文章基本信息

标题：Extremum Seeking for Maximizing Higher Derivatives of Unknown Maps in Cascade with Reaction-Advection-Diffusion PDEs
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作者：Tiago Roux Oliveira ; Jan Feiling ; Miroslav Krstic 等
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2019
卷号：52
期号：29
页码：210-215
DOI：10.1016/j.ifacol.2019.12.651
语种：English
出版社：Elsevier
摘要：We present a generalization of the scalar Newton-based extremum seeking algorithm, which maximizes the map’s higher derivatives in the presence of dynamics described by Reaction-Advection-Diffusion (RAD) equations. Basically, the effects of the Partial Differential Equations (PDEs) in the additive dither signals are canceled out using the trajectory generation paradigm. Moreover, the inclusion of a boundary control for the RAD process stabilizes the closed-loop feedback system. By properly demodulating the map output corresponding to the manner in which it is perturbed, the extremum seeking algorithm maximizes the n-th derivative only through measurements of the own map. The Newton-based extremum seeking approach removes the dependence of the convergence rate on the unknown Hessian of the higher derivative, an effort to improve performance and remove limitations of standard gradient-based extremum seeking. In particular, our RAD compensator employs the same perturbation-based (averaging-based) estimate for the Hessian’s inverse of the function to be maximized provided by a differential Riccati equation applied in the previous publications free of PDEs. We prove local stability of the algorithm, maximization of the map sensitivity and convergence to a small neighborhood of the desired (unknown) extremum by means of backstepping transformation, Lyapunov functional and the theory of averaging in infinite dimensions.
关键词：KeywordsAdaptive ControlExtremum SeekingPartial Differential EquationsAveraging TheoryBackstepping in Infinite Dimensions