Observer‐based linear parameter‐varying control with guaranteed L2‐gain and H2‐type performance objectives. (12th April 2013)

• Record Type: Journal Article
• Authors: Köroğlu, Hakan; Edwards, Christopher; Marcos, Andres; Balas, Gary
• Is Part Of: International journal of robust and nonlinear control. Volume 24:Number 14(2014)
• Page Start: 2000
• Page End: 2017
• Publication Date: 2013-04-12
• Subjects: Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.2996
• Languages: English
• ISSNs: 1049-8923

Abstract

<abstract abstract-type="main" id="rnc2996-abs-0001"> <title>SUMMARY</title> <p>Synthesis of an observer‐based linear parameter‐varying controller is considered for a general linear parameter‐varying plant. The parameter vector and its derivative are both assumed to take values in known bounded domains, whereas only the parameter vector is assumed to be measurable during online operation. The synthesis problem is considered for <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh11pz8xn5" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="block" altimg="urn:x-wiley:10498923:media:rnc2996:rnc2996-math-0003" 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>‐gain and <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh11pz8zm4" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="block" altimg="urn:x-wiley:10498923:media:rnc2996:rnc2996-math-0004" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi mathvariant="script">H</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>‐type performance objectives. Potentially conservative parameter‐dependent linear matrix inequality conditions are derived for the solvability of these two problems. To facilitate the reduction of conservatism, the conditions are expressed in a way to have bilinear dependence on an arbitrary positive scalar. In addition to employing a suitable relaxation scheme to reduce these conditions into finitely many constraints, a line search hence needs to be performed over the positive scalar to obtain the best achievable performance with an observer‐based controller. The online implementation of the observer‐based controller is relatively simpler if compared with a controller of unrestricted structure. Moreover, the observer‐based controller will have no dependence on the parameter derivatives irrespective of the choices of the design variables. Copyright © 2013 John Wiley & Sons, Ltd.</p> </abstract>