一类二阶时延神经网络的分岔分析和控制

讨论了一类二阶时延网络系统的非线性特性,应用线性化稳定性和分岔理论,提出了该系统从稳定到分岔的条件.结论指出利用延迟时间可以进行分岔控制、极限环幅值控制等,并给出了仿真的具体实例.     

Asymptotic stability criteria for a two-neuron network with different time delays

In this paper, the asymptotic stability of a two-neuron system with different time delays has been investigated. Some criteria for determining the global asymptotically stability of equilibrium are derived from the theory of monotonic dynamical system and the approach of Lyapunov functional. For local asymptotic stability, some elegant criteria are also obtained by the Nyquist criteria. We find that one of them depends on the length of delays while the other ones do not. In the latter case, the delays are sometimes called harmless delays. The results obtained have leading significance in the study of neural networks composed of a large number of neurons with different time delays.     

On the control of chaos via fractional delayed feedback method

In this paper the problem of controlling unstable fixed points (in discrete systems) and periodic orbits (in continuous system) is investigated via a new scheme involving fractional derivatives. This method is based on applying feedback of measured states and using the period of fixed points and periodic orbits. In this method there is no need of information for fixed point and periodic orbits, just the period is enough. The effectiveness of this method is investigated via some demonstrative example.     

时滞反馈力作用下含有分数阶阻尼的随机系统的响应与分叉研究

分析了时滞反馈力作用下含有分数阶阻尼的随机系统,并讨论了该系统的稳态响应及随机分叉.首先,通过对含有时滞项的近似处理以及基于广义谐和函数的随机平均法得到了该系统的稳态响应.然后使用算例对方法的有效性进行了验证,其中主要研究了时滞反馈作用力和分数阶阻尼对系统稳态响应的影响,结果表明上述两者的变化会影响系统的稳态响应并引发随机分叉现象.     

Bifurcation analysis in a discrete-time single-directional network with delays

In this paper, we consider a simple discrete-time single-directional network of four neurons. The characteristics equation of the linearized system at the zero solution is a polynomial equation involving very high-order terms. We first derive some sufficient and necessary conditions ensuring that all the characteristic roots have modulus less than 1. Hence, the zero solution of the model is asymptotically stable. Then, we study the existence of three types of bifurcations, such as fold bifurcations, flip bifurcations, and Neimark–Sacker (NS) bifurcations. Based on the normal form theory and the center manifold theorem, we discuss their bifurcation directions and the stability of bifurcated solutions. In addition, several codimension two bifurcations can be met in the system when curves of codimension one bifurcations intersect or meet tangentially. We proceed through listing smooth normal forms for all the possible codimension 2 bifurcations.     

脑皮层神经网络的线性时滞反馈控制

神经元的病态同步放电会破坏大脑的正常功能, 导致癫痫和帕金森等生理疾病. 本文采用神经元二维映射模型构建一个脑皮层神经网络, 当神经元之间的耦合强度超过某一阈值时, 网络中所有神经元同步放电. 通过施加线性时滞反馈控制, 可以有效的消除这种同步状态, 且不改变神经元本身的放电特性. 仿真结果表明线性时滞反馈 可以实现对脑皮层神经网络的去同步化控制, 且对刺激参数的变化具有鲁棒性.     

Delay-induced bifurcation in a tri-neuron fractional neural network

This paper investigates the issue of stability and bifurcation for a delayed fractional neural network with three neurons by applying the sum of time delays as the bifurcation parameter. Based on fractional Laplace transform and the method of stability switches, some explicit conditions for describing the stability interval and emergence of Hopf bifurcation are derived. The analysis indicates that time delay can effectively enhance the stability of fractional neural networks. In addition, it is found that the stability interval can be varied by regulating the fractional order if all the parameters are fixed including time delay. Finally, numerical examples are presented to validate the derived theoretical results.     

Bifurcation analysis of a cellular nonlinear network model via neural network approach

In this paper, receptor-based cellular nonlinear network model is studied. By applying neural network method, the ordinary differential equations being equivalent to the partial differential equations of the model are resulted. Also, the bifurcation analysis of the transformed system is presented. To support our theoretical results, some numerical examples are given.     

分数阶Chen混沌系统的径向基函数神经滑模控制

针对带有参数扰动和外部干扰的分数阶Chen混沌系统, 提出一种径向基函数(RBF)神经滑模控制方法. 设计滑模切换函数, 将其作为RBF神经网络的唯一输入, 网络的权值可依据滑模趋近条件在线调整. 基于Lyapunov稳定性理论, 分析了该方法的稳定性. 仿真结果表明该控制方法简化了常规神经网络控制结构的复杂性, 削弱了滑模控制的抖振程度, 对参数扰动和外部干扰具有较好的鲁棒性.     

