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Stochastic stability of quasi-integrable Hamiltonian systems with time delay by using Lyapunov function method

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Science china(Technological Sciences) 2010年第3期53卷 703-712页

作者： LING Quan 1,JIN XiaoLing 1 &HUANG ZhiLong 2.1 department of mechanics,{2.,Hangzhou 31002.,china 2.state key laboratory of fluid power transmission and control,{2.,Hangzhou 31002.,china 1. department of mechanics Zhejiang University Hangzhou 310027 China2. State Key Laboratory of Fluid Power Transmission and Control Zhejiang University Hangzhou 310027 China

The asymptotic Lyapunov stability of one quasi-integrable Hamiltonian system with time-delayed feedback control is studied by using Lyapunov functions and stochastic averaging ***,a quasi-integrable Hamiltonian system with time-delayed feedback control subjected to Gaussian white noise excitation is approximated by a quasi-integrable Hamiltonian system without time ***,stochastic averaging method for quasi-integrable Hamiltonian system is used to reduce the dimension of the original system,and after that the Lyapunov function of the averaged It equation is taken as the optimal linear combination of the corresponding independent first integrals in ***,the stability of the system is determined by using the largest eigenvalue of the linearized *** examples are used to illustrate the proposed procedure and the effects of delayed time on the Lyapunov stability are discussed as well.

关键词： Lyapunov stability Lyapunov function time delay stochastic averaging

Exact stationary solutions independent of energy for strongly nonlinear stochastic systems of multiple degrees of freedom

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Science china(Technological Sciences) 2009年第8期52卷 2424-2431页

作者： HUANG ZhiLong1,2.& JIN XiaoLing1 1 department of mechanics, {2., Hangzhou 31002., china 2.The state key laboratory of fluid power transmission and control, {2., Hangzhou 31002., china department of mechanics Zhejiang University Hangzhou 310027 China The state key laboratory of fluid power transmission and control Zhejiang University Hangzhou 310027 China

A new procedure is proposed to construct strongly nonlinear systems of multiple degrees of freedom subjected to parametric and/or external Gaussian white noises, whose exact stationary solutions are independent of energy. Firstly, the equivalent Fokker-Planck-Kolmogorov (FPK) equations are derived by using exterior differentiation. The main difference between the equivalent FPK equation and the original FPK equation lies in the additional arbitrary antisymmetric diffusion matrix. Then the exact stationary solutions and the structures of the original systems can be obtained by using the coefficients of antisymmetric diffusion matrix. The obtained exact stationary solutions, which are generally independent of energy, are for the most general class of strongly nonlinear stochastic systems multiple degrees of freedom (MDOF) so far, and some classes of the known ones dependent on energy belong to the special cases of them.

关键词： exact stationary solution nonlinear stochastic system equivalent system independent of energy

STABILITY IN THE CIRCULAR PIPE FLOW OF FIBER SUSPENSIONS

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Journal of Hydrodynamics 2003年第2期15卷 12-18页

作者： You Zhen jiang, Lin Jian zhong department of mechanics, {2., zhejiang university, Hangzhou 31002., china departmentofmechanics StateKeyLaboratoryofFluidPowerTransmissionandControlZhejiangUniversityHangzhou310027China

A linear stability analysis on the circular pipe flow of fiber suspensions ispresented. The fiber orientation tensors are used to describe the characteristics of theorientation dislribution of fibers. The constitutive equation for the fiber suspensions is set upand the modified Orr-Sommerfeld stability equation is derived. An improved finite difference methodwith high order accuracy is employed to solve the e-quation. The Newtonian pipe Poiseuille flowcorresponding to H = 0 is also analyzed for comparison. The results reveal that the fiber additiveswill enhance the flow stability, the degree of enhancement becomes high with the increases of theparameter H which accounts for the fiber resistance to the stretching along its axis. Fibersuspensions with large H can suppress the influence of high Reynolds number on the flow ***, fibers give a higher attenuation of the short waves of disturbance.

关键词： flow stability circular pipe flow fiber suspensions numerical simulation

Stochastic optimal control of partially observable nonlinear quasi-integrable Hamiltonian systems

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Science china(Physics,mechanics & Astronomy) 2010年第1期53卷 147-154页

作者： FENG Ju, ZHU WeiQiu & YING ZuGuang department of mechanics, {2., zhejiang university, Hangzhou 31002., china 1. department of mechanics State Key Laboratory of Fluid Power Transmission and Control Zhejiang University Hangzhou 310027 China

The stochastic optimal control of partially observable nonlinear quasi-integrable Hamiltonian systems is investigated. First, the stochastic optimal control problem of a partially observable nonlinear quasi-integrable Hamiltonian system is converted into that of a completely observable linear system based on a theorem due to Charalambous and Elliot. Then, the converted stochastic optimal control problem is solved by applying the stochastic averaging method and the stochastic dynamical programming principle. The response of the controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation and the Riccati equation for the estimated error of system states. As an example to illustrate the procedure and effectiveness of the proposed method, the stochastic optimal control problem of a partially observable two-degree-of-freedom quasi-integrable Hamiltonian system is worked out in detail.

