宽带激励下非线性振动系统响应的最小化控制

将一种基于广义谐和函数的随机平均法和随机动态规划原理相结合，提出了一种非线性随机最优控制方法，可以为受宽带激励的单自由度强非线性振动系统设计最优控制规律，以使得系统的稳态响应最小化。方法中的随机平均法用来得到受控系统位移幅值的Ito随机微分方程；用随机动态规划原理为系统稳态响应最小化建立动态规划方程；在控制力为有界的条件下，从动态规划方程中可以导出最优控制规律；通过求解FPK方程得到受控系统的响应。本文用一个具体的例子阐述了这一控制方法的实施过程。     

邻接高耸结构的随机最优控制

文基于随机动态规划原理与随机平均法，提出耦合相邻高耸结构的随机最优控制方法。先建立任意层数并在任意层高处控制联接的耦合结构的缩聚模型，再运用随机平均法导出关于模态能量的It6随机微分方程，应用随机动态规划原理建立动态规划方程，由此可确定最优控制律。将结构的响应控制化为模态能量控制，缩减控制系统的维数。用高斯随机过程模拟地震激励，可计及其功率谱特性。数值结果表明该耦合结构控制方法的有效性。     

地震激励下20层钢结构基准模型的非线性随机最优控制

建筑结构基准问题常用来比较各种振动控制策略的优劣。运用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(NSO)控制策略,研究了地震激励下20层钢结构基准模型的振动控制。建立基准模型的系统运动方程,通过模态变换转换到模态坐标下进行研究。由于结构的状态只有部分是可观测的,可通过分离原理将部分观测问题转化成完全可观测问题,由Kalman滤波方法得到系统状态的条件均值。运用拟可积Hamil-ton系统随机平均法得到随机平均方程,对部分模态进行控制求解。通过求解动态规划方程得到非线性的最优控制力,对结构的响应进行控制。将NSO控制得到的性能评价指标与线性二次型高斯(LQG)最优控制得到的评价指标进行对比,发现该非线性随机最优控制策略更加有效。     

迟滞的磁流变阻尼器的随机最优控制力

用Bouc-Wen迟滞模型描述磁流变阻尼器的动力学特性,分离阻尼器控制力的半主动部分和被动部分,被动部分结合到受控系统.先将该系统变换成等价的非迟滞的非线性随机控制系统,再运用随机平均法导出关于能量的It随机微分方程.根据随机动态规划原理,建立控制总能量的动态规划方程,并由此确定非clip的最优控制力.最后通过数值结果表明该控制力的有效性.     

拉索非线性随机振动的最优有界半连续控制

研究斜拉索非线性随机振动的最优有界半连续控制。建立受控拉索的横向非线性运动方程,运用伽辽金法推导多模态耦合的振动方程;考虑控制力的有界性,建立多自由度非线性索系统的随机最优控制问题方程,应用随机平均法、动态规划原理与变分原理确定HJB方程并得到最优有界半连续控制律,最后通过数值结果说明该最优控制对于斜拉索非线性随机振动能够达到较好的实际控制效果。     

地震激励邻接高层建筑的随机最优控制

采用控制设备联接相邻的高层建筑以降低其地震响应是一个切实有效的方法。基于随机动态规划原理与随机平均法,提出耦合相邻高层建筑的随机最优控制方法。先建立任意层数并在任意层高处控制联接的耦合结构的缩聚模型,再运用随机平均法导出关于模态能量的oIt随机微分方程,应用随机动态规划原理建立动态规划方程,由此可确定最优控制律。将结构的响应控制化为模态能量控制,缩减控制系统的维数。用高斯随机过程模拟地震激励,可计及其功率谱特性。数值结果表明该耦合结构随机最优控制方法的有效性。     