基于强化学习的倒立摆分数阶梯度下降RBF控制

为了提高强化学习的控制性能,提出一种基于分数梯度下降RBF神经网络的强化学习算法.通过评价神经网络和执行神经网络组成强化学习系统,利用神经网络记忆和联想,学会控制倒立摆,提高控制精度,使误差趋于零,直至学习成功,并证明闭环系统的稳定性.通过倒立摆的物理实验发现,当分数阶阶数较大,微分的作用更显著,对角速度和速度的控制效果更好,角速度和速度的均方误差和平均绝对误差较小;当分数阶阶数较小,积分的作用更显著,对倾斜角和位移的控制效果更好,因此倾斜角和位移的均方误差和平均绝对误差较小.仿真实验的结果表明,所提算法动态响应好,超调量小,调整时间短,精度高,泛化性能好.它优于基于RBF神经网络的强化学习算法和传统强化学习算法,能有效地加快梯度下降法的收敛速度,提高其控制性能.在引入适当的干扰后,所提算法能够快速地自我调节并恢复稳定状态,控制器的鲁棒性和动态性能满足实际要求.     

Bifurcation in model reference adaptive control systems

We study the effect of unmodeled dynamics on the performance of a simple model reference adaptive control mechanism. Exact stability boundaries are computed and different routes to chaotic behavior and global instability are described. Typically, we observed a region of period doubling and Hopf bifurcations similar to those observed in the Ziegler-Nichols approach to PID control design. The analysis applies to higher order and certain nonlinear systems as well.     

Decentralized control: a stable proper fractional approach

Three decentralized control problems are considered in a fractional setup for two-channel multivariable systems. All three problems are instances of decentralized control or local output feedback problems. The problems are: (i) making the system stabilizable and detectable through the first channel via dynamic output feedback around the second channel, (ii) the first problem with the constraint of internal stability, and (iii) the decentralized stabilization problem. All three problems are equivalent as far as the solvability conditions are concerned. A characterization of all solutions in each case is given. The results apply to a class of systems having fractional representations over an arbitrary principal ideal domain     

Stability map of multiple time delayed fractional order systems

In this paper, a novel method is presented to study the stability map of linear fractional order systems with multiple delays against uncertainties in delays. It is evident from the literature that the stability question of this class of dynamics has not been resolved yet. The backbone of the new methodology is inspired by an advanced clustering with frequency sweeping technique which enables the exhaustive determination of stability switching curves in the space of the delays. The proposed method detects all the stability regions exactly, in the parametric space of the time delays. An illustrative example is presented to confirm the proposed method results.     

机床无刷直流电机系统的分岔分析与控制

文章主要研究了机床无刷直流电机系统的Hopf分岔控制问题.首先,对系统进行分岔分析,通过计算极限环曲率系数判定系统的Hopf分岔类型;然后设计Washout滤波器对系统进行分岔控制,根据Hopf分岔理论给出使原系统Hopf分岔位置发生改变的参数条件,利用Normal Form方法计算出受控系统的Hopf分岔正规型,根据正规型的实部大小判定Hopf分岔类型,给出使原系统Hopf分岔类型发生改变的参数条件;并借助MATLAB软件对理论结果进行数值仿真,理论结果和数值仿真表明:控制器中的线性增益能使系统在所期望的参数值处发生Hopf分岔,甚至消除Hopf分岔,控制器中的非线性增益能改变原系统的Hopf分岔类型及极限环幅值的大小.研究结果对无刷直流电动机系统的工程实际具有一定的指导意义.     

Optimal control of a water distribution network in a supervisory control system

This paper deals with the use of optimal control techniques in water distribution networks. An optimal control tool, developed in the context of a European research project is described and the application to the city of Sintra (Portugal) is presented.     

一类耦合分数阶反应–扩散系统的边界控制

针对带有空间变化的反应项的耦合分数阶反应–扩散系统边界镇定问题,利用反步法设计了用于Robin边界条件的状态反馈控制.通过可逆的积分变换将原耦合系统转化为一个稳定的目标系统.利用变量代换和逐次逼近法分析了核函数矩阵的存在唯一性.借助分数阶Lyapunov直接法证明了闭环系统的Mittag-Leffler稳定性.数值仿真验证了所提出方法的有效性.     

Optimal control of a nonhomogeneous Dirichlet boundary fractional diffusion equation

We study a nonhomogeneous Dirichlet boundary fractional diffusion equation in a bounded domain. The fractional time derivative is considered in the Riemann-Liouville sense. We first prove by transposition the existence and the uniqueness of the solution of the boundary fractional diffusion equation. Then under some appropriate assumptions on the closed convex set of the admissible controls, we obtain a decoupled optimality system.     

Optimal control of a fractional diffusion equation with state constraints

This paper is concerned with the state constrained optimal control problems of a fractional diffusion equation in a bounded domain. The fractional time derivative is considered in the Riemann-Liouville sense. Under a Slater type condition we prove the existence a Lagrange multiplier and a decoupled optimality system.     

Effect of fractional orders in the velocity control of a servo system

The application of fractional-order PID controllers is now an active field of research. This article investigates the effect of fractional (derivative and integral) orders upon system’s performance in the velocity control of a servo system. The servo system consists of a digital servomechanism and an open-architecture software environment for real-time control experiments using MATLAB/Simulink tools. Experimental responses are presented and analyzed, showing the effectiveness of fractional controllers. Comparison with classical PID controllers is also investigated.