具有时变时滞的递归神经网络的渐近稳定性分析

当神经网络应用于最优化计算时,理想的情形是只有一个全局渐近稳定的平衡点,并且以指数速度趋近于平衡点,从而减少神经网络所需计算时间.研究了带时变时滞的递归神经网络的全局渐近稳定性.首先将要研究的模型转化为描述系统模型,然后利用Lyapunov-Krasovskii稳定性定理、线性矩阵不等式(LMI)技术、S过程和代数不等式方法,得到了确保时变时滞递归神经网络渐近稳定性的新的充分条件,并将它应用于常时滞神经网络和时滞细胞神经网络模型,分别得到了相应的全局渐近稳定性条件.理论分析和数值模拟显示,所得结果为时滞递归神经网络提供了新的稳定性判定准则.     

一类带有时延的非线性网络控制系统可靠模糊控制

研究了带有状态时延及执行器故障的非线性网络控制系统的可靠模糊控制问题. 利用输入时延方法, 将带有网络诱导时延和数据包丢失的非线性网络控制系统等价的转化为具有时变时延的Takagi-Sugeno(T-S)模糊系统. 时延对象的状态信息, 采用时滞分解方法, 得以充分的考虑. 并利用锥补线性化迭代算法, 将非凸的稳定性条件转化成可行的线性矩阵不等式(LMI)的形式. 文中将更紧的界处理方法(相互凸组合技术)与不相关增广矩阵项引入到Lyapunov函数的处理当中, 获得保守性更小的稳定性条件. 数值算例验证了该方法的有效性.     

飞行器自适应神经网络时滞控制

在飞行器稳定性控制问题的研究中,针对含有外部扰动、参数不确定性、状态和控制时滞的非线性飞行器系统,提出了一种时滞状态反馈控制与神经网络自适应估计相结合的方法.对非线性系统线性化处理得到飞行器线性模型,并由线性矩阵不等式(LMI)设计反馈控制律;采用径向基函数(RBF)神经网络自适应在线估计策略,对反馈控制律进行补偿以消除未知非线性影响;采用Lyapunov稳定性理论证明了在所设计控制律作用下,闭环系统渐近稳定同时满足H∞性能指标.仿真结果验证了上述方法的可行性及有效性.     

基于T-S模糊模型非线性网络控制系统改进H∞跟踪控制

研究一类非线性网络控制系统改进H∞跟踪控制问题, 该类网络控制系统中非线性被控对象和被跟踪对象分别采用Takagi-Sugeno(T-S)模糊模型和线性稳定参考模型描述. 首先通过综合考虑网络中的数据传输时滞和数据丢包影响, 采用输入时滞法和并行分布补偿技术, 建立基于零阶保持器刷新时刻的系统状态跟踪误差模型. 然后利用改进的自由权矩阵方法, 并结合Lyapunov直接法给出系统满足H∞跟踪性能的充分条件以及模糊控制器的设计方法. 最后仿真实例表明本文方法的有效性和相比已有方法的优越性.     

基于 M 矩阵理论的时滞细胞神经网络稳定性分析*

研究了时滞细胞神经网络的稳定性问题。通过M‐矩阵理论及其判定引理,运用适当的线性参数变换,推导出时滞细胞神经网络的稳定性条件,相比常用的Lyapunov方法,论文为研究多时滞细胞神经网络的稳定性提供了一个更为简单的新方法,降低了原有结论的保守性,进一步推导完善了全局渐近稳定平衡点为原点时的充分条件。仿真实例证明了文章提供的方法有效可行。     

基于LMI方法的时滞细胞神经网络稳定性分析

神经网络是一个复杂的大规模非线性系统，而时滞神经网络的动态行为更为丰富和复杂．现有的研究时滞神经网络稳定性的方法中最为流行的是Lyapunov方法．它把稳定性问题变为某些适当地定义在系统轨迹上的泛函，通过这些泛函相应的稳定性条件就可以获得．该文得到了时滞细胞神经网络渐近稳定性的一些充分条件．作者利用了泛函微分方程的Lyapunov—Krasovskii稳定性理论和线性矩阵不等式(LMI)方法，精炼和推广了一些已有的结果．它们比目前文献报道的结果更少保守．该文还给出了确定时滞细胞神经网络稳定性更多的判定准则．     

一种基于神经网络的数据驱动参数整定法

针对难以建立较准确数学模型的非线性被控对象,提出了一种基于神经网络的数据驱动控制器参数整定法.其设计思想是结合虚拟目标值和神经网络,跳过被控对象,直接得到控制器.此外,利用李亚普诺夫理论证明了神经网络的学习速率在一定范围内可以保证控制器的跟踪误差收敛,并且利用虚拟参考反馈整定(VRFT)算法中的滤波器,结合泰勒展开式,进一步验证了闭环控制系统的稳定性.仿真表明,该方法具有计算负担小,采用数据量少,调节参数方便,强跟踪性等优点.     

时滞Hopfield神经网络的随机稳定性分析

T-S模型提供了一种通过模糊集和模糊推理将复杂的非线性系统表示为线性子模型的方法。研究了时滞Hopfield神经网络的随机稳定性（SFVDHNNs）。首先描述了SFVDHNNs模型,然后用Lyapunov方法研究了SFVDHNNs全局均方指数稳定性,通过可以被一些标准的数值分析方法求解的线性矩阵不等式（LMIs）得出了稳定性标准。     

二次规划问题的变时滞神经网络模型的全局指数稳定

研究等式约束下二次规划问题最优解神经网络模型的稳定性,提出一种变时滞Lagrange神经网络求解方法.利用线性矩阵不等式(LMI)技术,得到两个变时滞神经网络模型全局指数稳定的条件.分析表明,此稳定判据能够适应慢变时滞和快变时滞两种情况,具有适用范围宽、保守性小且易于验证等特点.数值仿真结果验证了所提方法的有效性.     

