Adaptive estimation for nonlinear systems using reproducing kernel Hilbert spaces
Adaptive estimation for nonlinear systems using reproducing kernel Hilbert spaces
复制标题
使用再生核希尔伯特空间的非线性系统的自适应估计
DOI：
10.1007/s10444-018-9639-z
复制
发表时间：
2017
影响因子：
1.7
通讯作者：
J. Ferris
中科院分区：
文献类型：
--
作者：
Parag Bobade;Suprotim Majumdar;Savio Pereira;A. Kurdila;J. Ferris
本文扩展了由未知或不确定的非线性常微分方程控制的系统的在线自适应估计问题的传统通用框架。本文介绍的理论的核心特征是将未知函数表示为再生核希尔伯特空间（RKHS）的成员，并定义了一个分布参数系统（DPS）来控制状态估计和未知函数的估计。在全状态测量可用的假设下，本文(1)推导了无限维在线估计问题的存在性和稳定性的充分条件，(2)推导了无限维近似的有限维近似的存在性和稳定性，(3)确定了有限维近似收敛到无限维在线估计的充分条件。本文在评估函数方面引入了 RKHS 中激励持续性的新条件，该条件能够证明 RKHS 中未知函数的有限维近似的收敛性。本文研究了 RKHS 的两种特定选择，即由指数函数生成的选项和由多分辨率分析定义的多尺度核生成的选项。
This paper extends a conventional, general framework for online adaptive estimation problems for systems governed by unknown or uncertain nonlinear ordinary differential equations. The central feature of the theory introduced in this paper represents the unknown function as a member of a reproducing kernel Hilbert space (RKHS) and defines a distributed parameter system (DPS) that governs state estimates and estimates of the unknown function. Under the assumption that full state measurements are available, this paper (1) derives sufficient conditions for the existence and stability of the infinite dimensional online estimation problem, (2) derives existence and stability of finite dimensional approximations of the infinite dimensional approximations, and (3) determines sufficient conditions for the convergence of finite dimensional approximations to the infinite dimensional online estimates. A new condition for persistency of excitation in a RKHS in terms of its evaluation functionals is introduced in the paper that enables proof of convergence of the finite dimensional approximations of the unknown function in the RKHS. This paper studies two particular choices of the RKHS, those that are generated by exponential functions and those that are generated by multiscale kernels defined from a multiresolution analysis.