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Rong-hua HUAN Wei-qiu ZHU Yong-jun WU 《浙江大学学报(A卷英文版)》2008,9(3):351-357
A modified nonlinear stochastic optimal bounded control strategy for random excited hysteretic systems with actuator saturation is proposed. First, a controlled hysteretic system is converted into an equivalent nonlinear nonhysteretic stochastic system. Then, the partially averaged Itoe stochastic differential equation and dynamical programming equation are established, respectively, by using the stochastic averaging method for quasi non-integrable Hamiltonian systems and stochastic dynamical programming principle, from which the optimal control law consisting of optimal unbounded control and bang-bang control is derived. Finally, the response of optimally controlled system is predicted by solving the Fokker-Planck-Kolmogorov （FPK） equation associated with the fully averaged Itoe equation. Numerical results show that the proposed control strategy has high control effectiveness and efficiency. 相似文献
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Xue-ping LI Wei-qiu ZHU Zu-guang YING 《浙江大学学报(A卷英文版)》2008,9(3):330-337
An optimization method for time-delayed feedback control of partially observable linear building structures subjected to seismic excitation is proposed. A time-delayed control problem of partially observable linear building structure under horizontal ground acceleration excitation is formulated and converted into that of completely observable linear structure by using separation principle. The time-delayed control forces are approximately expressed in terms of control forces without time delay. The control system is then governed by Itoe stochastic differential equations for the conditional means of system states and then transformed into those for the conditional means of modal energies by using the stochastic averaging method for quasi-Hamiltonian systems. The control law is assumed to be modal velocity feedback control with time delay and the unknown control gains are determined by the modal performance indices. A three-storey building structure is taken as example to illustrate the proposal method and the numerical results are confirmed by using Monte Carlo simulation. 相似文献
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A stochastic optimal control strategy for partially observable nonlinear quasi Hamiltonian systems is proposed.The optimal control forces consist of two parts. The first part is determined by the conditions under which the stochastic optimal control problem of a partially observable nonlinear system is converted into that of a completely observable linear system. The second part is determined by solving the dynamical programming equation derived by applying the stochastic averaging method and stochastic dynamical programming principle to the completely observable linear control system. The response of the optimally controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation associated with the optimally controlled completely observable linear system and solving the Riccati equation for the estimated error of system states. An example is given to illustrate the procedure and effectiveness of the proposed control strategy. 相似文献
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On stochastic optimal control of partially observable nonlinear quasi Hamiltonian systems 总被引：1，自引：0，他引：1
INTRODUCTION Since many actual control systems such asthose in structural engineering are subjected torandom excitations and the system states are esti-mated from measurements with random noise,stochastic optimal control of partially observablesystems is a research subject of much significance.One basic approach to this problem is to convert itinto the stochastic optimal control of completelyobservable systems using separation theorem(Wonham, 1968; Fleming and Rishel, 1975; Ben-so… 相似文献
