论文标题
部分可观测时空混沌系统的无模型预测
Adaptive Identification with Guaranteed Performance Under Saturated-Observation and Non-Persistent Excitation
论文作者
论文摘要
本文研究了具有饱和观察结果的随机动力学系统的自适应识别和预测问题，这是由工程和社会系统中的各种领域引起的，但到目前为止，现在仍然缺乏全面的理论研究，包括实际应用所需的绩效保证。借助这一动力，本文提出了以下主要贡献：（i）引入两步的准Newton（TSQN）算法，以提高识别性能，该识别性能适用于典型类别的非线性固定系统，其输出可能在可能变化的饱和饱和效果下定位。 （ii）在最弱的非持久激发（PE）条件下，建立参数估计器和自适应预测变量的全局收敛，并证明渐近正态性，可以将其应用于具有一般非平稳性和相关系统信号或数据的随机反馈系统。 （iii）使用Martingale不平等或Monte Carlo实验，为任何给定的数据长度建立有用的概率估计误差界限。还提供了一个数值示例，以说明所提出的识别算法的性能。
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.
