A NEW STOCHASTIC OPTIMAL CONTROL STRATEGY FOR HYSTERETIC MR DAMPERS

A new stochastic optimal control strategy for randomly excited quasi-integrable Hamiltonian systems using magneto-rheological (MR) dampers is proposed. The dynamic be- havior of an MR damper is characterized by the Bouc-Wen hysteretic model. The control force produced by the MR damper is separated into a passive part incorporated in the uncontrolled system and a semi-active part to be determined. The system combining the Bouc-Wen hysteretic force is converted into an equivalent non-hysteretic nonlinear stochastic control system. Then It?o stochastic di?erential equations are derived from the equivalent system by using the stochastic averaging method. A dynamical programming equation for the controlled di?usion processes is established based on the stochastic dynamical programming principle. The non-clipping nonlin- ear optimal control law is obtained for a certain performance index by minimizing the dynamical programming equation. Finally, an example is given to illustrate the application and e?ectiveness of the proposed control strategy.

Nonlinear stochastic optimal bounded control of hysteretic systems with actuator saturation

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 It? 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 It? equation. Numerical results show that the proposed control strategy has high control effectiveness and efficiency.

Science Letters：On stochastic optimal control of partially observable nonlinear quasi Hamiltonian systems

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.

Optimal control strategies for stochastically excited quasi partially integrable Hamiltonian systems

In this paper two different control strategies designed to alleviate the response of quasi partially integrable Hamiltonian systems subjected to stochastic excitation are proposed. First, by using the stochastic averaging method for quasi partially integrable Hamiltonian systems, an n-DOF controlled quasi partially integrable Hamiltonian system with stochastic excitation is converted into a set of partially averaged It^↑o stochastic differential equations. Then, the dynamical programming equation associated with the partially averaged It^↑o equations is formulated by applying the stochastic dynamical programming principle. In the first control strategy, the optimal control law is derived from the dynamical programming equation and the control constraints without solving the dynamical programming equation. In the second control strategy, the optimal control law is obtained by solving the dynamical programming equation. Finally, both the responses of controlled and uncontrolled systems are predicted through solving the Fokker-Plank-Kolmogorov equation associated with fully averaged It^↑o equations. An example is worked out to illustrate the application and effectiveness of the two proposed control strategies.

STOCHASTIC OPTIMAL CONTROL FOR THE RESPONSE OF QUASI NON-INTEGRABLE HAMILTONIAN SYSTEMS

A strategy is proposed based on the stochastic averaging method for quasi non- integrable Hamiltonian systems and the stochastic dynamical programming principle.The pro- posed strategy can be used to design nonlinear stochastic optimal control to minimize the response of quasi non-integrable Hamiltonian systems subject to Gaussian white noise excitation.By using the stochastic averaging method for quasi non-integrable Hamiltonian systems the equations of motion of a controlled quasi non-integrable Hamiltonian system is reduced to a one-dimensional av- eraged It stochastic differential equation.By using the stochastic dynamical programming princi- ple the dynamical programming equation for minimizing the response of the system is formulated. The optimal control law is derived from the dynamical programming equation and the bounded control constraints.The response of optimally controlled systems is predicted through solving the FPK equation associated with It stochastic differential equation.An example is worked out in detail to illustrate the application of the control strategy proposed.

Optimal bounded control for maximizing reliability of Duhem hysteretic systems

The optimal bounded control of stochastic-excited systems with Duhem hysteretic components for maximizing system reliability is investigated. The Duhem hysteretic force is transformed to energy-depending damping and stiffness by the energy dissipation balance technique. The controlled system is transformed to the equivalent non- hysteretic system. Stochastic averaging is then implemented to obtain the It5 stochastic equation associated with the total energy of the vibrating system, appropriate for eval- uating system responses. Dynamical programming equations for maximizing system re- liability are formulated by the dynamical programming principle. The optimal bounded control is derived from the maximization condition in the dynamical programming equation. Finally, the conditional reliability function and mean time of first-passage failure of the optimal Duhem systems are numerically solved from the Kolmogorov equations. The proposed procedure is illustrated with a representative example.

Optimal nonlinear feedback control of quasi-Hamiltonian systems

An innovative strategy for optimal nonlinear feedback control of linear or nonlinear stochastic dynamic systems is proposed based on the stochastic averaging method for quasi-Hamiltonian systems and stochastic dynamic programming principle. Feedback control forces of a system are divided into conservative parts and dissipative parts. The conservative parts are so selected that the energy distribution in the controlled system is as requested as possible. Then the response of the system with known conservative control forces is reduced to a controlled diffusion process by using the stochastic averaging method. The dissipative parts of control forces are obtained from solving the stochastic dynamic programming equation.

