NDLI: Robust adaptive model tracking for distributed parameter control of linear infinite-dimensional systems in Hilbert space

Content Provider	IEEE Xplore Digital Library
Author	Balas, Mark J. Frost, Susan A.
Copyright Year	2014
Abstract	This paper is focused on adaptively controlling a linear infinite-dimensional system to track a finite-dimensional reference model. Given a linear continuous-time infinite-dimensional plant on a Hilbert space with disturbances of known waveform but unknown amplitude and phase, we show that there exists a stabilizing direct model reference adaptive control law with the properties of certain disturbance rejection and robustness. The plant is described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on the Hilbert space of states. The central result will show that all errors will converge to a prescribed neighborhood of zero in an infinite-dimensional Hilbert space. The result will not require the use of the standard Barbalat's lemma which requires certain signals to be uniformly continuous. This result is used to determine conditions under which a linear infinite-dimensional system can be directly adaptively controlled to follow a reference model. In particular, we examine conditions for a set of ideal trajectories to exist for the tracking problem. Our results are applied to adaptive control of general linear diffusion systems described by self-adjoint operators with compact resolvent.
Starting Page	294
Ending Page	301
Page Count	8
File Size	191159
File Format	PDF
ISSN	23299266
Volume Number	1
Issue Number	3
Language	English
Publisher Date	2014-01-01
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Chinese Association of Automation
Subject Keyword	Robustness Adaptation models Adaptive control Hilbert space Trajectory Learning (artificial intelligence) distributed parameter system adaptive control algorithm adaptive theory
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Artificial Intelligence Control and Systems Engineering Information Systems

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