基于随机牛顿算法的离散系统自适应参数估计

针对一类离散系统,提出一种基于随机牛顿算法的自适应参数估计新框架,相较于已有的参数估计算法,所提出方法仅要求系统满足有限激励条件,而非传统的持续激励条件.所提出算法的核心思想在于通过对原始代价函数的修正,在使用当前时刻误差信息的基础上融入历史误差信息,进而通过对历史信息和历史激励的复用使得持续激励条件转化为有限激励条件;然后,为了解决传统算法收敛速度慢的问题并避免潜在的病态问题,采用随机牛顿算法推导出参数自适应律,并引入含有历史信息的海森矩阵作为时变学习增益,保证参数估计误差指数收敛;最后,基于李雅普诺夫稳定性理论给出不同激励条件下所提出算法的收敛性结论和证明,并通过对比仿真验证所提出算法的有效性和优越性.

Adaptive parameter estimation of discrete-time systems based on stochastic Newton algorithm

This paper proposes a new framework for adaptive parameter estimation for discrete-time systems based on the stochastic Newton algorithm. Different to the classical parameter estimation algorithms, the convergence of the estimation error herein only requires the finite excitation(FE) condition rather than the persistent excitation(PE) condition. The main merit of the algorithm is that the original cost function is modified, where the past error information is used together with the current error information to construct the random gradient vector, so that reusing the historical information can help to relax the PE condition to the FE condition. Furthermore, to solve the problem of slow convergence of the stochastic steepest descent algorithm and avoid the potential ill-conditioned problem, the estimated inverse of the Hessian matrix is constructed as the learning gain and the stochastic Newton algorithm is used to derive the adaptive laws with its exponential convergence. Finally, the convergence of the proposed parameter estimation algorithm under different excitation conditions is evaluated via the Lyapunov theory. The effectiveness and superiority of the proposed algorithms are verified by comparative simulations.