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Discrete-time concurrent learning for system identification and applications: Leveraging memory usage for good learning

機譯：離散時間并發(fā)學(xué)習，以進行系統(tǒng)識別和應(yīng)用程序：利用內(nèi)存使用情況進行良好的學(xué)習

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Literature on system identification reveals that persistently exiting inputs are needed in order to achieve good parameter identification when using standard learning techniques such as Gradient Descent and/or Least Squares for function approximation. However, realizing persistency of excitation in itself is quite demanding, especially in the context of on-line approximation and adaptive control. Much recently, Concurrent Learning (CL), through its utilization of memory (and, in that regard, quite similarly to human learning), has been shown to be able to yield good learning without the need to resort to persistency of excitation. For all intents and purposes, we refer to "good learning" throughout this work as the ability to reconstruct the function(s) being approximated well when using the estimated parameters.;The continuous-time (CT) domain literature on CL has seen the larger share of researches. For our part, we have focused on the discrete-time (DT) domain. Tough many systems can be modeled as CT systems, usually, controlling such systems, especially real-time (or, rather close to real-time), is done via the use of digital computers and/or micro-controllers, therefore making DT framework studies compelling.;We have shown that, similarly to the CT domain, granted a less restrictive CL condition compared to that of persistency of excitation is verified, analogous CL results to that obtained in the CT domain can also be achieved in the DT domain. Before incorporating and making use of the concept of concurrent learning in our studies, we thoroughly study the Gradient Descent and Least Squares techniques for function approximation and system identification of a dimensionally complex uncertainty, which, to the best our knowledge, is yet to be done in literature. Our main contributions are however the derivations of a DT Normalized Gradient (DTNG) based CL algorithm as well as a DT Normalized Recursive Least Squared (DTNRLS) based CL algorithm for approximation of both DT structured and DT unstructured uncertainties, while showing analytically that our devised algorithms guarantee good parameter identification if the aforesaid CL condition is met.;Numerical simulations are provided to show how well the developed CL algorithms leverage memory usage to achieve good learning. The algorithms are also made use of in two applications: the discrete-time indirect adaptive control of a class of discrete-time single state plant bearing parametric or structured uncertainties and the system identification of a robot.
機譯：有關(guān)系統(tǒng)識別的文獻表明，在使用標準學(xué)習技術(shù)（例如梯度下降和/或最小二乘）進行函數(shù)逼近時，需要持續(xù)存在的輸入才能實現(xiàn)良好的參數(shù)識別。然而，實現(xiàn)激勵本身的持久性是非常有要求的，特別是在在線逼近和自適應(yīng)控制的情況下。最近，并發(fā)學(xué)習（CL）通過利用內(nèi)存（在這一點上與人類學(xué)習非常相似）被證明能夠產(chǎn)生良好的學(xué)習而無需求助于持久性。出于所有意圖和目的，我們在整個工作過程中都將“良好學(xué)習”稱為“使用估計的參數(shù)時可以很好地重構(gòu)函數(shù)的能力”。CL的連續(xù)時間（CT）領(lǐng)域文獻已經(jīng)看到研究份額更大。就我們而言，我們專注于離散時間（DT）域?？梢詫⒃S多系統(tǒng)建模為CT系統(tǒng)，通常，通過使用數(shù)字計算機和/或微控制器來完成對此類系統(tǒng)的控制，尤其是實時（或接近實時）的控制，因此可以構(gòu)建DT框架我們已經(jīng)證明，與CT域類似，與激發(fā)持久性相比，CL條件較寬松的條件得到了驗證，在DT域中也可以獲得與CT域類似的CL結(jié)果。在我們的研究中納入并利用并發(fā)學(xué)習的概念之前，我們對梯度下降和最小二乘技術(shù)進行了深入研究，以用于函數(shù)逼近和系統(tǒng)識別維度復(fù)雜的不確定性，據(jù)我們所知，這尚未完成。在文學(xué)中。然而，我們的主要貢獻是基于DT歸一化梯度（DTNG）的CL算法以及基于DT歸一化遞歸最小二乘（DTNRLS）的CL算法的推導(dǎo)，用于近似DT結(jié)構(gòu)化和DT非結(jié)構(gòu)化不確定性，同時通過分析顯示了我們的設(shè)計如果滿足上述CL條件，則算法可確保良好的參數(shù)識別。;提供了數(shù)值模擬，以顯示開發(fā)的CL算法如何充分利用內(nèi)存使用來實現(xiàn)良好的學(xué)習。該算法還用于兩個應(yīng)用中：一類具有參數(shù)或結(jié)構(gòu)不確定性的離散時間單狀態(tài)植物的離散時間間接自適應(yīng)控制，以及機器人的系統(tǒng)識別。

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    University of Dayton.;

  • 授予單位 University of Dayton.;
  • 學(xué)科 Electrical engineering.;Mathematics.;Applied mathematics.;Engineering.
  • 學(xué)位 Dr.Ph.
  • 年度 2017
  • 頁碼 220 p.
  • 總頁數(shù) 220
  • 原文格式 PDF
  • 正文語種 eng
  • 中圖分類 人類學(xué);
  • 關(guān)鍵詞

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