A robust output error identifier for continuous‐time systems. (13th March 2014)

• Record Type: Journal Article
• Authors: Wang, Lei; Ortega, Romeo; Su, Hongye; Liu, Zhitao; Liu, Xiangbin
• Is Part Of: International journal of adaptive control and signal processing. Volume 29:Number 4(2015:Apr.)
• Page Start: 443
• Page End: 456
• Publication Date: 2014-03-13
• Subjects: Adaptive control systems -- Periodicals; Adaptive signal processing -- Periodicals; 629.836
• DOI: 10.1002/acs.2483
• Languages: English
• ISSNs: 0890-6327

Abstract

<abstract abstract-type="main" id="acs2483-abs-0001"> <title>Summary</title> <p id="acs2483-para-0001">This paper shows that the adaptive output error identifier for linear time‐invariant continuous‐time systems proposed by Bestser and Zeheb is robust <italic>vis‐à‐vis</italic> finite energy measurement noise. More precisely, it is proven that the map from the noise to the estimation error is <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgjj26vsbv" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:8906327:media:acs2483:acs2483-math-0001" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi mathvariant="script">L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>–stable—provided a tuning parameter is chosen sufficiently large. A procedure to determine the required minimal value of this parameter is also given. If the noise is exponentially vanishing, asymptotic convergence to zero of the prediction error is achieved. Instrumental for the establishment of the results is a suitable decomposition of the error system equations that allows us to strengthen—to <italic>strict</italic>—the well‐known passivity property of the identifier. The estimator neither requires fast adaptation, a dead‐zone, nor the knowledge of an upperbound on the noise magnitude, which is an essential requirement to prove stability of standard output error identifiers. To robustify the estimator with respect to non‐square integrable (but bounded) noises, a prediction error‐dependent leakage term is added in the integral adaptation. <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgjj26vscc" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:8906327:media:acs2483:acs2483-math-0002" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi mathvariant="script">L</mml:mi></mml:mrow><mml:mrow><mml:mo class="MathClass-rel">∞</mml:mo></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>–stability of the modified scheme is established under a technical assumption. A simulated example, which is unstable for the equation error identifier and the output error identifier of Bestser and Zeheb, is used to illustrate the noise insensitivity property of the new scheme. Copyright © 2014 John Wiley & Sons, Ltd.</p> </abstract>