不确定性拉索非线性随机振动的最优控制

为实施不确定性斜拉索非线性随机振动的最优控制,建立受控拉索的横向非线性运动方程,运用伽辽金法推导多模态耦合的振动方程。同时,考虑系统的不确定参数,建立不确定性系统的随机最优控制问题。随后,应用随机平均法、微分对策理论与动态规划方法确定HJI方程并得到极大极小控制律,最后通过数值结果说明该最优控制对于斜拉索非线性随机振动能够达到较好控制效果。     

非线性系统随机振动响应限界极大极小控制

研究非线性系统随机振动的限界极大极小最优控制。引入调控变量放大振动峰响应,用高阶多项式作为性能指标函数,提高其中峰值占比,建立非线性随机振动峰响应的极小化最优控制问题方程;应用随机动态规划原理建立HJB方程,考虑控制作用的有界性,确定半连续与跳变型极大极小最优控制律;最后通过数值结果,说明该最优控制能够有效地抑制非线性随机振动,并调控变量、控制界限、跳变型控制等对于控制效果的影响。     

基于非线性随机最优控制的大跨度斜拉桥地震响应Benchmark问题研究

大跨度斜拉桥Benchmark问题的振动控制研究是当前国际结构控制研讨会的重要议题之一。以美国Bill Emerson Memorial斜拉桥第二阶段Benchmark模型为研究对象,在非线性随机动力学与控制的拟哈密顿理论体系框架下,运用基于随机平均法和随机动态规划原理的非线性随机最优（NSO）控制策略,对地震作用下的Benchmark模型进行MATLAB仿真分析。将最优控制力和性能评价指标与线性二次型Gauss（LQG）控制的计算结果进行对比,得出非线性随机最优控制策略能够更加有效地抑制斜拉桥的地震响应,提高结构的动力稳定性和抗震能力,具有更好的控制效果,对实际桥梁工程的振动控制具有较强的指导意义和适用价值。     

MRVE夹层梁随机振动的最优跳变参数控制

研究MRVE夹层梁随机振动的最优参数控制。建立夹层梁的运动微分方程,运用伽辽金法转化为含非线性参数控制项的振动方程;考虑控制参数的有界性,建立系统最优参数控制问题,应用随机动态规划原理与Bang-Bang策略确定HJB方程并得到最优有界非线性跳变参数控制律,最后通过数值结果说明该最优控制对于MRVE夹层梁随机振动能够达到显著控制效果。     

Nonlinear stochastic optimal control of Preisach hysteretic systems

The nonlinear stochastic optimal control of Preisach hysteretic systems is studied, and the control procedure is illustrated with an example of the single-degree-of-freedom Preisach system. The Preisach hysteretic system subjected to a stochastic excitation is first replaced by an equivalent non-hysteretic nonlinear stochastic system with displacement-amplitude-dependent damping and stiffness, by using the generalized harmonic balance technique. Then, the relationship between the displacement amplitude and total system energy is established, and the equivalent damping and stiffness coefficients are expressed as functions of the system energy. The averaged Itô stochastic differential equation for the system energy as one-dimensional controlled diffusion process, is derived by using the stochastic averaging method of energy envelope. For the semi-infinite time-interval ergodic control, the dynamical programming equation is obtained based on the stochastic dynamical programming principle, and is solved to yield the optimal control force. Finally, the Fokker–Planck–Kolmogorov equation associated with the averaged Itô equation is established, and the stationary probability density of the system energy is obtained, from which the variances of the controlled system response and the optimal control force are predicted and the control efficacy is evaluated. Numerical results show that the proposed control strategy for Preisach hysteretic systems is very effective and efficient.     

A bounded optimal control for maximizing the reliability of randomly excited nonlinear oscillators with fractional derivative damping

In this paper, a bounded optimal control for maximizing the reliability of randomly excited nonlinear oscillators with fractional derivative damping is proposed. First, the partially averaged It? equations for the energy processes of individual degree of freedom are derived by using the stochastic averaging method. Second, the dynamical programming equations for the control problems of maximizing the reliability function and maximizing the mean first passage time are established from the partially averaged It? equations by using the dynamical programming principle. The optimal control law is derived from the dynamical programming equation and control constraints. Third, the conditional reliability function and mean first passage time of the optimally controlled system are obtained by solving the backward Kolmogorov equation and Pontryagin equation associated with the fully averaged It? equation, respectively. The application of the proposed procedure and effectiveness of the control strategy are illustrated by using two examples. Besides, the effect of fractional derivative order on the reliability of the optimally controlled system is examined.     

