On the new method for the control of discrete nonlinear dynamic systems using neural networks

This correspondence points out an incorrect statement in Adetona et al., 2000, and Adetona et al., 2004, about the application of the proposed control law to nonminimum phase systems. A counterexample shows the limitations of the control law and, furthermore, its control capability to nonminimum phase systems is explained.     

Adaptive inverse control of linear and nonlinear systems using dynamic neural networks

In this paper, we see adaptive control as a three-part adaptive-filtering problem. First, the dynamical system we wish to control is modeled using adaptive system-identification techniques. Second, the dynamic response of the system is controlled using an adaptive feedforward controller. No direct feedback is used, except that the system output is monitored and used by an adaptive algorithm to adjust the parameters of the controller. Third, disturbance canceling is performed using an additional adaptive filter. The canceler does not affect system dynamics, but feeds back plant disturbance in a way that minimizes output disturbance power. The techniques work to control minimum-phase or nonminimum-phase, linear or nonlinear, single-input-single-output (SISO) or multiple-input-multiple-ouput (MIMO), stable or stabilized systems. Constraints may additionally be placed on control effort for a practical implementation. Simulation examples are presented to demonstrate that the proposed methods work very well.     

Stable control of nonlinear systems using neural networks

A neural-network-based direct control architecture is presented that achieves output tracking for a class of continuous-time nonlinear plants, for which the nonlinearities are unknown. The controller employs neural networks to perform approximate input/output plant linearization. The network parameters are adapted according to a stability principle. The architecture is based on a modification of a method previously proposed by the authors, where the modification comprises adding a sliding control term to the controller. This modification serves two purposes: first, as suggested by Sanner and Slotine,¹ sliding control compensates for plant uncertainties outside the state region where the networks are used, thus providing global stability; second, the sliding control compensates for inherent network approximation errors, hence improving tracking performance. A complete stability and tracking error convergence proof is given and the setting of the controller parameters is discussed. It is demonstrated that as a result of using sliding control, better use of the network's approximation ability can be achieved, and the asymptotic tracking error can be made dependent only on inherent network approximation errors and the frequency range of unmodelled dynamical modes. Two simulations are provided to demonstrate the features of the control method.     

Identification of nonlinear dynamic systems using functional linkartificial neural networks

We have presented an alternate ANN structure called functional link ANN (FLANN) for nonlinear dynamic system identification using the popular backpropagation algorithm. In contrast to a feedforward ANN structure, i.e., a multilayer perceptron (MLP), the FLANN is basically a single layer structure in which nonlinearity is introduced by enhancing the input pattern with nonlinear functional expansion. With proper choice of functional expansion in a FLANN, this network performs as good as and in some cases even better than the MLP structure for the problem of nonlinear system identification.     

不确定混沌系统的动态神经网络跟踪控制

针对不确定非线性混沌系统，提出了一种基于动态神经网络辨识器的自适应跟踪控制新方法，通过滑模控制技术在线调整动态神经网络辨识器权值，并在获取动态神经网络模型的基础上设计出优化控制器，实现混沌系统的轨道跟踪，对辨识误差和轨道跟踪误差进行分析并证明了它们的有界性，Lorenz混沌系统的仿真实验结果表明了控制策略的有效性。     

On the modelling of nonlinear dynamic systems using support vector neural networks

Though neural networks have the ability to approximate nonlinear functions with arbitrary accuracy, good generalization results are obtained only if the structure of the network is suitably chosen. Therefore, selecting the ‘best’ structure of the neural networks is an important problem. Support vector neural networks (SVNN) are proposed in this paper, which can provide a solution to this problem. The structure of the SVNN is obtained by a constrained minimization for a given error bound similar to that in the support vector regression (SVR). After the structure is selected, its weights are computed by the linear least squares method, as it is a linear-in-weight network. Consequently, in contrast to the SVR, the output of the SVNN is unbiased. It is further shown here that the variance of the modelling error of the SVNN is bounded by the square of the given error bound in selecting its structure, and is smaller than that of the SVR. The performance of the SVNN is illustrated by a simulation example involving a benchmark nonlinear system.     

Adaptive L2 control of nonlinear systems using neural networks

An adaptive neural network controller is developed to achieve output-tracking of a class of nonlinear systems. The global L2 stability of the closed-loop system is established. The proposed control design overcomes the limitation of the conventional adaptive neural control design where the modeling error brought by neural networks is assumed to be bounded over a compact set.Moreover,the generalized matching conditions are also relaxed in the proposed L2 control design as the gains for the external disturbances entering the system are allowed to have unknown upper bounds.     

