Delayed standard neural network models for control systems.

In order to conveniently analyze the stability of recurrent neural networks (RNNs) and successfully synthesize the controllers for nonlinear systems, similar to the nominal model in linear robust control theory, the novel neural network model, named delayed standard neural network model (DSNNM) is presented, which is the interconnection of a linear dynamic system and a bounded static delayed (or nondelayed) nonlinear operator. By combining a number of different Lyapunov functionals with S-procedure, some useful criteria of global asymptotic stability and global exponential stability for the continuous-time DSNNMs (CDSNNMs) and discrete-time DSNNMs (DDSNNMs) are derived, whose conditions are formulated as linear matrix inequalities (LMIs). Based on the stability analysis, some state-feedback control laws for the DSNNM with input and output are designed to stabilize the closed-loop systems. Most RNNs and neurocontrol nonlinear systems with (or without) time delays can be transformed into the DSNNMs to be stability-analyzed or stabilization-synthesized in a unified way. In this paper, the DSNNMs are applied to analyzing the stability of the continuous-time and discrete-time RNNs with or without time delays, and synthesizing the state-feedback controllers for the chaotic neural-network-system and discrete-time nonlinear system. It turns out that the DSNNM makes the stability conditions of the RNNs easily verified, and provides a new idea for the synthesis of the controllers for the nonlinear systems.     

Unified stabilizing controller synthesis approach for discrete-time intelligent systems with time delays by dynamic output feedback

A novel model, termed the standard neural network model (SNNM), is advanced to describe some delayed (or non-delayed) discrete-time intelligent systems com- posed of neural networks and Takagi and Sugeno (T-S) fuzzy models. The SNNM is composed of a discrete-time linear dynamic system and a bounded static nonlinear operator. Based on the global asymptotic stability analysis of the SNNMs, linear and nonlinear dynamic output feedback controllers are designed for the SNNMs to stabilize the closed-loop systems, respectively. The control design equations are shown to be a set of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms to determine the control signals. Most neural-network-based (or fuzzy) discrete-time intelligent systems with time delays or without time delays can be transformed into the SNNMs for controller synthesis in a unified way. Three application examples show that the SNNMs not only make controller synthesis of neural-network-based (or fuzzy) discrete-time intelligent systems much easier, but also provide a new approach to the synthesis of the controllers for the other type of nonlinear systems.     

Stability analysis of discrete-time recurrent neural networks based on standard neural network models

In order to conveniently analyze the stability of various discrete-time recurrent neural networks (RNNs), including bidirectional associative memory, Hopfield, cellular neural network, Cohen-Grossberg neural network, and recurrent multiplayer perceptrons, etc., the novel neural network model, named standard neural network model (SNNM) is advanced to describe this class of discrete-time RNNs. The SNNM is the interconnection of a linear dynamic system and a bounded static nonlinear operator. By combining Lyapunov functional with S-Procedure, some useful criteria of global asymptotic stability for the discrete-time SNNMs are derived, whose conditions are formulated as linear matrix inequalities. Most delayed (or non-delayed) RNNs can be transformed into the SNNMs to be stability analyzed in a unified way. Some application examples of the SNNMs to the stability analysis of the discrete-time RNNs shows that the SNNMs make the stability conditions of the RNNs easily verified.     

时滞标准神经网络模型及其应用

提出一种新的神经网络模型---时滞标准神经网络模型(DSNNM),它由线性动力学系统和有界静态时滞非线性算子连接而成.利用不同的Lyapunov泛函和S方法推导出DSNNM全局渐近稳定性和全局指数稳定性的充分条件,这些条件可表示为线性不等式(LMI)形式.大多数时滞(或非时滞)动态神经网络(DANN)稳定性分析或神经网络控制系统都可以转化为DSNNM,以便用统一的方法进行稳定性分析或镇定控制.从DSNNM应用于时滞联想记忆(BAM)神经网络的稳定性分析以及PH中和过程神经控制器的综合实例,可以看出,得到的稳定性判据扩展并改进了以往文献中的稳定性定理,而且可将稳定性分析推广到非线性控制系统的综合.     

Stability analysis of discrete-time recurrent neural networks

We address the problem of global Lyapunov stability of discrete-time recurrent neural networks (RNNs) in the unforced (unperturbed) setting. It is assumed that network weights are fixed to some values, for example, those attained after training. Based on classical results of the theory of absolute stability, we propose a new approach for the stability analysis of RNNs with sector-type monotone nonlinearities and nonzero biases. We devise a simple state-space transformation to convert the original RNN equations to a form suitable for our stability analysis. We then present appropriate linear matrix inequalities (LMIs) to be solved to determine whether the system under study is globally exponentially stable. Unlike previous treatments, our approach readily permits one to account for non-zero biases usually present in RNNs for improved approximation capabilities. We show how recent results of others on the stability analysis of RNNs can be interpreted as special cases within our approach. We illustrate how to use our approach with examples. Though illustrated on the stability analysis of recurrent multilayer perceptrons, the approach proposed can also be applied to other forms of time-lagged RNNs.     