Optimal bounded control of harmonically and stochastically excited strongly nonlinear oscillators

A procedure for designing optimal bounded control to minimize the response of harmonically and stochastically excited strongly nonlinear oscillators is proposed. First, the stochastic averaging method for controlled strongly nonlinear oscillators under combined harmonic and white noise excitations using generalized harmonic functions is introduced. Then, the dynamical programming equation for the control problem of minimizing response of the systems is formulated from the partially completed averaged Itô equations by using the dynamical programming principle. The optimal control law is derived from the dynamical programming equation and control constraint without solving the dynamical programming equation. Finally, the stationary probability density of the amplitude and mean amplitude of the optimally controlled systems are obtained from solving the reduced Fokker–Planck–Kolmogorov equation associated with fully completed averaged Itô equations. An example is given to illustrate the proposed procedure and the results obtained are verified by using those from digital simulation.     

Feedback stabilization of quasi nonintegrable Hamiltonian systems under combined Gaussian and Poisson white noise excitations

A procedure for designing a feedback control to asymptotic Lyapunov stability with probability one of quasi nonintegrable Hamiltonian systems under combined Gaussian and Poisson white noise excitations is proposed. First, a one dimensional partially averaged Itô stochastic differential equation for controlled Hamiltonian is derived from the motion equations of the system by using the stochastic averaging method. Second, the dynamical programming equation for the ergodic control problem of the averaged system with undetermined cost function is set up based on the dynamical programming principle and the jump–diffusion chain stochastic differential rules. The optimal control law is obtained by solving the dynamical programming equation. Third, the analytical expression for the largest Lyapunov exponent of the averaged system is derived. Finally, the asymptotic Lyapunov stability with probability one of the originally controlled system is analyzed approximately by using the largest Lyapunov exponent. The cost function and optimal control forces are determined by the requirements of stabilizing the system. An example is worked out in detail to illustrate the effectiveness of the proposed method for stabilization control, and the control effect of the proposed feedback stabilization varies with the change of parameters is also studied in this paper, such as, the greater the excitation intensity of Gaussian and Poisson white noise, the better the stabilization control effect.     

Feedback minimization of the first-passage failure of a hysteretic system under random excitations

The stochastic optimal bounded control of a hysteretic system for minimizing its first-passage failure is presented. The hysteretic system subjected to random excitation is firstly replaced by an equivalent nonlinear non-hysteretic system. The controlled non-hysteretic system is reduced to a one-dimensional controlled diffusion process by using the stochastic averaging of the energy envelope method. The dynamical programming equations and their associated boundary and final-time conditions for the problems of maximization of reliability and mean first-passage time are formulated. The optimal control law is derived from the dynamical programming equations and the control constraints. The dynamical programming equations for the maximum reliability problem and the mean first-passage time problem are finalized and solved numerically. Finally, numerical results are worked out to illustrate the application and effectiveness of the proposed method.     

随机最优控制下矩形薄板受面内随机参数激励的首次穿越研究

根据建立了四边简支受控矩形薄板受面内高斯白噪声激励的振动模型,并用Galerkin变分法将其化简为二自由度常微分非线性动力学方程。又利用拟不可积Hamilton系统平均理论将方程等价为一个一维的Ito随机过程,随后结合随机动态规划方法,得到了使系统可靠性最大的随机最优控制策略。最后建立了受控系统的条件可靠性函数所满足的Backward Kolmogorov(BK)方程,根据初始条件和边界条件得出数值结果。数值结果表明,随机最优控制对系统的可靠性提升有明显作用