基于梯度的扰动时变系统辨识算法及其收敛性

根据工程背景,提炼出了一类时变系统(亦称为广义时变系统或扰动时变系统)的数学描述模型．扰动时变系统是指参数随系统可测扰动量变化的一类时变系统．利用梯度搜索原理,提出了这类时变系统的投影算法、随机梯度和遗忘梯度辨识方法,并应用鞅超收敛定理分析了算法的收敛性．由于提出的随机梯度算法同时还利用了系统扰动量所含的信息,因而可以给出时变参数的一致估计．数字仿真验证了提出方法的有效性．

Gradient Based Identification Algorithm and Its Convergence for Disturbance Time-Varying Systems

Generalized time-varying systems (TVS) or disturbance TVS is a class of time-varying systems whose parameters change with some measurable disturbances of the systems, and exist widely in industry processes. The identification model of this class of time-varying systems and the projection algorithm, stochastic gradient algorithm and forgetting gradient algorithm for this class of TVS is presented by using the gradient search principle. Convergence analysis using the martingale hyperconvergence theorem indicates that the stochastic gradient algorithm can give consistent estimates of the time-varying parameters as it uses additive information of the disturbances besides input and output data. The digital simulation shows that the proposed algorithm is effective.