Stability Analysis of Discrete-Time Recurrent Neural Networks With Stochastic Delay

This paper is concerned with the stability analysis of discrete-time recurrent neural networks (RNNs) with time delays as random variables drawn from some probability distribution. By introducing the variation probability of the time delay, a common delayed discrete-time RNN system is transformed into one with stochastic parameters. Improved conditions for the mean square stability of these systems are obtained by employing new Lyapunov functions and novel techniques are used to achieve delay dependence. The merit of the proposed conditions lies in its reduced conservatism, which is made possible by considering not only the range of the time delays, but also the variation probability distribution. A numerical example is provided to show the advantages of the proposed conditions.      

Delay-dependent robust stability analysis for interval linear time-variant systems with delays and application to delayed neural networks

Some delay-dependent robust asymptotical stability criteria for uncertain linear time-variant systems with multiple delays are established by means of parameterized first-order model transformation and the transformation of the interval uncertainty into the norm-bounded uncertainty. The stable regions with respect to the delay parameters are also formulated. Based on these results, we investigate the stability issue of a class of delayed neural networks that can be transformed into linear time-variant systems, and then several new global asymptotical stability criteria are exploited. Numerical examples are presented to illustrate the effectiveness of our results.     

Robustly Exponential Stability Analysis for Discrete-Time Stochastic Neural Networks with Interval Time-Varying Delays

This paper deals with the problems of the global exponential stability and stabilization for a class of uncertain discrete-time stochastic neural networks with interval time-varying delay. By using the linear matrix inequality method and the free-weighting matrix technique, we construct a new Lyapunov–Krasovskii functional and establish new sufficient conditions to guarantee that the uncertain discrete-time stochastic neural networks with interval time-varying delay are globally exponential stable in the mean square. Furthermore, we extend our consideration to the stabilization problem for a class of discrete-time stochastic neural networks. Based on the state feedback control law, some novel delay-dependent criteria of the robust exponential stabilization for a class of discrete-time stochastic neural networks with interval time-varying delay are established. The controller gains are designed to ensure the global robust exponential stability of the closed-loop systems. Finally, numerical examples illustrate the effectiveness of the theoretical results we have obtained.     

Stable adaptive neurocontrol for nonlinear discrete-time systems

This paper presents a novel approach in designing neural network based adaptive controllers for a class of nonlinear discrete-time systems. This type of controllers has its simplicity in parallelism to linear generalized minimum variance (GMV) controller design and efficiency to deal with complex nonlinear dynamics. A recurrent neural network is introduced as a bridge to compensation simplify controller design procedure and efficiently to deal with nonlinearity. The network weight adaptation law is derived from Lyapunov stability analysis and the connection between convergence of the network weight and the reconstruction error of the network is established. A theorem is presented for the conditions of the stability of the closed-loop systems. Two simulation examples are provided to demonstrate the efficiency of the approach.     

Global exponential stability of neural networks with discrete and distributed delays and general activation functions on time scales

By employing time scale calculus theory, free weighting matrix method and linear matrix inequality (LMI) approach, several delay-dependent sufficient conditions are obtained to ensure the existence, uniqueness and global exponential stability of the equilibrium point for the neural networks with both infinite distributed delays and general activation functions on time scales. Both continuous-time and discrete-time neural networks are described under the same framework by the reported method. Illustrated numerical examples are given to show the effectiveness of the theoretical analysis. It is noteworthy that the activation functions are assumed to be neither bounded nor monotone.     

A Global Asymptotic Stability Result for a Class of Totally Asynchronous Discrete Nonlinear Systems

This paper proves a global stability result for a class of nonlinear discrete-time systems that are subject to regular desynchronization, also known as total asynchronism. The class of systems studied has its origins in a discrete-time neural net model. The techniques used are of interest in terms of the use of a Lyapunov function for the study of convergence of asynchronous nonlinear dynamical systems and also in terms of applications to neural networks. In the latter context, the main result of this paper strengthens a result of an earlier paper on neural networks, and shows that a class of discrete-time continuous-valued neural nets of the Hopfield type displays global convergence properties even when there exists total asynchronism in the updating of neuron states. Date received: May 2, 1995. Date revised: October 19, 1998.     

