On Linear-Quadratic Optimal Control and Robustness of Differential-Algebraic Systems

Voigt, Matthias

ISBN 10: 3832541187 / ISBN 13: 9783832541187

Editore: Logos Verlag Berlin, 2015

2015. Paperback. . . . . . Books ship from the US and Ireland. Codice articolo V9783832541187

Riassunto:

This thesis considers the linear-quadratic optimal control problem for differential-algebraic systems. In this first part, a complete theoretical analysis of this problem is presented. The basis is a new differential-algebraic version of the Kalman-Yakubovich-Popov (KYP) lemma. One focus is the analysis of the solution structure of the associated descriptor KYP inequality. In particular, rank-minimizing, stabilizing, and extremal solutions are characterized which gives a deep insight into the structure of the problem. Further contributions include new relations of the descriptor KYP inequality to structured matrix pencils, conditions for the existence of nonpositive solutions, and the application of the new theory to the characterization of dissipative systems and the factorization of rational matrix-valued functions. The second part of this thesis focuses on robustness questions, i.e., the influence of perturbations on system properties like dissipativity and stability is discussed. Characterizations for the distance of a dissipative systems to the set of non-dissipative systems are given which lead to a numerical method for computing this distance. Furthermore, the problem of computing the H-infinity-norm of a large-scale differential-algebraic system is considered. Two approaches for this computation are introduced and compared to each other.

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Titolo: On Linear-Quadratic Optimal Control and ...
Casa editrice: Logos Verlag Berlin
Data di pubblicazione: 2015
Legatura: Brossura
Condizione: New