非线性系统神经网络自适应控制的发展现状及展望

简要回顾了神经网络控制及其应用的发展历程,重点论述了人们在连续、离散时间非线性系统的神经网络以及神经模糊稳定自适应控制研究方面所取得的主要进展,探讨了神经网络自适应控制研究方面存在的主要问题及解决问题的基本途径.作为当前解决神经网络自适应控制问题的途径之一,介绍了近来人们对二阶模糊神经网络以及量子神经网络的研究.最后,总结并指出了这一领域下一步的发展方向和有待解决的新课题.     

Identification of linear and nonlinear dynamic systems using recurrent neural networks

This paper describes the use of Elman-type recurrent neural networks to identify dynamic systems. Networks as originally designed by Elman (Cognitive Sci., 1990, 14, 179–211) and also those in which self-connections are made to the context units were employed to identify a variety of linear and nonlinear systems. It was found that the latter networks were more versatile than the basic Elman nets in being able to model the dynamic behaviour of high order linear and nonlinear systems.     

Adaptive L_2 control of nonlinear systems using neural networks

An adaptive neural network controller is developed to achieve output-tracking of a class of nonlinear systems. The global L2 stability of the closed-loop system is established. The proposed control design overcomes the limitation of the conventional adaptive neural control design where the modeling error brought by neural networks is assumed to be bounded over a compact set. Moreover,the generalized matching conditions are also relaxed in the proposed L2 control design as the gains for the external disturbances entering the system are allowed to have unknown upper bounds.     

Decentralized adaptive control of nonlinear systems using radialbasis neural networks

Stable direct and indirect decentralized adaptive radial basis neural network controllers are presented for a class of interconnected nonlinear systems. The feedback and adaptation mechanisms for each subsystem depend only upon local measurements to provide asymptotic tracking of a reference trajectory. Due to the functional approximation capabilities of radial basis neural networks, the dynamics for each subsystem are not required to be linear in a set of unknown coefficients as is typically required in decentralized adaptive schemes. In addition, each subsystem is able to adaptively compensate for disturbances and interconnections with unknown bounds     

Robust and adaptive backstepping control for nonlinear systems using RBF neural networks

In this paper, two different backstepping neural network (NN) control approaches are presented for a class of affine nonlinear systems in the strict-feedback form with unknown nonlinearities. By a special design scheme, the controller singularity problem is avoided perfectly in both approaches. Furthermore, the closed loop signals are guaranteed to be semiglobally uniformly ultimately bounded and the outputs of the system are proved to converge to a small neighborhood of the desired trajectory. The control performances of the closed-loop systems can be shaped as desired by suitably choosing the design parameters. Simulation results obtained demonstrate the effectiveness of the approaches proposed. The differences observed between the inputs of the two controllers are analyzed briefly.     

Robot discrete adaptive control based on dynamic inversion using dynamical neural networks

A stable discrete time adaptive control approach using dynamic neural networks (DNNs) is developed in this paper for the trajectory tracking of a robotic manipulator with unknown nonlinear dynamics. By using dynamic inversion constructed by a DNN, the assumption under which the system state should be on a compact set can be removed. This assumption is usually required in neuro-adaptive control. The NN-based variable structure control is designed to guarantee the stability and improve the dynamic performance of the closed-loop system. The proposed control scheme ensures the global stability and desired tracking as well.     

Diagonal recurrent neural networks for dynamic systems control

A new neural paradigm called diagonal recurrent neural network (DRNN) is presented. The architecture of DRNN is a modified model of the fully connected recurrent neural network with one hidden layer, and the hidden layer comprises self-recurrent neurons. Two DRNN's are utilized in a control system, one as an identifier called diagonal recurrent neuroidentifier (DRNI) and the other as a controller called diagonal recurrent neurocontroller (DRNC). A controlled plant is identified by the DRNI, which then provides the sensitivity information of the plant to the DRNC. A generalized dynamic backpropagation algorithm (DBP) is developed and used to train both DRNC and DRNI. Due to the recurrence, the DRNN can capture the dynamic behavior of a system. To guarantee convergence and for faster learning, an approach that uses adaptive learning rates is developed by introducing a Lyapunov function. Convergence theorems for the adaptive backpropagation algorithms are developed for both DRNI and DRNC. The proposed DRNN paradigm is applied to numerical problems and the simulation results are included.     

