The performance of the controller is also compared with fixed‐gain controller. Copyright © 2015 John Wiley & Sons, Ltd.     

Direct adaptive neural control of nonlinear strict‐feedback systems with unmodeled dynamics using small‐gain approach

In this paper, a novel direct adaptive neural control approach is presented for a class of single‐input and single‐output strict‐feedback nonlinear systems with nonlinear uncertainties, unmodeled dynamics, and dynamic disturbances. Radial basis function neural networks are used to approximate the unknown and desired control signals, and a direct adaptive neural controller is constructed by combining the backstepping technique and the property of hyperbolic tangent function. It is shown that the proposed control scheme can guarantee that all signals in the closed‐loop system are semi‐globally uniformly ultimately bounded in mean square. The main advantage of this paper is that a novel adaptive neural control scheme with only one adaptive law is developed for uncertain strict‐feedback nonlinear systems with unmodeled dynamics. Simulation results are provided to illustrate the effectiveness of the proposed scheme. Copyright © 2015 John Wiley & Sons, Ltd.     

Adaptive recurrent Chebyshev neural network control for PM synchronous motor servo‐drive electric scooter with V‐belt continuously variable transmission

Because of unknown nonlinearity and time‐varying characteristics of electric scooter with V‐belt continuously variable transmission (CVT) driven by permanent magnet synchronous motor (PMSM), its accurate dynamic model is difficult to establish for the design of the linear controller in whole system. In order to conquer this difficulty and raise robustness, an adaptive recurrent Chebyshev neural network (NN) control system is proposed to control for PMSM servo‐drive electric scooter with V‐belt CVT under lumped nonlinear external disturbances in this study. The adaptive recurrent Chebyshev NN control system consists of a recurrent Chebyshev NN control and a compensated control with estimation law. In addition, the online parameters tuning methodology of the recurrent Chebyshev NN and the estimation law of the compensated controller can be derived by using the Lyapunov stability theorem. Moreover, the two optimal learning rates of the recurrent Chebyshev NN based on a discrete‐type Lyapunov function are proposed to guarantee the convergence of tracking error. Finally, comparative studies are demonstrated by experimental results in order to show the effectiveness of the proposed control scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

Multiple‐model adaptive robust dynamic surface control with estimator resetting

A multiple‐model adaptive robust dynamic surface control with estimator resetting is investigated for a class of semi‐strict feedback nonlinear systems in this paper. The transient performance is mainly considered. The multiple models are composed of fixed models, one adaptive model, and one identification model that can be obtained when the persistent exciting condition is satisfied. The transient performance of the final tracking system can be improved significantly by designing proper switching mechanism during the parameter tuning procedure. The semi‐globally uniformly ultimately bounded stability of the closed‐loop system can be easily achieved because of the framework of adaptive robust dynamic surface control. Numerical examples are provided to demonstrate the effectiveness of the proposed multiple‐model controller. Copyright © 2014 John Wiley & Sons, Ltd.     

Adaptive neural network control for stochastic constrained block structure nonlinear systems with dynamical uncertainties

Stochastic adaptive dynamic surface control is presented for a class of uncertain multiple‐input–multiple‐output (MIMO) nonlinear systems with unmodeled dynamics and full state constraints in this paper. The controller is constructed by combining the dynamic surface control with radial basis function neural networks for the MIMO stochastic nonlinear systems. The nonlinear mapping is applied to guarantee the state constraints being not violated. The unmodeled dynamics is disposed through introducing an available dynamic signal. It is proved that all signals in the closed‐loop system are bounded in probability and the error signals are semiglobally uniformly ultimately bounded in mean square or the sense of four‐moment and the state constraints are confirmed in probability. Simulation results are offered to further illustrate the effectiveness of the control scheme.     

Comparisons of adaptive fault‐tolerant insensitive control methods for a class of linear systems

In this paper, the problem of fault‐tolerant insensitive control is addressed for a class of linear time‐invariant continuous‐time systems against bounded time‐varying actuator faults and controller gain variations. Adaptive mechanisms are developed to adjust controller gains in order to compensate for the detrimental effects of partial loss of control effectiveness and bias‐actuator faults. Variations of controller gains arise from time‐varying and bounded perturbations that are supposed to always exist in adaptive mechanisms. Based on the disturbed outputs of adaptive mechanisms, three different adaptive control strategies are constructed to achieve bounded stability results of the closed‐loop adaptive fault‐tolerant control systems in the presence of actuator faults and controller gain variations. Furthermore, comparisons of convergence boundaries of states and limits of control inputs among adaptive strategies are developed in this paper. The efficiency of the proposed adaptive control strategies and their comparisons are demonstrated by a rocket fairing structural‐acoustic model.     

Direct adaptive neural tracking control for a class of stochastic pure‐feedback nonlinear systems with unknown dead‐zone

This paper considers the problem of adaptive neural tracking control for a class of nonlinear stochastic pure‐feedback systems with unknown dead zone. Based on the radial basis function neural networks' online approximation capability, a novel adaptive neural controller is presented via backstepping technique. It is shown that the proposed controller guarantees that all the signals of the closed‐loop system are semi‐globally, uniformly bounded in probability, and the tracking error converges to an arbitrarily small neighborhood around the origin in the sense of mean quartic value. Simulation results further illustrate the effectiveness of the suggested control scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

Stability analysis and adaptive control for nonlinear discrete‐time systems with time delays and dead zone via state‐feedback technique

This research addresses the stability analysis and adaptive state‐feedback control for a class of nonlinear discrete‐time systems with multiple interval time‐varying delays and symmetry dead zone. The multiple interval time‐varying delays and symmetry dead zone are considered in the nonlinear discrete‐time system. The multiple interval time‐varying delays are bounded by the nonlinear function with unknown coefficients, and the symmetry dead zone is considered without the knowledge of the dead zone parameters. The adaptive state‐feedback controller is designed for the nonlinear discrete‐time systems with multiple interval time‐varying delays and dead zone. The discrete Lyapunov‐Krasovskii functional is introduced, such that the solutions of the closed‐loop error system converge to an adjustable bounded region and the state errors can be rendered arbitrarily small by adjusting the adaptive parameters. The designed adaptive state‐feedback controller does not require the knowledge of maximum and minimum values for the characteristic slopes of the dead zone. Finally, three simulation examples are given to show the effectiveness of the proposed methods.     

Robust adaptive control for uncertain time‐delay systems

The problem of robust stabilization for uncertain dynamic time‐delay systems is considered. Firstly a class of time‐delay systems with uncertainties bounded by high‐order polynomials and unknown coefficients are considered. The corresponding controller is designed by employing adaptive method. It is shown that the controller designed can render the closed‐loop system uniformly ultimately bounded stable based on Lyapunov–Krasovskii method and Lyapunov stability theory. Then the proposed adaptive idea is applied to stabilizing a class of large‐scale time‐delay systems with strong interconnections. A decentralized feedback adaptive controller is designed which guarantees the closed‐loop large‐scale systems uniformly ultimately bounded stable. Finally, numerical examples are given to show the potential of the proposed techniques. Copyright © 2005 John Wiley & Sons, Ltd.