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.     

Identification of nonlinear dynamical systems using multilayered neural networks

A novel multilayer discrete-time neural net paradigm is presented for the identification of multi-input multi-output (MIMO) nonlinear dynamical systems. The major novelty of this approach is a rigorous proof of identification error convergence that reveals a requirement for a new identifier structure and nonstandard weight tuning algorithms. The NN identifier includes modified delta rule weight tuning and exhibits a learning-while-functioning feature instead of learning-then-functioning, so that the identification is on-line with no explicit off-line learning phase needed. The structure of the neural net (NN) identifier is derived using a passivity aproach. Linearity in the parameters is not required and certainty equivalence is not used. The notion of persistency of excitation (PE) and passivity properties of the multilayer NN are defined and used in the convergence analysis of both the identification error and the weight estimates.     

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 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.     

Stabilization of unknown nonlinear systems using neural networks

This paper deals with stabilization of unknown nonlinear systems using a nonlinear controller made with a backpropagation neural network. Control strategies based on an inverse state neural model built from an off-line learning step are proposed. The proposed strategies can be implemented following two approaches. The first one consists on computing control horizon based on actual state vector and desired one at a future instant. The second approach applies control action in the sense of a receding horizon. Adaptive control has been considered where the updating of the neural controller is accomplished to optimize different control objectives.     

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.     

Disturbance rejection in nonlinear systems using neural networks

Neural networks with different architectures have been successfully used for the identification and control of a wide class of nonlinear systems. The problem of rejection of input disturbances, when such networks are used in practical problems is considered. A large class of disturbances, which can be modeled as the outputs of unforced linear or nonlinear dynamic systems, is treated. The objective is to determine the identification model and the control law to minimize the effect of the disturbance at the output. In all cases, the method used involves expansion of the state space of the disturbance-free plant in an attempt to eliminate the effect of the disturbance. Several stages of increasing complexity of the problem are discussed in detail. Theoretical justification is provided for the existence of solutions to the problem of complete rejection of the disturbance in special cases. This provides the rationale for using similar techniques in situations where such theoretical analysis is not available.     

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

A new controller design method for nonaffine nonlinear dynamic systems is presented in this paper. An identified neural network model of the nonlinear plant is used in the proposed method. The method is based on a new control law that is developed for any discrete deterministic time-invariant nonlinear dynamic system in a subregion Psi(x), of an asymptotically stable equilibrium point of the plant. The performance of the control law is not necessarily dependent on the distance between the current state of the plant and the equilibrium state if the nonlinear dynamic system satisfies some mild requirements in Psi(x). The control law is simple to implement and is based on a novel linearization of the input-output model of the plant at each instant in time. It can be used to control both minimum phase and nonminimum phase nonaffine nonlinear plants. Extensive empirical studies have confirmed that the control law can be used to control a relatively general class of highly nonlinear multiinput-multioutput (MIMO) plants.     

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.     

基于回归神经网络的非线性时变系统辨识

为克服基于前馈神经网络的非线性系统辨识算法存在需预先估计系统输入输出滞后阶数的缺陷，提出一种基于回归神经网络的非线性时变系统的辨识算法，针对现有的回归网络学习算法大多采用梯度算法，收敛速度缓慢问题，提出一种具有快速收敛性的扩展卡尔曼滤波学习算法，大大提高了学习收敛速度，并推导了一种基于单个神经元的局部化算法，减少了计算量，仿真实例证明，所提出的算法是有效的。     

Nonlinear systems identification using dynamic multi-time scale neural networks

In this paper, two Neural Network (NN) identifiers are proposed for nonlinear systems identification via dynamic neural networks with different time scales including both fast and slow phenomena. The first NN identifier uses the output signals from the actual system for the system identification. The on-line update laws for dynamic neural networks have been developed using the Lyapunov function and singularly perturbed techniques. In the second NN identifier, all the output signals from nonlinear system are replaced with the state variables of the neuron networks. The on-line identification algorithm with dead-zone function is proposed to improve nonlinear system identification performance. Compared with other dynamic neural network identification methods, the proposed identification methods exhibit improved identification performance. Three examples are given to demonstrate the effectiveness of the theoretical results.     

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     

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.     

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.     

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.     

Control of dynamic systems using fuzzy logic and neural networks

The use of artificial neural network is proposed for high-speed processing of rules in fuzzy logic controller (FLC). the logic element of an FLC is replaced by a single hidden layer feedforward network. the input and output fuzzy subsets are expressed it of numerical patterns. the network is trained using the back-propagation algori to establish fuzzy associations between the input and output fuzzy subsets. the inference mechanism of the network is compared with that of compositional law of inference. In the proposed implementation of FLC, all the rules are processed in paralle. This implementation has potential for high-speed processing of rules if the network is realized in hardware. the use of neural networks in fuzzy logic self-organizing is also ivestigated. © 1993 John Wiley & Sons, Inc.     

Identification of nonlinear systems with outliers using wavelet neural networks based on annealing dynamical learning algorithm

This paper presents an annealing dynamical learning algorithm (ADLA) to train wavelet neural networks (WNNs) for identifying nonlinear systems with outliers. In ADLA–WNNs, wavelet-based support vector regression (WSVR) is adopted to determine the initial translation and dilation of a wavelet kernel and the weights of WNNs due to the similarity between WSVR and WNNs. After initialization, ADLA with nonlinear time-varying learning rates is applied to train the WNNs. In the ADLA, the determination of the learning rates would be a key work for the trade-off between stability and speed of convergence. A computationally efficient optimization method, particle swarm optimization (PSO), is adopted to find the optimal learning rates to overcome the stagnation in the training procedure of WNNs. Due to the advantages of WSVR and ADLA (WSVR–ADLA), the WSVR-based ADLA–WNNs (WSVR–ADLA–WNNs) can robust against outliers and achieve the promising efficiency of system identifications. Three examples are simulated to confirm the performance of the proposed algorithm. From the simulated results, the feasibility and superiority of the proposed WSVR–ADLA–WNNs for identifying nonlinear systems with artificial outliers are verified.     

非线性动态系统的Wiener神经网络辨识法

提出了一种新的Wiener神经网络结构并将其应用于非线性动态系统辨识问题.首先,用Wiener模型对非线性动态系统进行描述,将其分解成线性动态子环节串接非线性静态增益的形式.其次,设计一种新型的神经网络结构,使网络权值对应于相应的Wiener模型参数;并推导了基于反向传播的网络权值调整方法.最后,通过网络迭代训练,可同时得到线性动态子环节和非线性静态增益的模型参数.通过一个Wiener模型的数值仿真来验证方法的有效性,仿真结果表明所提辨识方法切实可行.     

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。     

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.