A novel adaptive control design method for stochastic nonlinear systems using neural network

This paper presents a novel method for designing an adaptive control system using radial basis function neural network. The method is capable of dealing with nonlinear stochastic systems in strict-feedback form with any unknown dynamics. The proposed neural network allows the method not only to approximate any unknown dynamic of stochastic nonlinear systems, but also to compensate actuator nonlinearity. By employing dynamic surface control method, a common problem that intrinsically exists in the back-stepping design, called “explosion of complexity”, is resolved. The proposed method is applied to the control systems comprising various types of the actuator nonlinearities such as Prandtl–Ishlinskii (PI) hysteresis, and dead-zone nonlinearity. The performance of the proposed method is compared to two different baseline methods: a direct form of backstepping method, and an adaptation of the proposed method, named APIC-DSC, in which the neural network is not contributed in compensating the actuator nonlinearity. It is observed that the proposed method improves the failure-free tracking performance in terms of the Integrated Mean Square Error (IMSE) by 25%/11% as compared to the backstepping/APIC-DSC method. This depression in IMSE is further improved by 76%/38% and 32%/49%, when it comes with the actuator nonlinearity of PI hysteresis and dead-zone, respectively. The proposed method also demands shorter adaptation period compared with the baseline methods.

     

Robust output feedback control of nonlinear stochastic systems using neural networks

We present an adaptive output feedback controller for a class of uncertain stochastic nonlinear systems. The plant dynamics is represented as a nominal linear system plus nonlinearities. In turn, these nonlinearities are decomposed into a part, obtained as the best approximation given by neural networks, plus a remaining part which is treated as uncertainties, modeling approximation errors, and neglected dynamics. The weights of the neural network are tuned adaptively by a Lyapunov design. The proposed controller is obtained through robust optimal design and combines together parameter projection, control saturation, and high-gain observers. High performances are obtained in terms of large errors tolerance as shown through simulations.     

Non-affine nonlinear adaptive control of decentralized large-scale systems using neural networks

This paper introduces a new decentralized adaptive neural network controller for a class of large-scale nonlinear systems with unknown non-affine subsystems and unknown interconnections represented by nonlinear functions. A radial basis function neural network is used to represent the controller’s structure. The stability of the closed loop system is guaranteed through Lyapunov stability analysis. The effectiveness of the proposed decentralized adaptive controller is illustrated by considering two nonlinear systems: a two-inverted pendulum and a turbo generator. The simulation results verify the merits of the proposed controller.     

Direct adaptive control for a class of MIMO nonlinear systems using neural networks

In this note, direct adaptive neural network (NN) control is studied for a class of multiple-input-multiple-output nonlinear systems based on input-output discrete-time model with unknown interconnections between subsystems. By finding an orthogonal matrix to tune the NN weights, the closed-loop system is proven to be semiglobally uniformly ultimately bounded. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters.     

Indirect adaptive control of nonlinear dynamic systems using self recurrent wavelet neural networks via adaptive learning rates

This paper proposes an indirect adaptive control method using self recurrent wavelet neural networks (SRWNNs) for dynamic systems. The architecture of the SRWNN is a modified model of the wavelet neural network (WNN). However, unlike the WNN, since a mother wavelet layer of the SRWNN is composed of self-feedback neurons, the SRWNN can store the past information of wavelets. In the proposed control architecture, two SRWNNs are used as both an identifier and a controller. The SRWNN identifier approximates dynamic systems and provides the SRWNN controller with information about the system sensitivity. The gradient-descent method using adaptive learning rates (ALRs) is applied to train all weights of the SRWNN. The ALRs are derived from discrete Lyapunov stability theorem, which are applied to guarantee the convergence of the proposed control system. Finally, we perform some simulations to verify the effectiveness of the proposed control scheme.     

A new method for control of nonlinear networked systems

Networked control of a class of nonlinear systems is considered. For this purpose, the previously proposed variable selective control (VSC) methodology is extended to the nonlinear systems. This extension is based upon the decomposition of the nonlinear system to a set fuzzy-blended locally linearized subsystems, and further application of the VSC methodology to each subsystem. Using the idea of parallel distributed compensation (PDC) method, the closed-loop stability of the overall networked system is guaranteed, using new linear matrix inequalities (LMIs). For the real-time implementation, real-time control signals are constructed for every entry of pre-specified vector of time delays, which is selected based on the presumed upper-bound of the network time delay. Similar to the traditional packet-base control methodology, such control signals are then packed as a control-side packet and transmitted back to a time delay compensator (TDC) located on the plant-side of the network. According to the most recent network time delay, the TDC selects just one entry of the control vector and applies it to the actuator through a zero order hold element. A sufficient condition for closed-loop asymptotic stability is determined. Simulation studies on nonlinear benchmark problems demonstrate the effectiveness of the proposed method.