具有条件马尔科夫结构的离散随机系统最优控制

基于Bellman随机非线性动态规划法,提出了具有条件马尔科夫跳变结构的离散随机系统的最优控制方法,应用随机变结构系统的性质对最优控制算法进行了简化处理,并将后验概率密度函数用条件高斯函数来逼近,针对一类具有条件马尔科夫跳变结构的线性离散随机系统,给出了其逼近最优控制算法.

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.

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^o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。

一种基于随机平均的最优时滞控制方法

基于时滞系统的随机平均法与随机动态规划原理,提出一种非线性系统的随机最优时滞控制方法.先应用时滞随机平均法,将非线性系统的随机最优时滞控制问题变换成非时滞的最优控制问题;再根据随机动态规划原理,建立其动态规划方程;由此确定最优时滞控制律;最后,通过一个例子说明该时滞控制方法的控制效果.

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It 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It 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 .

基于随机平均的非线性随机最优控制

首先建立非线性随机系统的最优控制问题,并介绍通过随机平均法导出平均系统、再由随机动态规划原理确定控制律的平均系统的非线性随机最优控制方法。然后,对于非线性随机系统的动态规划方程,提出应用随机平均法简化该方程、从而得到最优平均控制律的方法,并证明该最优平均控制律等价于平均系统的最优控制律。最后用一个例子说明方法及等价性,并指出在一定条件下,最优平均控制律将是动态规划方程的精确解。

邻接高耸结构的随机最优控制

本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Ito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。

谐和与宽带随机激励下拟可积哈密顿系统的最优时滞控制

研究在谐和与宽带随机激励下拟可积哈密顿系统的最优时滞控制。首先,简要叙述谐和与宽带随机激励下的最优时滞控制问题的提法;其次,将时滞的控制力用非时滞的状态变量近似表示,从而将原时滞控制系统转换为非时滞的控制系统;然后,考虑到系统固有频率与谐和激励频率之间可能的共振关系,运用随机平均法,得到部分平均It随机微分方程,再运用随机动态规划原理,建立动态规划方程,即Hamilton-Jacobi-Bellman(HJB)方程,求解得到控制力,通过求解与完全平均的It随机微分方程对应的Fokker-Planck-Kolmogorov(FPK)方程或者Monte Carlo数值模拟得到系统的响应;最后,将上述控制策略应用于潜水艇纵轴振动控制,并通过Monte Carlo数值模拟结果来评估这一控制策略的控制效果和控制效率。

不确定结构非线性随机最优控制的鲁棒性

对地震地面运动引起的不确定剪切结构振动的非线性随机最优控制的鲁棒性进行了研究.基于系统参数不确定性与激励随机性的独立性假定,将具平均参数的名义结构进行模态变换解耦,运用拟可积哈密顿系统随机平均法与随机动态规划原理得到非线性随机最优控制力;利用随机平均法与概率分析估算受控的具有不确定参数结构的均方根响应、控制效果与控制效率的均值和标准差;以受控结构均方根响应、控制效果与控制效率的变差系数对不确定参数变差系数的敏感度作为鲁棒性评价指标,对非线性随机最优控制进行评价.通过对一个承受宽带随机基础激励的含不确定参数的三层剪切结构的数值计算与分析表明,该非线性随机最优控制策略对不确定参数具有很好的鲁棒性.

多自由度拟不可积哈密顿系统的随机分数阶最优控制

推广了适用于分数阶系统控制的随机分数阶最优控制策略,提出了高斯白噪声激励下多自由度拟不可积哈密顿系统以响应最小化为目标的随机分数阶最优控制策略.首先,应用拟不可积哈密顿系统随机平均法,将受控系统简化为关于能量的部分平均伊藤方程.然后,将控制性能指标中关于控制力的部分表示为分数阶形式,结合随机动态规划原理,建立并求解部分平均系统的无界遍历控制的随机动态规划方程,获得了随机分数阶最优控制律.最后,采用一个算例验证了随机分数阶控制策略的控制效果和控制效率.研究表明,随机分数阶最优控制策略对传统的整数阶随机动力学系统同样适用,能比传统的整数阶控制策略取得更好的控制效果.另外,随着激励强度增加,整数阶控制策略的控制效率显著降低;而分数阶控制策略的控制效率虽比整数阶控制策略的控制效率略低,但随着激励强度的增加,分数阶控制策略的控制效率缓慢上升并趋于平稳,可以有效地缓解控制效率与控制效果之间的矛盾.

Feedback maximization of reliability of MDOF quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations

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 It 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.