| 李杰,彭勇波.基于广义密度演化方程的结构随机最优控制[J].计算力学学报,2010,27(6):976~982 |
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| 基于广义密度演化方程的结构随机最优控制 |
| Generalized density evolution equation based structural stochastic optimal control |
| 投稿时间：2008-12-22 修订日期：2009-11-06 |
| DOI：10.7511/jslx20106004 |
| 中文关键词: 广义密度演化方程 Pontryagin极大值原理 LQG控制 权矩阵选择 结构性态 |
| 英文关键词:general density evolution equation Pontryagin’s maximum principles LQG control weighting matrices choices structural performance |
| 基金项目:国家自然科学基金委创新研究群体科学基金(50621062);国家高技术研究发展计划(863计划,2008AA05Z413)资助项目. |
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| 中文摘要: |
| 基于广义密度演化方程和Pontryagin极大值原理,推导了一般随机激励作用下闭环系统随机最优控制中状态向量和控制力向量的物理解答,讨论了基于二阶统计量评价的控制律参数设计准则。以物理随机地震动模型为输入,考察了单层框架结构主动锚索系统的随机最优控制,并与经典LQG控制做了比较分析。结果表明,本文提出的随机最优控制方法具有适用性和有效性。 |
| 英文摘要: |
| The celebrated Pontryagin’s maximum principles is employed in this paper to conduct the physical solutions of the state vector and the control force vector of stochastic optimal controls of closed-loop systems by synthesizing deterministic optimal control solutions of a collection of representative excitation driven systems using the generalized density evolution equation. The optimal control scheme extends the classical stochastic optimal control methods, which is practically useful to general nonlinear systems driven by non-stationary and non-Gaussian stochastic processes, and can govern the evolution details of stochastic dynamical systems, while the classical stochastic optimal control methods, such as the LQG control, essentially hold the system statistics, and cannot govern the desirable evolution details. Further, the selection strategy of weighting matrices of stochastic optimal controls is discussed to construct optimal control policies based on the control criterion of system second-order statistics assessment. The stochastic optimal control of an active tendon control system, subjected to the random ground motion represented by the physical stochastic earthquake model is investigated. Numerical investigations reveal that the structural seismic performance is significantly improved when the optimal control strategy is applied. The LQG control, however, using the nominal Gaussian white noise as the external excitation cannot design the reasonable control system for civil engineering structures. It is indicated that the developed physical stochastic optimal control methodology has the validity and applicability. |
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