Neural Network Adaptive Robust Control Of Siso Nonlinear Systems In A Normal Form

In this paper, performance oriented control laws are synthesized for a class of single‐input‐single‐output (SISO) n‐th order nonlinear systems in a normal form by integrating the neural networks (NNs) techniques and the adaptive robust control (ARC) design philosophy. All unknown but repeat‐able nonlinear functions in the system are approximated by the outputs of NNs to achieve a better model compensation for an improved performance. While all NN weights are tuned on‐line, discontinuous projections with fictitious bounds are used in the tuning law to achieve a controlled learning. Robust control terms are then constructed to attenuate model uncertainties for a guaranteed output tracking transient performance and a guaranteed final tracking accuracy. Furthermore, if the unknown nonlinear functions are in the functional ranges of the NNs and the ideal NN weights fall within the fictitious bounds, asymptotic output tracking is achieved to retain the perfect learning capability of NNs. The precision motion control of a linear motor drive system is used as a case study to illustrate the proposed NNARC strategy.     

Adaptive Neural Dynamic Surface Control for Stochastic Nonlinear Time‐Delay Systems with Input and Output Constraints

This paper presents an adaptive neural tracking control approach for uncertain stochastic nonlinear time‐delay systems with input and output constraints. Firstly, the dynamic surface control (DSC) technique is incorporated into adaptive neural control framework to overcome the problem of ‘explosion of complexity’ in the control design. By employing a continuous differentiable asymmetric saturation model, the input constraint problem is solved. Secondly, the appropriate Lyapunov‐Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown time‐delay terms, RBF neural network is utilized to identify the unknown systems functions, and barrier Lyapunov functions (BLFs) are designed to avoid the violation of the output constraint. Finally, based on adaptive backstepping technique, an adaptive neural control method is proposed, and it decreases the number of learning parameters. Using Lyapunov stability theory, it is proved that the designed controller can ensure that all the signals in the closed‐loop system are 4‐Moment (or 2 Moment) semi‐globally uniformly ultimately bounded (SGUUB) and the tracking error converges to a small neighborhood of the origin. Two simulation examples are provided to further illustrate the effectiveness of the proposed approach.     

Observer‐based adaptive neural control for a class of nonlinear singular systems

The problem of observer‐based adaptive neural control via output feedback for a class of uncertain nonlinear singular systems is studied in this article. The nonlinear singular systems can be regarded as two subsystems that are coupled with each other: differential subsystem and algebraic subsystem. The differential systems can be nonstrict feedback structures. To guarantee that the singular system is regular and impulse‐free, two new conditions are proposed. By the conditions, the linear controller and observer, which are used to estimate the immeasurable state variables, are obtained. Then, an output feedback scheme through adaptive neural backstepping is proposed to ensure that all states of the closed‐loop system are semiglobally uniformly ultimately bounded and converge to a small neighborhood of the origin. Simulation examples illustrate the effectiveness of the presented method.     

Adaptive neural control for a class of uncertain nonlinear systems with unknown time delay

A neural network (NN)‐based robust adaptive control design scheme is developed for a class of nonlinear systems represented by input–output models with an unknown nonlinear function and unknown time delay. By approximating on‐line the unknown nonlinear functions with a three‐layer feedforward NN, the proposed approach does not require the unknown parameters to satisfy the linear dependence condition. The control law is delay independent and possible controller singularity problem is avoided. It is proved that with the proposed neural control law, all the signals in the closed‐loop system are semiglobally bounded in the presence of unknown time delay and unknown nonlinearity. A simulation example is presented to demonstrate the method. Copyright © 2008 John Wiley & Sons, Ltd.     

NN‐Based Output‐Feedback Control for Stochastic Nonlinear Systems with Unknown Control Directions

This paper addresses the neural network‐based output‐feedback control problem for a class of stochastic nonlinear systems with unknown control directions. The restrictions on the drift and diffusion terms are removed and the conditions on unknown control directions are relaxed. By introducing a proper coordinate transformation, and combining dynamic surface control (DSC) technique with radial basis function neural network (RBF NN) approximation approach, we construct an adaptive output‐feedback controller to guarantee the closed‐loop system to be mean square semi‐globally uniformly ultimately bounded (M‐SGUUB). A simulation example demonstrates the effectiveness of the proposed scheme.     

