拟不可积Hamilton系统响应的随机最优控制

提出了一种基于拟不可积Hamilton系统随机平均法和随机动态规划原理的控制策略.它可以对受高斯白噪声激励的拟不可积Hamilton系统进行非线性随机最优控制,以使系统的响应最小化.利用拟不可积Hamilton系统随机平均法可以将受控的拟不可积Hamilton系统降维成一维的Ito随机微分方程.利用随机动态规划原理可以为系统响应最小化问题建立动态规划方程.在控制力为有界的条件下,从动态规划方程中可以确定出最优控制规律.受控系统的响应是通过求解与Ito随机微分方程相联系的FPK方程得到的,用一个例子阐述了这一随机最优控制策略的实施过程.     

STOCHASTIC OPTIMAL VIBRATION CONTROL OF PARTIALLY OBSERVABLE NONLINEAR QUASI HAMILTONIAN SYSTEMS WITH ACTUATOR SATURATION

An optimal vibration control strategy for partially observable nonlinear quasi Hamiltonian systems with actuator saturation is proposed. First,a controlled partially observable non-linear system is converted into a completely observable linear control system of finite dimension based on the theorem due to Charalambous and Elliott. Then the partially averaged It stochastic differential equations and dynamical programming equation associated with the completely observable linear system are derived by using the stochastic averaging method and stochastic dynamical programming principle,respectively. The optimal control law is obtained from solving the final dynamical programming equation. The results show that the proposed control strategy has high control effectiveness and control effciency.     

STOCHASTIC OPTIMAL CONTROL OF HYSTERETIC SYSTEMS UNDER EXTERNALLY AND PARAMETRICALLY RANDOM EXCITATIONS

A stochastic optimal control method for nonlinear hysteretic systems under exter-nally and/or parametrically random excitations is presented and illustrated with an example ofhysteretic column system.A hysteretic system subject to random excitation is first replaced bya nonlinear non-hysteretic stochastic system.An It stochastic differential equation for the to-tal energy of the system as a one-dimensional controlled diffusion process is derived by usingthe stochastic averaging method of energy envelope.A dynamical programming equation is thenestablished based on the stochastic dynamical programming principle and solved to yield the op-timal control force.Finally,the responses of uncontrolled and controlled systems are evaluatedto determine the control efficacy.It is shown by numerical results that the proposed stochasticoptimal control method is more effective and efficient than other optimal control methods.     

ON THE STABILITY BOUNDARY OF HAMILTONIAN SYSTEMS

ＩｎｔｒｏｄｕｃｔｉｏｎＭａｎｙｍｅｃｈａｎｉｃａｌｓｙｓｔｅｍｓｃａｎｂｅｖｉｅｗｅｄａｓｌｉｎｅａｒＨａｍｉｌｔｏｎｉａｎｓｙｓｔｅｍｓ.Ｗｈｅｎｗｅｓｔｕｄｙｔｈｅｅｆｆｅｃｔｓｏｆｓｙｓｔｅｍｐａｒａｍｅｔｅｒｓｏｎｔｈｅｂｅｈａｖｉｏｒｏｆｔｈｅｓｙｓｔｅｍｓ,ｔｈｅｓｙｓｔｅｍｃａｎｂｅｒｅｇａｒｄｅｄａｓｔｈｅｓｙｓｔｅｍｄｅｐｅｎｄｉｎｇｏｎｐａｒａｍｅｔｅｒｓ.Ｖｅｒｙｉｍｐｏｒｔａｎｔｓｙｓｔｅｍｐａｒａｍｅｔｅｒｓ ,ｓｕｃｈａｓｃｒｉｔｉｃａｌｌｏａｄ ,ｃｒｉｔｉｃａｌａｎｇ…     

NEW METHOD FOR THE CONSTRUCTION OF INTEGRABLE HAMILTONIAN SYSTEMS

ＡＮＥＷＭＥＴＨＯＤＦＯＲＴＨＥＣＯＮＳＴＲＵＣＴＩＯＮＯＦＩＮＴＥＧＲＡＢＬＥＨＡＭＩＬＴＯＮＩＡＮＳＹＳＴＥＭＳＧａｏＰｕｙｕｎ（高普云)（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮａｎｊｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｎａｎｉｊｉｎｇ２１０?..     

