随机最优控制方法识别动力学系统局部非线性

IDENTIFICATION OF LOCAL NONLINEARITIES IN DYNAMIC SYSTEM VIA STOCHASTIC OPTIMAL CONTROL APPROACH

利用随机动态规划方法可以得到线性二次型高斯问题的最优控制解．基于这一结果与系统辨识问题最优控制解的概念，将动力学系统中局部非线性结构参数的辨识问题转化为求解对应线性系统的最优控制问题，利用线性系统随机最优控制的理论与方法，结合FSM（ForceStateMapping）方法，提出了识别动力学系统中局部非线性回复力类型及结构参数的新方法．所研究系统由大的线性子结构与一个或多个非线性子结构组成，其中线性结构的模型参数已知，待辨识量为局部非线性结构参数．

In the analysis of dynamic characteristics of space structures, the connecting elementsplay an important role in the overall dynamics of the structure, which often lead to the structureexhibits local nonlinearities. Generally speaking, the main part of the structure can be regardedas linear with sufficient accuracy, but it is often difficult to model these local nonlinear elementsbecause the complexity of their configuration and operating mode. Therefore, an increasing amountof attention has recently been devoted to the identification of local nonlinearities and structureparameters of dynamic system.A new identification technique of local nonlinearities in dynamic system via stochastic optimalcontrol approach is introduced in this paper. In optimal control theory, the Linear-Quadratic-Gaussian problem have been successfully solved via stochastic dynamic programming. Based onthis result and the concept of optimal control solution of system identification problem, localnonlinearities identification of dynamic system is transformed into a stochastic optimal controlproblem. Combining this transformation with the Force-State-Mapping method, the identificationtechnique is presented in this paper to identify the types of restoring force transmitted by localnonlinear elements and their parameters. The dynamic system discussed here can be decomposedinto a large linear substructure and one or more nonlinear substructures. While the model parameters of linear substructure is known prior. Numerical simulation examples are also given tovalidate the effectiveness of the proposed method.