基于控制性能的MIMO非线性系统动态面控制

针对一类不确定非线性MIMO(multiple-input multiple-output)系统,在动态面控制方法的基础上,提出了自适应跟踪控制方案.通过引入性能函数和输出误差转换,保证输出信号具有指定的跟踪速度、跟踪误差、最大超调量.为了避免控制奇异问题,采用神经网络直接逼近期望控制信号.该方案无需估计神经网络的权值,仅对1个参数进行自适应律设计.理论证明了闭环系统所有信号有界,仿真结果验证了所提方案的有效性.     

Adaptive fault‐tolerant control for a class of output‐constrained nonlinear systems

In this work, by incorporating a tan‐type barrier Lyapunov function into the Lyapunov function design, we present a novel adaptive fault‐tolerant control (FTC) scheme for a class of output‐constrained multi‐input single‐output nonlinear systems with actuator failures under the perturbation of both parametric and nonparametric system uncertainties. We show that under the proposed adaptive FTC scheme, exponential convergence of the output tracking error into a small set around zero is guaranteed, while the constraint requirement on the system output will not be violated during operation. In the end, two illustrative examples are presented to demonstrate the effectiveness of the proposed FTC scheme. Copyright © 2015 John Wiley & Sons, Ltd.     

Neural‐network‐based predictive controller design: An application to temperature control of a plastic injection molding process

This paper presents a neural‐network‐based predictive control (NPC) method for a class of discrete‐time multi‐input multi‐output (MIMO) systems. A discrete‐time mathematical model using a recurrent neural network (RNN) is constructed and a learning algorithm adopting an adaptive learning rate (ALR) approach is employed to identify the unknown parameters in the recurrent neural network model (RNNM). The NPC controller is derived based on a modified predictive performance criterion, and its convergence is guaranteed by adopting an optimal algorithm with an adaptive optimal rate (AOR) approach. The stability analysis of the overall MIMO control system is well proven by the Lyapunov stability theory. A real‐time control algorithm is proposed which has been implemented using a digital signal processor, TMS320C31 from Texas Instruments. Two examples, including the control of a MIMO nonlinear system and the control of a plastic injection molding process, are used to demonstrate the effectiveness of the proposed strategy. Results from both numerical simulations and experiments show that the proposed method is capable of controlling MIMO systems with satisfactory tracking performance under setpoint and load changes. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust Adaptive Neural Network Control For A Class Of Multiple‐Input Multiple‐Output Nonlinear Time Delay System With Hysteresis Inputs And Dynamic Uncertainties

This paper studies an adaptive neural control for nonlinear multiple‐input multiple‐output systems with dynamic uncertainties, hysteresis input, and time delay. The studied systems are composed of N nonlinear time‐delay subsystems and the interconnection terms are contained in every equation of each subsystem. Adaptive neural control algorithms are developed by introducing a well‐defined smooth function. The unknown time‐varying delays and the unmodeled dynamics are dealt with by constructing appropriate Lyapunov–Krasovskii functions and introducing an available dynamic signal. The main advantage of the proposed controllers is that they contain fewer parameter estimates that need to be updated online. Consequently, the accuracy of ultimate tracking errors asymptotically approaches a pre‐defined bound, and all signals in the closed‐loop systems are also ensured to be uniformly ultimately bounded. Finally, a simulation example is provided to illustrate the effectiveness and merits of the proposed adaptive neural network control schemes.     

An RBF neural network-based adaptive control for SISO linearisable nonlinear systems

An RBF neural network-based adaptive control is proposed for Single-Input and Single-Output (SISO) linearisable nonlinear systems in this paper. It is shown that a SISO nonlinear system is first linearised by using the differential geometric approach in the state space, and the linearised nonlinear system is then treated as a partially known system. The known dynamics are used to design a nominal feedback controller to stabilise the nominal system, and an adaptive RBF neural network-based compensator is then designed to compensate for the effects of uncertain dynamics. The main function of the RBF neural network in this work is to adaptively learn the upper bound of the system uncertainty, and the output of the neural network is then used to adaptively adjust the gain of the compensator so that the strong robustness with respect to unknown dynamics can be obtained, and the tracking error between the plant output and the desired reference signal can asymptotically converge to zero. A simulation example is performed in support of the proposed scheme.     