Optimal Bounded Control for Minimizing the Response of Quasi Non-Integrable Hamiltonian Systems

A strategy for designing optimal bounded control to minimize theresponse of quasi non-integrable Hamiltonian systems is proposed basedon the stochastic averaging method for quasi non-integrable Hamiltoniansystems and the stochastic dynamical programming principle. Theequations of motion of a controlled quasi non-integrable Hamiltoniansystem are first reduced to an one-dimensional averaged Itô stochasticdifferential equation for the Hamiltonian by using the stochasticaveraging method for quasi non-integrable Hamiltonian systems. Then, thedynamical programming equation for the control problem of minimizing theresponse of the averaged system is formulated based on the dynamicalprogramming principle. The optimal control law is derived from thedynamical programming equation and control constraints without solvingthe equation. The response of optimally controlled systems is predictedthrough solving the Fokker–Planck–Kolmogrov (FPK) equation associatedwith completely averaged Itô equation. Finally, two examples are workedout in detail to illustrate the application and effectiveness of theproposed control strategy.     

随机结构动力反应分析的概率密度演化方法

提出了随机结构动力反应分析的概率密度演化方法．基于有限单元法基本原理,导出了含有随机参数的结构反应状态方程,进而,通过引入扩展状态向量,建立了随机结构反应的概率密度演化方程．将精细时程积分方法与Lax-Wendroff差分格式相结合,探讨了求解概率密度演化方程的数值方法．对一个8层层间剪切型随机结构进行了算例分析,并与Monte Carlo方法的结果进行了比较．研究表明,随机结构反应的概率密度具有演化特征,且概率密度曲线与正态分布差异甚大,甚至可能出现双峰曲线．     

First-passage time of quasi-non-integrable-Hamiltonian system

Studies on first-passage failure are extended to the multi-degree-of-freedom quasi-non-integrable-Hamiltonian systems under parametric excitations of Gaussian white noises in this paper. By the stochastic averaging method of energy envelope, the system's energy can be modeled as a one-dimensional approximate diffusion process by which the classical Pontryagin equation with suitable boundary conditions is applicable to analyzing the statistical moments of the first-passage time of an arbitrary order. An example is studied in detail and some numerical results are given to illustrate the above procedure. The project supported by the Post-Doctoral Foundation of China     

拟哈密顿系统非线性随机最优控制

主要介绍近十几年来拟哈密顿系统非线性随机最优控制理论方法及其应用的研究成果, 包括基于拟哈密顿系统随机平均法与随机动态规划原理的非线性随机最优控制基本策略, 即响应极小化控制、随机稳定化、首次穿越损坏最小化控制、以概率密度为目标的控制, 为将它们应用于工程实际而作的部分可观测系统最优控制、有界控制、时滞控制、半主动控制、极小极大控制的进一步研究, 以及综合考虑这些实际问题的非线性随机最优控制的综合策略, 非线性随机最优控制在滞迟系统、分数维系统等中的若干应用, 介绍与这些研究有关的背景, 并指出今后有待进一步研究的问题.     

