学习辨识:最小二乘算法及其重复一致性

针对重复时变系统, 提出学习辨识方法用于估计系统的时变参数. 讨论了有限时间作业区间上重复运行的时变系统以及周期时变系统两种情形. 文中给出最小二乘学习算法的推导过程, 并分析了所提算法的收敛性. 结果表明, 当重复持续激励条件成立时, 提出的学习算法具有重复一致性, 能够给出时变参数的完全估计. 通过数值算例进一步验证了学习算法的有效性.

Learning Identification: Least Squares Algorithms and Their Repetitive Consistency

This paper presents a learning identification method for stochastic systems with time-varying parametric uncertainties. The systems undertaken perform tasks repetitively over a pre-specified finite-time interval, and a least squares learning algorithm is derived on the basis of the repetitive operations. The learning identification method applies to periodically time-varying systems. It is shown that the estimates converge to the time-varying values of the parameters, and the complete estimation can be achieved under repetitive persistent excitation condition, a sufficient condition for establishing repetitive consistency of the learning algorithms. Numerical results are presented to demonstrate the effectiveness of the proposed learning algorithms.