基于神经网络滑模的智能车辆横向控制

以智能车辆为研究对象,针对车辆模型存在高度非线性动态特性、参数不确定性以及行驶时受外部干扰较多导致控制精度不高、鲁棒性差等问题,提出了采用径向基函数(RBF)神经网络滑模控制方法.建立2自由度线性车辆模型和自由度非线性整车模型,在传统2自由度车辆控制模型状态方程的基础上推导出新的状态方程并以此设计了相应控制器.利用李雅普诺夫(Lyapunov)稳定性理论推导出神经网络的权,并证明控制系统的稳定性.仿真结果表明:与传统的滑模控制方法相比,该方法控制精度高,有较强的鲁棒性.     

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.     

Discrete-time delayed standard neural network model and its application

The research on the theory and application of artificial neural networks has achieved a great success over the past two decades. Recently, increasing attention has been paid to recurrent neural networks, which are rich in dynamics, highly parallelizable, and easily implementable with VLSI. Due to these attractive features, RNNs have widely been applied to system identification, control, optimization and associative memories[1]. Stability analysis, which is critical to any applications of R…     

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.     

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.     

A delayed neural network for solving linear projection equations and its analysis

In this paper, we present a delayed neural network approach to solve linear projection equations. The Lyapunov-Krasovskii theory for functional differential equations and the linear matrix inequality (LMI) approach are employed to analyze the global asymptotic stability and global exponential stability of the delayed neural network. Compared with the existing linear projection neural network, theoretical results and illustrative examples show that the delayed neural network can effectively solve a class of linear projection equations and some quadratic programming problems.     

区间时变细胞神经网络的全局鲁棒指数稳定性

研究了一类区间时变扰动、变时滞细胞神经网络的全局鲁棒指数稳定性问题．利用Leibniz-Newton公式对原系统进行模型变换,并分析了变换模型和原始模型的等价性．基于变换模型,运用线性矩阵不等式的方法,通过选择适当的Lyapunov-Krasovskii泛函,推导了该系统全局鲁棒指数稳定的时滞相关的充分条件．通过数值实例将所得结果与前人的结果相比较,表明了本文所提出的稳定判据具有更低的保守性．     

New criteria for globally exponential stability of delayed Cohen–Grossberg neural network

This paper is concerned with analysis problem for the global exponential stability of the Cohen–Grossberg neural networks with discrete delays and with distributed delays. We first prove the existence and uniqueness of the equilibrium point under mild conditions, assuming neither differentiability nor strict monotonicity for the activation function. Then, we employ Lyapunov functions to establish some sufficient conditions ensuring global exponential stability of equilibria for the Cohen–Grossberg neural networks with discrete delays and with distributed delays. Our results are not only presented in terms of system parameters and can be easily verified and also less restrictive than previously known criteria. A comparison between our results and the previous results admits that our results establish a new set of stability criteria for delayed neural networks.     

基于逆系统的赖氨酸发酵多变量解耦内模控制

针对赖氨酸发酵过程的时变、非线性和高耦合性,提出基于逆系统的赖氨酸发酵多变量解耦内模控制方法。根据动态递归模糊神经网络(DRFNN)的非线性辨识原理离线建立发酵过程的逆模型,将得到的逆模型串联在发酵系统之前,实现了发酵过程输入输出解耦线性化,从而得到伪线性系统;对复合后的伪线性系统采用内模控制。仿真结果表明,该方法能够适应赖氨酸发酵过程模型的不确定性和参数的时变性,具有较强的鲁棒性,且结构简单,易于实现。     

Adaptive RTRL based neurocontroller for damping subsynchronous oscillations using TCSC

Modern interconnected electrical power systems are complex and require perfect planning, design and operation. Hence the recent trends towards restructuring and deregulation of electric power supply has put great emphasis on the system operation and control. Flexible AC transmission system (FACTS) devices such as thyristor controlled series capacitor (TCSC) are capable of controlling power flow, improving transient stability and mitigating subsynchronous resonance (SSR). In this paper an adaptive neurocontroller is designed for controlling the firing angle of TCSC to damp subsynchronous oscillations. This control scheme is suitable for non-linear system control, where the exact linearised mathematical model of the system is not required. The proposed controller design is based on real time recurrent learning (RTRL) algorithm in which the neural network (NN) is trained in real time. This control scheme requires two sets of neural networks. The first set is a recurrent neural network (RNN) which is a fully connected dynamic neural network with all the system outputs fed back to the input through a delay. This neural network acts as a neuroidentifier to provide a dynamic model of the system to evaluate and update the weights connected to the neurons. The second set of neural network is the neurocontroller which is used to generate the required control signals to the thyristors in TCSC. This is a single layer neural network. Performance of the system with proposed neurocontroller is compared with two linearised controllers, a conventional controller and with a discrete linear quadratic Gaussian (DLQG) compensator which is an optimal controller. The linear controllers are designed based on a linearised model of the IEEE first benchmark system for SSR studies in which a modular high bandwidth (six-samples per cycle) linear time-invariant discrete model of TCSC is interfaced with the rest of the system. In the proposed controller, since the response time is highly dependent on the number of states of the system, it is often desirable to approximate the system by its reduced model. By using standard Hankels norm approximation technique, the system order is reduced from 27 to 11th order by retaining the dominant dynamic characteristics of the system. To validate the proposed controller, computer simulation using MATLAB is performed and the simulation studies show that this controller can provide simultaneous damping of swing mode as well as torsional mode oscillations, which is difficult with a conventional controller. Moreover the fast response of the system can be used for real-time applications. The performance of the controller is tested for different operating conditions.