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We studied the response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control using the stochastic averaging method. First, the time-delayed feedback bang-bang control force is expressed approximately in terms of the system state variables without time delay. Then the averaged It6 stochastic differential equations for the system are derived using the stochastic averaging method. Finally, the response of the system is obtained by solving the Fokker-Plank-Kolmogorov （FPK） equation associated with the averaged lt6 equations. A Duffing oscillator with time-delayed feedback bang-bang control under combined harmonic and white noise excitations is taken as an example to illus- trate the proposed method. The analytical results are confirmed by digital simulation. We found that the time delay in feedback bang-bang control will deteriorate the control effectiveness and cause bifurcation of stochastic jump of Duffing oscillator. 相似文献
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A rectangular thin plate vibration model subjected to inplane stochastic excitation is simplified to a quasinonintegrable Hamiltonian system with two degrees of freedom. Subsequently a one-dimensional Ito? stochastic differential equation for the system is obtained by applying the stochastic averaging method for quasi-nonintegrable Hamiltonian systems. The conditional reliability function and conditional probability density are both gained by solving the backward Kolmogorov equation numerically. Finally, a stochastic optimal control model is proposed and solved. The numerical results show the effectiveness of this method. 相似文献
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A stochastic averaging method for predicting the response of quasi partially integrable and non-resonant Hamiltonian systems to fractional Gaussian noise (fGn) with the Hurst index 1/2<H<1 is proposed. The averaged stochastic differential equations (SDEs) for the first integrals of the associated Hamiltonian system are derived. The dimension of averaged SDEs is less than that of the original system. The stationary probability density and statistics of the original system are obtained approximately from solving the averaged SDEs numerically. Two systems are worked out to illustrate the proposed stochastic averaging method. It is shown that the results obtained by using the proposed stochastic averaging method and those from digital simulation of original system agree well, and the computational time for the former results is less than that for the latter ones. 相似文献
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We studied the feedback maximization of reliability of multi-degree-of-freedom （MDOF） quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations. First, the partially averaged Ito equations are derived by using the stochastic averaging method for quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations. Then, the dynamical programming equation and its boundary and final time conditions for the control problems of maximizing the reliability is established from the partially averaged equations by using the dynamical programming principle. The nonlinear stochastic optimal control for maximizing the reliability is determined from the dynamical programming equation and control constrains. The reliability function of optimally controlled systems is obtained by solving the final dynamical programming equation. Finally, the application of the proposed procedure and effectiveness of the control strategy are illustrated by using an example. 相似文献
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In this paper, a numerical method for solving the optimal control (OC) problems is presented. The method is enlightened by the Chebyshev-Legendre (CL) method for solving the partial differential equations (PDEs). The Legen-dre expansions are used to approximate both the control and the state functions. The constraints are discretized over the Chebyshev-Gauss-Lobatto (CGL) collocation points. A Legendre technique is used to approximate the integral involved in the performance index. The OC problem is changed into an equivalent nonlinear programming problem which is directly solved. The fast Legendre transform is employed to reduce the computation time. Several further illustrative examples demonstrate the efficiency of the proposed method. 相似文献
