基于忆阻器的时滞分数阶神经网络系统的动力学分析

发布时间：2019-04-02 06:36

【摘要】：近年来,分数阶神经网络系统由于其良好的动力学性质,已经成为非线性学科领域研究的一个重要课题。相对于整数阶神经网络系统,分数阶神经网络系统能够有效描述系统的整体功能,并提高其计算能力。此外,对神经元进行建模时加入忆阻器电路元件,可以更加准确地模拟人类大脑神经系统。另一方面,神经网络系统在信号传输过程中会产生时滞现象,能够造成系统的不稳定甚至导致混沌。因此,本文提出了基于忆阻器的时滞分数阶神经网络系统,并讨论了该系统的稳定性问题,具体工作如下:1.对给定的基于忆阻器的时滞分数阶神经网络系统,分析其动力学行为。通过应用分数阶系统的比较定理和时滞系统的稳定性理论,给出了该系统实现局部渐近稳定性的条件。此外,对于实际运行的系统,由于测量误差和传输噪声的存在,有界扰动是不可避免的。因此,本文考虑了有界扰动对该系统的影响,讨论了在有界扰动条件下,该系统满足一致稳定的条件。并通过构造一个全局渐近稳定的系统具体估计了该系统一致稳定的范围。2.在控制系统中,外界干扰的不确定性使得理论与实际结果存在一定的差距,特别是参数的不确定性,可能会导致稳定的系统出现震荡现象。此外,由于系统中包含复值信号,此种信号能够使时域信号对应的频谱具有共轭对称性。因此研究复平面上的具有不确定参数的分数阶神经网络系统是很有必要的。在Filippov意义下,通过利用分数阶比较原理、时滞系统的稳定性理论,M-矩阵及同态原理,在复值传递函数可转化为实部与虚部条件下,证明了在参数未知条件下系统平衡点的存在唯一性。并在此基础上,给出了相应的参数及函数条件,讨论了系统的全局渐近稳定性。而当复值传递函数不可转化时,通过加入复值传递函数有界条件保证了系统平衡点的存在性,并得出了系统实现局部渐近稳定的条件。
[Abstract]:In recent years, fractional neural network (FNN) system has become an important subject in the field of nonlinear science because of its good dynamic properties. Compared with integer-order neural network system, fractional-order neural network system can effectively describe the whole function of the system and improve its computing ability. In addition, it is more accurate to simulate the neural system of human brain by adding the circuit element of memotor to the neuron modeling. On the other hand, the neural network system will produce time-delay phenomenon in the process of signal transmission, which can cause instability and even chaos of the system. Therefore, in this paper, a delay fractional neural network system based on memory is proposed, and the stability of the system is discussed. The specific work is as follows: 1. The dynamic behavior of a given time-delay fractional-order neural network system based on memory is analyzed. By applying the comparison theorem of fractional-order systems and the stability theory of time-delay systems, the conditions for achieving local asymptotic stability of the system are given. In addition, due to the existence of measurement error and transmission noise, bounded disturbance is inevitable for the practical system. Therefore, in this paper, the influence of bounded perturbation on the system is considered, and the condition of uniform stability of the system is discussed under the condition of bounded perturbation. By constructing a globally asymptotically stable system, the range of uniform stability of the system is estimated. In the control system, the uncertainty of the external interference leads to a certain gap between the theoretical and practical results, especially the uncertainty of the parameters, which may lead to the oscillation of the stable system. In addition, because the system contains complex-valued signals, such signals can make the corresponding spectrum of time-domain signals have conjugate symmetry. Therefore, it is necessary to study the fractional neural network system with uncertain parameters on the complex plane. In the sense of Filippov, by using the fractional comparison principle, the stability theory of time-delay system, the M-matrix and homomorphism principle, under the condition that the complex-valued transfer function can be transformed into real part and imaginary part, The existence and uniqueness of the equilibrium point of the system under the condition of unknown parameters are proved. On this basis, the corresponding parameters and function conditions are given, and the global asymptotic stability of the system is discussed. When the complex-valued transfer function is non-convertible, the existence of the equilibrium point is guaranteed by adding the bounded condition of the complex-valued transfer function, and the conditions for the system to achieve local asymptotic stability are obtained.
【学位授予单位】：北京交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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