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The Dissipation Inequality for Differential‐Algebraic Systems
Author(s) -
Reis Timo,
Voigt Matthias
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410004
Subject(s) - controllability , mathematics , algebraic number , impulse (physics) , quadratic differential , optimal control , dissipation , differential (mechanical device) , quadratic equation , control theory (sociology) , mathematical optimization , mathematical analysis , control (management) , computer science , physics , classical mechanics , geometry , artificial intelligence , thermodynamics
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 & Co. KGaA, Weinheim)