Finding nondegenerate Hopf bifurcation points for four-dimensional two-parametric systems

We establish a numerically feasible algorithm to find a simplicial approximation A to a certain part of the boundary of the set of stable (or Hurwitz) polynomials of degree 4. Moreover, we have that . Using this, we build an algorithm to find a piecewise-linear approximation to the intersection curve of a given surface contained in ⁴ with . We have also devised an efficient computer program to perform all these operations. The main motivation is to find the curve of nondegenerate bifurcation points in parameter space for a given 2-parametric Hopf bifurcation problem of dimension 4.     

Delayed Hopf bifurcation in time-delayed slow-fast systems

This paper presents an investigation on the phenomenon of delayed bifurcation in time-delayed slow-fast differential systems.Here the two delayed's have different meanings.The delayed bifurcation means that the bifurcation does not happen immediately at the bifurcation point as the bifurcation parameter passes through some bifurcation point,but at some other point which is above the bifurcation point by an obvious distance.In a time-delayed system,the evolution of the system depends not only on the present ...     

一类两自由度碰撞振动系统的Hopf分岔和混沌

分析了一类两自由度碰撞振动系统的周期运动,并通过计算Poincare映射的线性化矩阵,确定周期运动的稳定性.分析表明,在一定的参数条件下系统存在周期倍化分岔和Hopf分岔,并通过数值模拟方法得到了以Poincare截面上的不变圈表示的拟周期响应.简明地讨论了系统通向混沌的道路.     

Hopf bifurcation via Volterra series

The Hopf bifurcation theorem gives a method of predicting oscillations which appear in a nonlinear system when a parameter is varied. There are many different ways of proving the theorem and of using its results, but the way which is probably the most useful, to control and system theorists, uses Nyquist loci in much the same way as the describing function method does. The main advantages of this method are dimensionality reduction, which eases the calculation, and the ability to cope with higher-order approximations than are used in the original Hopf theorem. This paper shows how such an approach to the Hopf bifurcation follows naturally and easily from Volterra series methods. Such use of Volterra series in nonlinear oscillations appears to be new. In many problems, the calculations involved are simplified when the Volterra series approach is taken, so the approach has practical merits as well as theoretical ones.     

The Hopf bifurcation theorem for quasilinear differential-algebraic equations

We prove a generalization of the Hopf bifurcation theorem for quasilinear differential equations (DAEs), i.e. equations of the form A(μ, χ)χ = G(μ, χ) where the matrix A(χ, μ) has constant but not full rank and hence the system cannot be made into an explicit ODE. The paper includes an appendix by J. Ernsthausen addressing the numerical calculation of the Hopf points in the DAE setting.     

时延神经元的Hopf分岔控制

通过对时延神经元的分析得到相应的控制器,使时间延迟作为分岔参数得到有效的控制;由线性化理论确定出Hopf分岔点的位置,得到相应的控制条件,并从理论上证明了控制器的可行性.实例分析表明该理论与仿真结果相一致.     

A new decentralized controller for large scale systems

In this paper we develop a new approach to the design of near-optimal decentralized controllers for large-scale linear interconnected dynamical systems. All calculations in the design stage are done on subsystems. This is achieved by using a simple reduced order model for the interactions. The resulting controller is decentralized, independent of initial conditions and capable of accommodating constant unknown disturbances. The approach is illustrated on a 22nd order river pollution control example. In addition, it is shown that by a simple modification it is possible to ensure that the controller is asymptotically stable with a pre-specified degree of stability and we show that the modified controller is also connectively asymptotically stable under structural perturbations.     

大规模存储系统可靠性参数最优化分析

在大规模存储系统中,数据的可靠性越来越受到人们的关注。已有的研究分析了在系统规模已知的条件下,某些系统参数,如副本分布策略、存储对象数目等,对可靠性的粗略影响,但较少提及它们的最优值或者最优组合。提出了一种基于对象粒度恢复的可靠性新模型;基于该模型,在分析三种主流的副本分布策略的基础上,分别计算出了各个系统参数的独立最优值及其组合最优值。与已有模型相比,该模型更易于求解,且获得了更加综合实用的最优值,这些最优参数值能直接有效地指导系统设计者构建更可靠的大规模存储系统。     

Pole placement for controlling a large scale power system

We propose an efficient approach to pole placement for the problem of centralized control over a large scale power system with state feedback. Our approach is based on a specific homothetic transformation of the original system representation. The representation of a transformed system contains explicit elements that can be changed with feedback and provide for a given pole placement in the closed system. We give examples of solving the exact pole placement problem in systems whose state space dimension reaches several thousands.     