NUMERICAL SOLUTIONS OF OPTIMAL CONTROL FOR THERMALLY CONVECTIVE FLOWS

We study the numerical solution of optimal control problems associated with two-dimensional viscous incompressible thermally convective flows. Although the techniques apply to more general settings, the presentation is confined to the objectives of minimizing the vorticity in the steady state case and tracking the velocity field in the non-stationary case with boundary temperature controls. In the steady state case we develop a systematic way to use the Lagrange multiplier rules to derive an optimality system of equations from which an optimal solution can be computed; finite element methods are used to find approximate solutions for the optimality system of equations. In the time-dependent case a piecewise-in-time optimal control approach is proposed and the fully discrete approximation algorithm for solving the piecewise optimal control problem is defined. Numerical results are presented for both the steady state and time-dependent optimal control problems. © 1997 John Wiley & Sons, Ltd.     

A NEW STOCHASTIC OPTIMAL CONTROL STRATEGY FOR HYSTERETIC MR DAMPERS

I. INTRODUCTION Magneto-rheological (MR) ?uid as a smart material possesses fairly good essential characteristics suchas reversible change between liquid and semi-solid in milliseconds with a controllable yield strengthwhen exposed to a magnetic ?eld. A…     

FEEDBACK CONTROL OPTIMIZATION FOR SEISMICALLY EXCITED BUILDINGS

A feedback control optimization method of partially observable linear structures via stationary response is proposed and analyzed with linear building structures equipped with control devices and sensors. First, the partially observable control problem of the structure under horizontal ground acceleration excitation is converted into a completely observable control problem. Then the It6 stochastic differential equations of the system are derived based on the stochastic averaging method for quasi-integrable Hamiltonian systems and the stationary solution to the Fokker-Plank-Kolmogorov （FPK） equation associated with the It6 equations is obtained. The performance index in terms of the mean system energy and mean square control force is established and the optimal control force is obtained by minimizing the performance index. Finally, the numerical results for a three-story building structure model under E1 Centro, Hachinohe, Northridge and Kobe earthquake excitations are given to illustrate the application and the effectiveness of the proposed method.     

Stochastic Stabilization of Quasi-Partially Integrable Hamiltonian Systems by Using Lyapunov Exponent

A procedure for designing a feedback control to asymptoticallystabilize, with probability one, a quasi-partially integrableHamiltonian system is proposed. First, the averaged stochasticdifferential equations for controlled r first integrals are derived fromthe equations of motion of a given system by using the stochasticaveraging method for quasi-partially integrable Hamiltonian systems.Second, a dynamical programming equation for the ergodic control problemof the averaged system with undetermined cost function is establishedbased on the dynamical programming principle. The optimal control law isderived from minimizing the dynamical programming equation with respectto control. Third, the asymptotic stability with probability one of theoptimally controlled system is analyzed by evaluating the maximalLyapunov exponent of the completely averaged Itô equations for the rfirst integrals. Finally, the cost function and optimal control forces aredetermined by the requirements of stabilizing the system. An example isworked out in detail to illustrate the application of the proposedprocedure and the effect of optimal control on the stability of thesystem.     

IMPULSIVE CONTROL FOR THE STABILIZATION AND SYNCHRONIZATION OF LUR'E SYSTEMS

IntroductionInpractice ,thereexistmanyexamplesofimpulsivecontrolsystems (seeRefs.[1 ,2 ,3 ] ) .Recently ,impulsivecontrolhasbeenwidelyusedtostabilizeandsynchronizechaoticsystems(seeRefs.[4～ 1 5] ) .Forexample,thepredictivePoincarecontrol[4 ]andtheoccasionalproportionalfeedbackcontrol[5 ]aretwoimpulsivecontrolschemeswithvaryingimpulsiveintervals.Yangetal.inRefs.[7,1 1 ]studied ,respectively ,thestabilizationandsynchronizationofaclassofchaoticsystemscalledLorenzsystems .YangandChuainRef.[1 …     

