饱和观测与非持续激励下保证性能的自适应辨识
Adaptive Identification with Guaranteed Performance Under Saturated-Observation and Non-Persistent Excitation
AI总结：
本文研究饱和观测随机系统的自适应辨识与预测问题，提出两步拟牛顿算法，在非持续激励条件下证明全局收敛与渐近正态性，并建立有限数据概率误差界。
摘要：
本文研究了具有饱和观测的随机动态系统的自适应辨识和预测问题，这类问题源于工程和社会系统的多个领域，但迄今为止仍缺乏包含实际应用所需性能保证的全面理论研究。基于此动力，本文做出了以下主要贡献：(i) 引入两步拟牛顿（TSQN）算法以提升辨识性能，该算法适用于一类典型的非线性随机系统，其输出在可能变化的饱和状态下被观测。(ii) 在尽可能弱的非持续激励（PE）条件下，建立参数估计器和自适应预测器的全局收敛性，并证明其渐近正态性，该条件可应用于具有一般非平稳和相关系统信号或数据的随机反馈系统。(iii) 利用鞅不等界或Monte Carlo实验，为任意给定有限长度数据建立有用的概率估计误差界。此外，还提供了一个数值例子以说明所提辨识算法的性能。
英文摘要：
This paper investigates the adaptive identification and prediction problems for stochastic dynamical systems with saturated observations, which arise from various fields in engineering and social systems, but up to now still lack comprehensive theoretical studies including performance guarantees needed in practical applications. With this impetus, the paper has made the following main contributions: (i) To introduce a two-step Quasi-Newton (TSQN) algorithm to improve the performance of the identification, which is applicable to a typical class of nonlinear stochastic systems with outputs observed under possibly varying saturation. (ii) To establish the global convergence of both the parameter estimators and adaptive predictors and to prove the asymptotic normality, under the weakest possible non-persistent excitation (PE) condition, which can be applied to stochastic feedback systems with general non-stationary and correlated system signals or data. (iii) To establish useful probabilistic estimation error bounds for any given finite length of data, using either martingale inequalities or Monte Carlo experiments. A numerical example is also provided to illustrate the performance of the proposed identification algorithm.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