一类经济模型的分岔周期解

讨论了一类经济模型的稳定性及Hopf分岔．根据特征根给出系统失稳的条件后,利用伪振子法和迭代法得到了Hopf分岔的方向以及周期解的振幅估计,计算式较简洁,最后的数值算例很好地验证了方法的准确性．特别地,当周期解振幅较大时,迭代法的估算更准确．尽管系统失稳后,产生分岔周期解,但适当调整参数大小,仍然可以保证周期解稳定,也就意味着经济的良性发展．     

Local feedback stabilization and bifurcation control, I. Hopf bifurcation

Local bifurcation control problems are defined and employed in the study of the local feedback stabilization problem for nonlinear systems in critical cases. Sufficient conditions are obtained for the local stabilizability of general nonlinear systems whose linearizations have a pair of simple, nonzero imaginary eigenvalues. The conditions show, in particular, that generically these nonlinear critical systems can be stabilized locally, even if the critical modes are uncontrollable. The analysis also yields a direct method for computing stabilizing feedback controls. Use is made of bifurcation formulae which require only a series expansion of the vector field.     

Survey of decentralized control methods for large scale systems

This paper surveys the control theoretic literature on decentralized and hierarchical control, and methods of analysis of large scale systems.     

Real-time state estimation for large power systems using multicomputer systems

This paper presents in detail an efficient and simple state estimation method suitable for real-time calculations in large power systems. According to this method state estimators of large power systems can be obtained easily using single computers as well as multicomputer systems. Various problems connected with use of this method are discussed and some important numerical results are given.     

Estimation of distribution and differential evolution cooperation for large scale economic load dispatch optimization of power systems

Economic Load Dispatch (ELD) is an important and difficult optimization problem in power system planning. This article aims at addressing two practically important issues related to ELD optimization: (1) analyzing the ELD problem from the perspective of evolutionary optimization; (2) developing effective algorithms for ELD problems of large scale. The first issue is addressed by investigating the fitness landscape of ELD problems with the purpose of estimating the expected performance of different approaches. To address the second issue, a new algorithm named “Estimation of Distribution and Differential Evolution Cooperation” (ED-DE) is proposed, which is a serial hybrid of two effective evolutionary computation (EC) techniques: estimation of distribution and differential evolution. The advantages of ED-DE over the previous ELD optimization algorithms are experimentally testified on ELD problems with the number of generators scaling from 10 to 160. The best solution records of classical 13 and 40-generator ELD problems with valve points, and the best solution records of 10, 20, 40, 80 and 160-generator ELD problems with both valve points and multiple fuels are updated in this work. To further evaluate the efficiency and effectiveness of ED-DE, we also compare it with other state-of-the-art evolutionary algorithms (EAs) on typical function optimization tasks.     

Hopf bifurcation control: A new approach

In this paper we find conditions to control a Hopf bifurcation in a class of nonlinear systems whose linear approximation has two eigenvalues on the imaginary axis, without assuming that the system is controllable. We use the center manifold theorem to project the dynamics on a two dimensional manifold, and design a controller that permits us to decide the stability and direction of the emerging periodic solution.     

分数阶随机Duffing系统的Hopf分岔

运用正交多项式逼近原理，研究了分数阶随机Duffing系统在零平衡点的Hopf分岔．首先，运用Laguerre正交多项式逼近法将含有随机参数的分数阶Duffing系统转化为等价的确定性系统，然后通过数值计算求得其响应．最后，利用两个引理求得等价系统发生Hopf分岔行为的临界值，并通过数值模拟验证了理论分析结果．     

Optimal decentralized control of large scale systems

This paper presents a new optimized decentralized controller design method for solving the tracking and disturbance rejection problems for large-scale linear time-invariant systems, using only low-order decentralized controllers. To illustrate the type of results which can be obtained using the new optimized decentralized control design method, the control of a large flexible space structure is studied and compared with the standard centralized LQR-observer controller. The order of the resultant decentralized controller is much smaller than that of the standard centralized LQR-observer controller. The proposed controller also has certain fail-safe properties and, in addition, it can be five orders of magnitude more robust than the standard LQR-observer controller based on their real stability radii. The new decentralized controller design method is applied to a large flexible space structure system with 5 inputs and 5 outputs and of order 24.