Adaptive tracking H-infinity control for switched nonlinear systems with unknown control gain sign

This paper addresses the adaptive tracking control scheme for switched nonlinear systems with unknown control gain sign. The approach relaxes the hypothesis that the upper bound of function control gain is known constant and the bounds of external disturbance and approximation errors of neural networks are known. RBF neural networks (NNs) are used to approximate unknown functions and an H-infinity controller is introduced to enhance robustness. The adaptive updating laws and the admissible switching signals have been derived from switched multiple Lyapunov function method. It’s proved that the resulting closed loop system is asymptotically Lyapunov stable such that the output tracking error performance and H-infinity disturbance attenuation level are well obtained. Finally, a simulation example of Forced Duffing systems is given to illustrate the effectiveness of the proposed control scheme and improve significantly the transient performance.     

Prescribed performance adaptive neural output feedback dynamic surface control for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics

This paper studies the output feedback tracking control problem for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics using a prescribed performance adaptive neural dynamic surface control design approach. A nonlinear mapping technique is employed to address the state constraints. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions. The unmodeled dynamics is addressed by introducing an available dynamic signal. Subsequently, we construct the controller and parameter adaptive laws using a backstepping technique. Based on Lyapunov stability theory, it is shown that all signals in the closed‐loop system are semiglobally uniformly ultimately bounded and that the tracking error always remains within the prescribed performance bound. Simulation results are presented to demonstrate the effectiveness of the proposed control scheme.     

FPGA‐based adaptive dynamic sliding‐mode neural control for a brushless DC motor

In the adaptive neural control design, since the number of hidden neurons is finite for real‐time applications, the approximation errors introduced by the neural network cannot be inevitable. To ensure the stability of the adaptive neural control system, a switching compensator is designed to dispel the approximation error. However, it will lead to substantial chattering in the control effort. In this paper, an adaptive dynamic sliding‐mode neural control (ADSNC) system composed of a neural controller and a fuzzy compensator is proposed to tackle this problem. The neural controller, using a radial basis function neural network, is the main controller and the fuzzy compensator is designed to eliminate the approximation error introduced by the neural controller. Moreover, a proportional‐integral‐type adaptation learning algorithm is developed based on the Lyapunov function; thus not only the system stability can be guaranteed but also the convergence of the tracking error and controller parameters can speed up. Finally, the proposed ADSNC system is implemented based on a field programmable gate array chip for low‐cost and high‐performance industrial applications and is applied to control a brushless DC (BLDC) motor to show its effectiveness. The experimental results demonstrate the proposed ADSNC scheme can achieve favorable control performance without encountering chattering phenomena. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

带有输出约束条件的随机多智能体系统容错控制

在有向通讯拓扑图下,针对一类具有输出约束和执行器偏差增益故障的非严格反馈随机多智能体系统,提出一种自适应神经网络容错控制设计方案.采用神经网络逼近未知非线性函数,构造障碍李雅普诺夫函数处理系统的输出约束问题,以反步法和动态面技术为框架,结合Nussbaum函数设计自适应神经网络容错控制方法.基于李雅普诺夫稳定性理论,证明所有跟随者输出与领导者输出达到一致,闭环系统的所有信号依概率半全局一致最终有界且系统输出限制在给定紧集内.论文最后通过仿真实验验证所给出控制方案的有效性.     

Prescribed performance adaptive neural output control for a class of switched nonstrict‐feedback nonlinear time‐delay systems: State‐dependent switching law approach

This paper investigates the tracking problem for a class of uncertain switched nonlinear delayed systems with nonstrict‐feedback form. To address this problem, by introducing a new common Lyapunov function (CLF), an adaptive neural network dynamic surface control is proposed. The state‐dependent switching rule is designed to orchestrate which subsystem is active at each time instance. In order to compensate unknown delay terms, an appropriate Lyapunov‐Krasovskii functional is considered in the constructing of the CLF. In addition, a novel switched neural network–based observer is constructed to estimate system states through the output signal. To maintain the tracking error performance within a predefined bound, a prescribed performance bound approach is employed. It is proved that by the proposed output‐feedback control, all the signals of the closed‐loop system are bounded under the switching law. Moreover, the transient and steady‐state tracking performance is guaranteed by the prescribed performance bound. Finally, the effectiveness of the proposed method is illustrated by two numerical and practical examples.     