关键词： quasi-integrable Hamiltonian system partial observation stochastic optimal control

Compensation for time-delayed feedback bang-bang control of quasi-integrable Hamiltonian systems

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Science china(Technological Sciences) 2009年第3期52卷 688-697页

作者： LIU ZhongHua1 & ZHU WeiQiu2.1 department of Civil Engineering, Xiamen university, Xiamen 361005, {2. 2.department of mechanics, state key laboratory of fluid power transmission and control, zhejiang university, Hangzhou 31002., {2. department of Civil Engineering Xiamen University Xiamen 361005 China department of mechanics State Key Laboratory of Fluid Power Transmission and Control Zhejiang University Hangzhou 310027 China

The stochastic averaging method for quasi-integrable Hamiltonian systems with time-delayed feedback bang-bang control is first introduced. Then, two time delay compensation methods, namely the method of changing control force amplitude (CFA) and the method of changing control delay time (CDT), are proposed. The conditions applicable to each compensation method are discussed. Finally, an example is worked out in detail to illustrate the application and effectiveness of the proposed methods and the two compensation methods in combination.

关键词： time-delayed feedback control compensation method bang-bang control quasi-integrable Hamiltonian system

First passage failure of dynamical power systems under random perturbations

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Science china(Technological Sciences) 2010年第9期53卷 2495-2500页

作者： CHEN LinCong1 & ZHU WeiQiu2.1 College of Civil Engineering,Huaqiao university,Xiamen 36102.,china {2.,state key laboratory of fluid power transmission and control,zhejiang university,Hangzhou 31002.,china 1. College of Civil Engineering Huaqiao University Xiamen 361021 China2. Department of Mechanics State Key Laboratory of Fluid Power Transmission and Control Zhejiang University Hangzhou 310027 China

The first-passage problem of dynamical power system of a single-machine-infinite-bus (SMIB) system under random perturbations is ***,the stochastic averaging method for quasi non-integrable generalized Hamiltonian systems is applied to reduce the equations of the SMIB system under random perturbations to a set of averaged It ***,the backward Kolmogorov equation governing the conditional reliability function and the Pontryagin equation governing the conditional mean of first passage time are established and solved numerically,***,the proposed method is verified by using the Monte Carlo simulation of the original system.

关键词： dynamical power system random perturbation stochastic averaging first passage failure

NUMERICAL SIMULATION ON VELOCITIES OF TWO INTERACTING FIBERS IN FIBER SUSPENSION

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Journal of Hydrodynamics 2003年第3期15卷 10-16页

作者： Lin Jian-zhong, Bao Fu-bing, Zhang Zhi-chao department of mechanics, {2., zhejiang university, Hangzhou 31002., china, department of mechanics State Key Laboratory of Fluid Power Transmission and Control Zhejiang University Hangzhou 310027 China

A mathematical model was put forward to describe the mechanical interactionsof two contacting fibers, then a numerical simulation was carried out. The results of the simulationaccord with experimental results well. It turns out that the initial contacting point and theinitial orientation of the settling fiber have much effect on the translational and rotationalvelocities of the settling fiber, along with the increase in the length or the decrease in theradius of the fiber, the translational and rotational velocities of the settling fiber decrease; thesame trend remains when the viscosity of the solvent increases or the density of the fiberdecreases.

关键词： fiber suspension mechanical interaction numerical simulation

A　NEW　METHOD　FOR　SOLVING　TURBULENT　VELOCITY　CORRELATION　FUNCTIONS　AND　ITS　APPLICATION　TO　THE　CHANNEL　FLOW

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Journal of Hydrodynamics 1996年第4期8卷 69-77页

作者： Lin Jian-zhong Wang Yu-zhi(department of mechanics, the {2., zhejiang university Hangzhou 31002., P. R. china) zhejiang Univ Hangzhou China

A new kind of method, the method of successive substitution, for solving velocity correlation functions is presented. As application of this method, the first order approximation solution in the turbulent channel flow is given numerically and then put into the equations of turbulent fluctuation which are solved numerically within the range of micro-scale by means of spectrum method and finite-difference method. By averaging fluctuating velocity, the second order approximation solutions of double fluctuating velocity correlation and other higher order correlations are obtained by computation. Putting the second approximation solution into equations of turbulent fluctuation, the solutions of different order correlations are given. These results are in good agreement with experimental results [1, 2. 3].

关键词： turbulence correlation functions computation method

Time-delayed feedback control optimization for quasi linear systems under random excitations

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Acta Mechanica Sinica 2009年第3期25卷 395-402页

作者： Xueping Li Demin Wei Weiqiu Zhu School of Civil Engineering and Transportation, South china university of Technology, 510640 Guangzhou, china department of mechanics, state key laboratory of fluid power transmission and control, zhejiang university, 31002. Hangzhou, china School of Civil Engineering and Transportation South China University of Technology 510640 Guangzhou China department of mechanics State Key Laboratory of Fluid Power Transmission and Control Zhejiang University 310027 Hangzhou China

A strategy for time-delayed feedback control optimization of quasi linear systems with random excitation is proposed. First, the stochastic averaging method is used to reduce the dimension of the state space and to derive the stationary response of the system. Secondly, the control law is assumed to be velocity feedback control with time delay and the unknown control gains are determined by the performance indices. The response of the controlled system is predicted through solving the Fokker-Plank-Kolmogorov equation associated with the averaged Ito equation. Finally, numerical examples are used to illustrate the proposed control method, and the numerical results are confirmed by Monte Carlo simulation .

关键词： Quasi linear system Time-delayed feedback Stochastic averaging method Random excitation