伪谱法在非线性结构系统随机最优控制中的应用

Wei Song, S. Dyke
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引用次数: 6

摘要

本文给出了非线性随机系统最优控制策略的数值研究结果。所研究的系统是机械振荡器和阻尼装置。得到最优控制策略的数值方法涉及求解非线性偏微分方程- Hamilton-Jacobi-Bellman方程。由于土木工程结构系统在极端荷载条件下通常表现出非线性滞回行为,因此所获得的控制策略的潜在应用可以提供最优反馈控制律,以减小系统在随机激励(如地震、风荷载和海浪)下的响应。通过数值算例验证了所提最优控制方案的最优性和有效性。首先,利用线性振荡器与封闭形式的解进行比较,验证得到的解确实是最优解。然后将该方法应用于若干非线性系统。在每种情况下,通过比较最优控制下的系统响应和成本与使用线性最优控制获得的系统响应和成本来证明最优性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Application of pseudospectral method in stochastic optimal control of nonlinear structural systems
This paper presents the results of numerical study on the optimal control strategy of nonlinear stochastic systems. The systems under investigation are mechanical oscillators and a damping device. The numerical approach to obtain the optimal control strategy involves solving a nonlinear partial differential equation - the Hamilton-Jacobi-Bellman equation. Since civil engineering structural systems usually exhibit nonlinear hysteretic behavior under extreme loading conditions, the potential application of the obtained control strategy could provide an optimal feedback control law to reduce the system response under the random excitations (such as earthquakes, wind load and sea waves). Several numerical examples are presented to verify optimality and demonstrate the efficacy of the proposed optimal control solution. First, a linear oscillator is used to verify that the obtained solution is indeed the optimal solution by comparing it to the closed form solution. Then the proposed method is applied to several nonlinear systems. In each case, optimality is demonstrated by comparing the system responses and costs under optimal control with those obtained using linearized optimal control.
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