NEURAL NETWORK‐BASED OPTIMAL ADAPTIVE TRACKING USING GENETIC ALGORITHMS

This paper presents the use of neural networks (NNs) and genetic algorithms (GAs) to enhance the output tracking performance of partly known robotic systems. Two of the most potential approaches of adaptive control, i.e., the concept of variable structure control (VSC) and NN‐based adaptive control, are ingeniously combined using GAs to achieve high‐performance output tracking. GA is used to make the maximum use of different performance characteristics of two self‐adaptive NN modules by finding the switching function which best combines them. The method will be valid for any rigid revolute robot system. Computer simulations on our active binocular head are included for illustration and verification.     

Controller Design Using Walsh‐Basis‐Function Neural Networks

ABSTRACT This paper investigates the function approximation problem by using Walsh functions to establish a Walsh‐basis‐function neural network (WBFNN). The proposed novel system avoids the possible heavy computation problem of a controller usually encountered in adaptive neural controller design. With the developed adaptation scheme combined with the sliding mode control strategy for a class of nonlinear systems, the proposed WBFNN‐based controller can guarantee global stability of the closed‐loop system in the Lyapunov sense. The output tracking error then converges to zero asymptotically, and boundedness of all the signals in the whole system is ensured. Simulation validation for a nonlinear unstable system was performed to verify the effectiveness of the proposed controller design.     

Adaptive neural output feedback tracking control for a class of nonlinear systems

In this paper, an adaptive neural output feedback control scheme based on backstepping technique and dynamic surface control (DSC) approach is developed to solve the tracking control problem for a class of nonlinear systems with unmeasurable states. Firstly, a nonlinear state observer is designed to estimate the unmeasurable states. Secondly, in the controller design process, radial basis function neural networks (RBFNNs) are utilised to approximate the unknown nonlinear functions, and then a novel adaptive neural output feedback tracking control scheme is developed via backstepping technique and DSC approach. It is shown that the proposed controller ensures that all signals of the closed-loop system remain bounded and the tracking error converges to a small neighbourhood around the origin. Finally, two numerical examples and one realistic example are given to illustrate the effectiveness of the proposed design approach.     

Filtering adaptive neural network controller for multivariable nonlinear systems with mismatched uncertainties

This paper synthesizes a filtering adaptive neural network controller for multivariable nonlinear systems with mismatched uncertainties. The multivariable nonlinear systems under consideration have both matched and mismatched uncertainties, which satisfy the semiglobal Lipschitz condition. The nonlinear uncertainties are approximated by a Gaussian radial basis function (GRBF)‐based neural network incorporated with a piecewise constant adaptive law, where the adaptive law will generate adaptive parameters by solving the error dynamics between the real system and the state predictor with the neglection of unknowns. The combination of GRBF‐based neural network and piecewise constant adaptive law relaxes hardware limitations (CPU). A filtering control law is designed to handle the nonlinear uncertainties and deliver a good tracking performance with guaranteed robustness. The matched uncertainties are cancelled directly by adopting their opposite in the control signal, whereas a dynamic inversion of the system is required to eliminate the effect of the mismatched uncertainties on the output. Since the virtual reference system defines the best performance that can be achieved by the closed‐loop system, the uniform performance bounds are derived for the states and control signals via comparison. To validate the theoretical findings, comparisons between the model reference adaptive control method and the proposed filtering adaptive neural network control architecture with the implementation of different sampling time are carried out.     

Neural adaptive prescribed performance control for interconnected nonlinear systems with output dead zone

This paper is concerned with the neural‐based decentralized adaptive control for interconnected nonlinear systems with prescribed performance and unknown dead zone outputs. In the controller design procedure, neural networks are employed to identify unknown auxiliary functions, and the control design obstacle caused by the output nonlinearity is resolved via introducing Nussbaum function. Then, a reliable neural decentralized adaptive control is developed through incorporating the backstepping method and the prescribed performance technique. In the light of Lyapunov stability theory, it is verified that the proposed control scheme can ensure that all the closed‐loop signals are bounded, and can also guarantee that the tracking errors remain within a small enough compact set with the prescribed performance bounds. Finally, some simulation results are given to illustrate the feasibility of the devised control strategy.