几类时滞神经网络的鲁棒控制与状态估计

发布时间：2018-04-30 09:38

本文选题：神经网络 + 线性矩阵不等式　；参考：《电子科技大学》2017年博士论文

【摘要】：近年来,神经网络理论得到了快速发展,理论不断完善,应用范围也越来越广。众所周知,神经网络能够在许多工程领域中得到成功应用的前提条件是神经网络模型是稳定的。当神经网络具体实现时,时滞不可避免出现在存储和传输过程中。时滞是造成不稳定和振荡主要原因,因此神经网络数学建模时要考虑时滞。Lyapunov稳定性理论是研究神经网络稳定性的基本方法,本文正是以稳定性理论为基础,研究了时滞神经网络鲁棒控制和状态估计问题。研究内容如下:1.针对带有时变时滞和参数不确定性的神经网络模型,研究了其鲁棒镇定和H_∞控制问题,得到了鲁棒镇定控制器和H_∞控制器设计方法。通过构造恰当的包含多重积分项的Lyapunov-Krasovskii(L-K)泛函,给出了时滞依赖的鲁棒镇定条件。利用二次凸组合方法,二次凸函数的性质和激活函数的信息,并借助系统方程引入自由权矩阵,降低结果的保守性。随后得到了鲁棒H_∞控制器设计方法。数值算例验证了所得鲁棒镇定控制器和H_∞控制器设计准则的有效性。2.针对带有混合时滞和参数不确定性的神经网络模型,研究了其鲁棒镇定和H_∞控制问题,得到了鲁棒镇定控制器和H_∞控制器设计方法。根据系统的结构特点,构造恰当的包含多重积分项的Lyapunov-Krasovskii(L-K)泛函,给出了时滞依赖的鲁棒镇定条件。考虑了多种激活函数,使所得到的结果具有普适性。在神经元激活函数的约束条件下获得了一组不等式,并利用二次凸组合方法,二次凸函数的性质,降低结果的保守性,使控制器设计方法能处理更大时滞的神经网络。进一步得到了鲁棒H_∞控制器的设计条件,鲁棒H_∞控制器能保证闭环系统是渐近稳定的且具有预定的H_∞性能。数值算例验证了所得鲁棒镇定控制器和H_∞控制器设计准则的有效性。3.针对带有时滞的静态神经网络模型,研究了保H_∞性能状态估计问题,得到了保H_∞性能状态估计器设计方法。考虑的时变时滞在一个区间内变动,并不要求时滞下界为零,具有更好的普适性。利用了时滞划分方法,通过构造增广的LK泛函得到了时滞依赖状态估计器设计条件,这个状态估计器保证误差系统是全局指数稳定且有预定H_∞性能。在神经元激活函数的约束条件下获得了一组不等式,结合自由权矩阵方法和倒凸方法减少了结果的保守性,使状态估计器设计方法能处理更大时滞的静态神经网络。数值算例通过和其他文献结果比较可以看出所得到的结论具有可行性和优越性。4.针对带有时变时滞静态神经网络模型,进一步研究了保H_∞性能状态估计问题,得到了保H_∞性能状态估计器设计的进一步结果。我们改变了时滞划分区间,选择了新的L-K泛函,并利用了保守性更低的积分不等式得到了状态估计器设计的充分条件。在神经元激活函数的约束条件下获得了一组不等式,并利用系统方程引入自由权矩阵减少了结果的保守性。增益矩阵和最优性能指数可通过求解线性矩阵不等式(LMI)获得。数值算例通过和其他文献结果比较可以看出所得到的结论具有可行性和优越性。5.针对带有时变时滞静态神经网络模型,研究了保广义2性能状态估计问题,得到了保广义2性能状态估计器设计方法。该状态估计器保证误差系统是全局指数稳定且有预定广义2性能。结合时滞划分方法和自由权矩阵方法,通过构造增广的L-K泛函得到了得到了保广义2性能状态估计器设计的充分条件。数值算例说明了本文所得设计方法的有效性。
[Abstract]:In recent years, the theory of neural network has been developed rapidly, the theory has been perfected, and the application scope is more and more widely. It is well known that neural network can be successfully applied in many engineering fields as the premise is the neural network model is stable. When the neural network is realized, time delay inevitably appears in the storage and transmission process. Time delay is the main cause of instability and oscillation, so the time delay.Lyapunov stability theory should be considered when modeling neural network is the basic method to study the stability of neural networks. This paper is based on the stability theory and studies the robust control and state estimation problem of time-delay neural networks. The contents of this paper are as follows: 1. The robust stabilization and H_ control problem of neural networks with time delay and parameter uncertainty are studied. The robust stabilization controller and the H_ infinity controller design method are obtained. The robust stabilization condition of time delay dependence is given by constructing the appropriate Lyapunov-Krasovskii (L-K) functional containing multiple integral terms. The two times convexity is used. The combination method, the properties of the two convex functions and the information of the activation function, and the introduction of the free weight matrix by the system equation, and reduce the conservatism of the results. Then the robust H_ infinity controller design method is obtained. The numerical example shows that the effectiveness of the robust stabilization controller and the H_ infinity controller design criterion are.2. with mixed delay and time delay. The robust stabilization and H_ control problem of neural networks with uncertain parameters are studied. The robust stabilization controller and the H_ infinity controller design method are obtained. According to the structure characteristics of the system, a proper Lyapunov-Krasovskii (L-K) functional containing multiple