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DENG Mao-lin ZHU Wei-qiu 《浙江大学学报(A卷英文版)》2007,8(9):1401-1407
An important functioning mechanism of biological macromolecules is the transition between different conformed states due to thermal fluctuation. In the present paper,a biological macromolecule is modeled as two strands with side chains facing each other,and its stochastic dynamics including the statistics of stationary motion and the statistics of conformational transition is studied by using the stochastic averaging method for quasi Hamiltonian systems. The theoretical results are confirmed with the results from Monte Carlo simulation. 相似文献
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ＩＮＴＲＯＤＵＣＴＩＯＮＩｎｒｅｃｅｎｔｙｅａｒｓ,ｏｒｔｈｏｇｏｎａｌｐｏｌｙｎｏｍｉａｌｓａｎｄｆｕｎｃｔｉｏｎｓｄｅｖｅｌｏｐｅｄｂｙＣｈａｎｇｅｔａｌ.( 1 986)ｈａｖｅｂｅｅｎｓｕｃｃｅｓｓｆｕｌｌｙａｐｐｌｉｅｄｉｎｔｈｅｆｉｅｌｄｏｆｄｙｎａｍｉｃｓｙｓｔｅｍｓ,ｆｏｒａｎａｌｙｓｉｓａｎｄｉｄｅｎｔｉｆｉｃａｔｉｏｎｏｆｌｉｎｅａｒｓｙｓｔｅｍｓａｎｄｔｈｅｏｐｔｉｍａｌｃｏｎｔｒｏｌ (Ｔｓａｙｅｔａｌ.,1 987) .Ｔｈｅｍａｉｎａｄｖａｎｔａｇｅｏｆｔｈｉｓｔｅｃｈｎｉｑｕｅｉｓｔｈｅ… 相似文献
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An approximate method for predicting the stationary response of stochastically excited nonlinear systems with continuous-time Markov jump is proposed. By using the stochastic averaging method, the original system is reduced to one governed by a 1D averaged Itô equation for the total energy with the Markov jump process as parameter. A Fokker-Planck- Kolmogorov (FPK) equation is then deduced, from which the approximate stationary probability density of the response of the original system is obtained for different jump rules. To illustrate the effectiveness of the proposed method, a stochastically excited Markov jump Duffing system is worked out in detail. 相似文献
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采用带有随机微分方程的非线性混合效应模型对群体药物代谢动力学数据建模,通过在状态方程中引入随机项,将常微分方程扩展到随机微分方程.和常微分方程相比,随机微分方程可解决群体药物代谢动力学模型中相关残差问题.利用贝叶斯估计对非线性混合效应随机微分方程模型参数进行估计,给出群体参数及个体参数的精确后验分布,将Gibbs和Metropolis-Hastings算法相结合,给出参数估计值.通过计算机模拟和实例分析验证了方法的可靠性,结果表明利用非线性混合效应随机微分方程模型及贝叶斯估计方法分析群体药物代谢动力学数据是可行的. 相似文献
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本文考虑多项的分数阶常微分方程。证明了其解的存在性与唯一性;导出了多项的分数阶常微分方程的解;提出了三种数值解法来近似多项的分数阶常微分方程解。第一种方法,利用Diethelm等技巧;第二种方法,利用Caputo分数阶导数,Riemann-Liouville分数阶导数,分数阶导数之间的关系;第三种方法,把多项的分数阶常微分方程转化为分数阶微分方程组,然后利用分数阶预估-校正法。最后给出了一些实际应用例子。 相似文献
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在实际的生产销售中,由于存在很多不确定因素,需求也是不确定的.在生产率确定且仓库容量有限条件下,建立了随机需求的存贮模型,并求出最优生产量,最优生产时间.最后用算例说明此模型的合理性. 相似文献
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鄂国康 《上海大学学报(英文版)》1999,3(1):25-29
１ Ｉｎｔｒｏｄｕｃｔｉｏｎ Ｔｈｅｓｔｏｃｈａｓｔｉｃｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ（ＳＤＥ）ａｒｅｕｓｅｄｉｎｍａｎｙａｒｅａｓｏｆｓｃｉｅｎｃｅａｎｄｅｎｇｉｎｅｅｒｉｎｇ．ＴｈｅｍａｉｎｐｕｒｐｏｓｅｆｏｒｓｏｌｖｉｎｇｐｒｏｂｌｅｍｓｗｉｔｈＳＤＥｉｓｔｏｏｂｔａｉｎｔｈｅｐｒｏｂａｂｉｌｉｔｙｄｅｎｓｉｔｙｆｕｎｃｔｉｏｎ（ＰＤＦ）ｏｆｔｈｅｓｔａｔｅｖａｒｉａｂｌｅｓｇｏｖｅｒｎｅｄｂｙｔｈｅＳＤＥｂｅｃａｕｓｅｍａｎｙｏｔｈｅｒｓｔａｔｉｓｔｉｃａｌａｎａｌｙｓｉｓａ… 相似文献
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Based on energy considerations, it is possible to obtain the differential equations of motion of any physical system. A statement of equilibrium involving operations on energy functions is the Lagrange equation d / OT a7' D aOV dt (aq,) -aq aq + aq. Providing that the kinetic energy T, potential energy V, and dissipation function D can be written, the differential equations of the system are obtained by following a straightforward systematic procedure. It is not necessary to employ Kirchhoff's laws or Newton's force law to obtain the equations of electrical and mechanical systems. Rather, the two kinds of systems fall within the scope of this general method. The energy method is particularly useful in dealing with electromechanical systems and with mechanical systems that combine rotation and translation. Nonlinear as well as linear systems can be handled with equal ease. Versatility of the method is shown by its application to various examples, chosen in more or less increasing order of complexity. A set of tables is provided, listing the energy functions for each basic type of electrical, mechanical and electromechanical element. Those charged with teaching students the different disciplines of dynamics and electric circuits should find herein a common meeting ground wherein one general method suffices to yield the necessary differential equations. 相似文献