Stability analysis for recurrent neural networks with time-varying delay

This paper is concerned with the stability analysis for static recurrent neural networks （RNNs） with time-varying delay. By Lyapunov functional method and linear matrix inequality technique, some new delay-dependent conditions are established to ensure the asymptotic stability of the neural network. Expressed in linear matrix inequalities （LMIs）, the proposed delay-dependent stability conditions can be checked using the recently developed algorithms. A numerical example is given to show that the obtained conditions can provide less conservative results than some existing ones.     

递归多层感知器的稳定性分析——LMI方法

递归多层感知器(RMLP)在工程上应用比较多,但对其稳定性的研究还比较少.本文提出一种新的神经网络模型———标准神经网络模型(SNNM),通过状态空间扩展法,将RMLP转化为SNNM,而SNNM的稳定性分析可转化为一组线性矩阵不等式(LMI)的求解,利用Matlab/LMIToolbox求解LMI,从而判定RMLP的Lyapunov稳定性,并考虑非零阈值对稳定性的影响.该方法也适用于其他类型的递归神经网络(RNN)的稳定性分析.     

Bounds of the induced norm and model reduction errors for systemswith repeated scalar nonlinearities

The class of nonlinear systems described by a discrete-time state equation containing a repeated scalar nonlinearity as in recurrent neural networks is considered. Sufficient conditions are derived for the stability and induced norm of such systems using positive definite diagonally dominant Lyapunov functions or storage functions, satisfying appropriate linear matrix inequalities. Results are also presented for model reduction errors for such systems     

Hybrid feedback laws for a class of cascade nonlinear controlsystems

A stabilization problem for a class of nonlinear control systems is considered. Systems in this class can be viewed as a cascade connection of a linear time-invariant subsystem, a nonlinear time-periodic static subsystem, and an integrator. Hybrid logic-based feedback controllers are constructed to globally stabilize these systems to the origin. The controllers operate by switching between various time-periodic control functions at discrete-time instants. As specific applications, we consider stabilization of nonholonomic control systems in power form to the origin and stabilization of trajectories for a class of nonlinear control systems. Numerical examples of global stabilization and tracking are reported     

Stabilization and performance synthesis for systems with repeatedscalar nonlinearities

The class of nonlinear systems described by a discrete-time state-equation containing a repeated scalar nonlinearity as in recurrent neural networks is considered. Given a plant of this form, sufficient conditions are derived for: 1) the parametrization of all controllers of the same form such that the closed loop is stable in the sense of a diagonally dominant Lyapunov function; and (2) the synthesis of a controller of the same form so that the induced norm of the closed loop is under a prescribed level. Several of these conditions can be written into linear matrix inequalities     

Robust stability analysis for uncertain recurrent neural networks with leakage delay based on delay-partitioning approach

This paper focuses on the issue of robust stability analysis for recurrent neural networks (RNNs) with leakage delay. By constructing a novel Lyapunov–Krasovskii functional together with the reciprocally convex approach and the free-weighting matrix technique, some less conservative stability criteria in terms of linear matrix inequalities for RNNs are derived. The new contribution of this paper is that a novel delay-partitioning method is proposed, and some new zero equalities are introduced. Finally, several examples are given to demonstrate the effectiveness of the proposed methods. The simulated results reveal that the leakage delay has great influence on the dynamical systems, and it cannot be neglected.

     

Adaptive synchronization of the complex dynamical network with double non-delayed and double delayed coupling

To simulate more realistic networks, we introduce a complex dynamical network model with double non-delayed and double delayed coupling and further investigate its synchronization phenomenon in this paper. Based on Lyapunov stability theory, adaptive synchronization criteria is obtained. Analytical result shows that under the designed adaptive controllers, the complex dynamical network with double non-delayed and double delayed coupling can asymptotically synchronize to a given trajectory. What is more, the coupling matrix is not assumed to be symmetric or irreducible. Finally, simulation results show the method is effective.     

基于神经网络与多模型的非线性自适应广义预测解耦控制

针对一类非线性多变量离散时间动态系统,提出了基于神经网络与多模型的非线性自适应广义预测解耦控制方法.该控制方法由线性鲁棒广义预测解耦控制器和神经网络非线性广义预测解耦控制器以及切换机构组成.线性鲁棒广义预测解耦控制器用于保证闭环系统输入输出信号有界,神经网络非线性广义预测解耦控制器能够改善系统性能.切换策略通过对上述两种控制器的切换,保证系统稳定的同时,改善系统性能.同时本文给出了所提自适应解耦控制方法的稳定性和收敛性分析.最后,通过仿真实例验证了该方法的有效性.