The Dissipation Inequality for Differential‐Algebraic Systems. Issue 1 (December 2014)

• Record Type: Journal Article
• Authors: Reis, Timo; Voigt, Matthias
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 14:Issue 1(2014)
• Page Start: 11
• Page End: 14
• Publication Date: 2014-12
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201410004
• Languages: English
• ISSNs: 1617-7061

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>We discuss the infinite time‐horizon linear‐quadratic optimal control problem for differential‐algebraic equations. In contrast to previous approaches we do not impose any assumptions on the system except for impulse controllability. In particular, we show that the optimal control problem is feasible if and only if a dissipation inequality has a solution. Moreover, we discuss conditions under which the problem has a minimizing (instead of only an infimizing) solution and furthermore, when this minimizing solution is unique. (© 2014 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)</p> </abstract>