integral terms is constructed, and the robust stabilization condition of time delay dependence is given. The result is universal. A group of inequalities is obtained under the constraint of neuron activation function, and the two convex combination method is used to reduce the conservatism of the two convex function. The controller design method can handle the more time-delay neural network. The robust H_ infinity control is further obtained. The design condition of the device, the robust H_ infinity controller can ensure that the closed-loop system is asymptotically stable and has a predetermined H_ infinity performance. The numerical example validates the effectiveness of the robust stabilization controller and the H_ infinity controller design criterion..3. for the static neural network model with time delay, the problem of preserving the H_ infinity performance state estimation problem is studied. The H_ infinity performance state estimator design method. The time-varying delay is considered to be changed in one interval, which does not require the lower bound of time delay and has a better universality. By using the time-delay division method, the design conditions of the time-delay dependent state estimator are obtained by constructing an augmented LK functional. The state estimator ensures the error system is global. The exponential stability and predetermined H_ infinity performance. A set of inequalities is obtained under the constraint conditions of the neuron activation function, which reduces the conservatism of the results combined with the free weight matrix method and the salient method, so that the state estimator design method can handle more time-delay static neural networks. Numerical examples are compared with other literature results. In view of the feasibility and superiority of the obtained conclusion,.4. is further studied for the H_ infinity performance state estimation problem for the static neural network model with time-varying delay, and further results are obtained for the design of the guaranteed H_ infinity estimator. We change the interval of the time delay division, select the new L-K functional and use the conservatism. The lower integral inequality obtains sufficient conditions for the design of the state estimator. A set of inequalities is obtained under the constraints of the neuron activation function, and the conservation of the results is reduced by introducing the system equation into the free weight matrix. The gain matrix and the optimal performance index can be obtained by solving linear matrix inequalities (LMI). By comparing with the results of other literature, it can be seen that the obtained conclusion is feasible and advantageous.5. for the static neural network model with time-varying delay, the generalized 2 performance state estimation problem is studied and the generalized 2 performance state estimator design method is obtained. The state estimator guarantees the global exponential stability of the error system. And there is a predetermined generalized 2 performance. Combining the time-delay division method and the free weight matrix method, a sufficient condition for the design of the guaranteed generalized 2 performance state estimator is obtained by constructing an augmented L-K functional. The numerical example shows the effectiveness of the proposed design method.

【学位授予单位】：电子科技大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：TP13;TP183

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