系统辨识算法的复杂性、收敛性及计算效率研究

Complexity, convergence and computational efficiency for system identification algorithms

实践中经常会遇到大型计算问题和优化问题,使得求解问题算法的复杂性、计算量和计算精度等成为突出问题,特别是大规模非线性多变量系统的辨识.对此,提出几个有趣的研究课题:1)利用信息滤波技术和多新息辨识理论研究能提高辨识精度的大规模系统辨识理论与方法;2)利用递阶辨识原理研究维数高、变量数目多、计算量小的多变量系统递阶辨识方法;3)利用鞅收敛理论建立非线性多变量系统辨识方法的收敛理论;4)利用并行计算与递阶计算技术提高辨识算法的计算效率,以解决一类大规模非线性多变量系统的模型化问题.

In practice, one often encounters large-scale computational problems and optimization problems, so that the complexity, computation and computational accuracy of algorithms for solving these problems become a prominent issue, especially for the identification algorithms of large-scale nonlinear multi-variable systems. Therefore, the interesting research projects are proposed as follows： 1） the information filtering technology and the multi-innovation identification theory are used to study the identification methods for large-scale nonlinear systems, which can improve the identification accuracy; 2） the hierarchical identification principle is used to study the hierarchical identification methods for multi-variable systems with high dimensionalities and more variables so as to reduce computational complexity; 3） the martingale convergence theory is used to establish the convergence theory of the identification methods for nonlinear multi-variable systems; 4） the parallel computing and the hierarchical computation are used to enhance the computational efficiency so as to solve the modeling problems of a class of large-scale nonlinear multi-variable systems.