Infinite-dimensional linear systems, optimal control and algebraic Riccati equations

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Doctoral thesis (monograph)
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Date
2002-10-18
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en
Pages
3 nid.
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Research reports / Helsinki University of Technology, Institute of Mathematics. A, Teknillisen korkeakoulun matematiikan laitoksen tutkimusraporttisarja. A, 452
Abstract
In this monograph, we solve rather general linear, infinite-dimensional, time-invariant control problems, including the H∞ and LQR problems, in terms of algebraic Riccati equations and of spectral or coprime factorizations. We work in the class of (weakly regular) well-posed linear systems (WPLSs) in the sense of G. Weiss and D. Salamon. Moreover, we develop the required theories, also of independent interest, on WPLSs, time-invariant operators, transfer and boundary functions, factorizations and Riccati equations. Finally, we present the corresponding theories and results also for discrete-time systems.
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Keywords
suboptimal H-infinity control, standard H-infinity problem, H-infinity full information control problem, LQR control, H2 problem, positive real lemma, dynamic stabilization, (J,S)-spectral factorization, (J,S)-inner coprime factorization, weakly regular well-posed linear systems, discrete-time, time-invariant operators, transfer functions, H-infinity boundary functions, Bochner integral
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https://urn.fi/urn:nbn:fi:tkk-001943