随机激励下滞迟系统的稳态响应闭合解

滞迟系统属于一类典型的强非线性系统,滞迟力不仅取决于系统的瞬时变形,还与变形历程有关.虽然滞迟系统的随机振动问题已被广泛研究,但至今尚未得到滞迟系统随机响应概率密度函数的精确闭合解.本文运用迭代加权残值法获得了高斯白噪声激励下Bouc-Wen滞迟系统稳态响应概率密度函数的近似闭合解.首先,运用等效线性化法求出系统的稳态高斯概率密度函数;然后以此构造权函数,应用加权残值法求得了系统指数多项式形式的非高斯概率密度函数;最后引入迭代的过程,逐步优化权函数,提高计算所得结果的精度.以随机地震激励下钢纤维陶粒混凝土结构的稳态响应作为算例,其中Bouc-Wen模型的参数是基于拟静力学试验数据,并应用最小二乘法辨识获得.与Monte Carlo模拟结果相比,等效线性化法得到的结果精度较差;由加权残值法得到的结果能够表现出非线性特征,但其精度依然无法令人满意;采用迭代加权残值法得到的近似闭合解与Monte Carlo模拟的结果吻合非常好;对于较强随机激励情形,采用渐进迭代加权残值法具有较高的求解效率,所获得的理论解析解具有较高的精度.结果表明,所获得的近似闭合解不仅对于土木工程领域具有重要的实际应用价值,而且还可作为检验其他非线性系统随机响应预测方法的精度的标准.     

随机激励的耗散的哈密尔顿系统的平稳解

本文首先为一般的随机激励的耗散的哈密尔顿系统得到精确的平稳解,然后在此基础上为类似而更为一般的系统发展了等效非线性系统法。     

KALMAN-FILTER-BASED OBSERVER DESIGN AROUND OPTIMAL CONTROL POLICY FOR GAS PIPELINES

Seeking the optimal operating policy by an off-line controller for pipelines carrying natural gas has an inherent state estimation problem associated with deviations from demand forecast. This paper presents a Kalman-filter-based observer for the real-time estimation of deviations from the states previously obtained by an off-line controller optimally, around an expected demand function. The observer is based on the linearized form of the non-linear partial differential equations which are the state space representation of isothermal and unidirectional gas flow through a pipeline. Data for the observer are produced by a dynamic simulator. The simulator and linearized observer equations are solved using an implicit finite element method. The observer has been tested on a pipeline subject to certain deviations from demand forecast. It converge s in a short span of time. © 1997 by John Wiley & Sons, Ltd.     

THE OPTIMAL CONTROL VARIATIONAL PRINCIPLE AND FINITEELEMENTS ANALYSIS FOR VISCOPLASTIC DYNAMICS

I.Viscoplastic-DynamicsConstitutiveRelationThestructurematerialwouldarisesimultaneouslytheelasticity,viscosityandplasticityindynamichighstraincondition.Atpresent,theovcrstressmodel,viscoplasticitymodel,quasi-linearconstitutiverelationtheoryandintrinsicvar…     

结构控制中输出反馈鲁棒极点配置优化方法

给出了输出反馈鲁棒性极点配置的数学描述和数值解法,基于任何结构控制都要求极点对系统矩阵元素的改变不敏感,通过选择鲁棒度量,并以其尽可能小为判据,用优化方法寻求近似解,最后将该方法应用于一个大跨度桥在确定的运动载荷作用下的控制,计算结果表明方法合理、有效。     

随机激励的耗散的Hamilton系统理论的研究进展

近几年中,利用Ｈａｍｉｌｔｏｎ系统的可积性与共振性概念及Ｐｏｉｓｓｏｎ括号性质等,提出了高斯白噪声激励下多自由度非线性随机系统的精确平稳解的泛函构造与求解方法,并在此基础上提出了等效非线性系统法,提出了拟Ｈａｍｉｌｔｏｎ系统的随机平均法,并在该法基础上研究了拟Ｈａｍｉｌｔｏｎ系统随机稳定性、随机分岔、可靠性及最优非线性随机控制,从而基本上形成了一个非线性随机动力学与控制的Ｈａｍｉｌｔｏｎ理论框架．本文简要介绍了这方面的进展．