Model Reference Adaptive Control of 2 \times 2 Coupled Linear Hyperbolic PDEs

We solve a model reference adaptive control problem for a class of linear <inline-formula><tex-math notation="LaTeX"> 2 \times 2</tex-math></inline-formula> hyperbolic partial differential equations (PDEs) with uncertain system parameters subject to harmonic disturb...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 63; no. 8; pp. 2405 - 2420
Main Authors Anfinsen, Henrik, Aamo, Ole Morten
Format Journal Article
LanguageEnglish
Published IEEE 01.08.2018
Subjects
Adaptation models
Adaptive control
Backstepping
distributed parameter systems
Harmonic analysis
linear systems
Mathematical model
Observers
Sensors
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Summary:We solve a model reference adaptive control problem for a class of linear <inline-formula><tex-math notation="LaTeX"> 2 \times 2</tex-math></inline-formula> hyperbolic partial differential equations (PDEs) with uncertain system parameters subject to harmonic disturbances, from a single boundary measurement anticollocated with the actuation. This is done by transforming the system into a canonical form, from which filters are designed so that the states can be expressed as linear combinations of the filters and uncertain parameters, a representation facilitating for the design of adaptive laws. A stabilizing controller is then combined with the adaptive laws to make the measured signal asymptotically track the output of a reference model. The reference model is taken as a simple transport PDE. Moreover, pointwise boundedness of all variables in the closed loop is proved, provided the reference signal is bounded. The theory is demonstrated in a simulation.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2017.2767378