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Adaptive distributed parameter systems identification with enforceable identifiability conditions and reduced-order spatial differentiation

机译:具有可执行的可识别性条件和降阶空间差异的自适应分布式参数系统识别

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摘要

Presents the synthesis of adaptive identifiers for distributed parameter systems (DPS) with spatially varying parameters described by partial differential equations (PDEs) of parabolic, elliptic, and hyperbolic type. The features of the PDE setting are utilized to obtain the not directly intuitive parameter estimation algorithms that use spatial derivatives of the output data with the order reduced from that of the highest spatial plant derivative. The tunable identifier parameters are passed through the integrator block, which forms their orthogonal expansions. The latter are shown to be pointwise plant parameter estimates. In this regard, the approach of the paper is in the spirit of finite-dimensional observer realization in integrating rather than differentiating the output data, only applied to the spatial rather than temporal domain. The constructively enforceable identifiability conditions, formulated in terms of the sufficiently rich input signals referred to as generators of persistent excitation, are shown to guarantee the existence of a unique zero steady state for the parameter errors. Under such inputs, the tunable parameters in the adaptive identifiers proposed are shown to converge to plant parameters in L/sub 2/ and the orthogonal expansions of these tunable parameters-pointwise.
机译:提出了具有空间变化参数的分布式参数系统(DPS)的自适应标识符的合成,该参数由抛物线形,椭圆形和双曲线型的偏微分方程(PDE)描述。利用PDE设置的功能来获得非直接直观的参数估计算法,该算法使用输出数据的空间导数,其顺序从最高空间植物导数的顺序开始减小。可调标识符参数通过积分器块,该积分器块形成正交扩展。后者显示为逐点工厂参数估计。在这方面,本文的方法本着有限维观察者实现的精神,即集成而不是区分输出数据,仅应用于空间而不是时间域。构造上可强制执行的可识别性条件,用足够丰富的输入信号(被称为持续激励的生成器)来表示,可以保证存在针对参数误差的唯一零稳态。在这样的输入下,所提出的自适应标识符中的可调参数显示为收敛到L / sub 2 /中的工厂参数,并且这些可调参数的正交扩展是逐点收敛的。

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