Adaptive State Feedback Controllers

Anfinsen, Henrik; Aamo, Ole Morten

doi:10.1007/978-3-030-05879-1_9

Henrik Anfinsen⁷ &
Ole Morten Aamo⁷

Part of the book series: Communications and Control Engineering ((CCE))

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Abstract

In this chapter, we present the book’s first adaptive stabilizing controllers for $ 2 \times 2 $ systems. These are state-feedback solutions requiring full state measurements. The first result on adaptive control of $ 2 \times 2 $ systems is given in the back-to-back papers Anfinsen and Aamo (2016a, b), for a system in the form (7.1), but with constant in-domain parameters, that is

$$ u_t(x, t) + \lambda u_x(x, t) = c_{11} u(x, t) + c_{12} v(x, t)$$

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References

Anfinsen H, Aamo OM (2018) Adaptive control of linear $ 2 \times 2 $ hyperbolic systems. Automatica 87:69–82
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Anfinsen H, Aamo OM (2016a) Stabilization of linear $ 2 \times 2 $ hyperbolic systems with uncertain coupling coefficients - Part I: identifier-based design. In: 2016 Australian control conference. Newcastle, New South Wales, Australia
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Anfinsen H, Aamo OM (2016b) Stabilization of linear $ 2 \times 2 $ hyperbolic systems with uncertain coupling coefficients - Part II: swapping design. In: 2016 Australian control conference. Newcastle, Australia, New South Wales
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Anfinsen H, Aamo OM (2017) Adaptive stabilization of linear $ 2 \times 2 $ hyperbolic PDEs with spatially varying coefficients using swapping. In: 2017 Asian control conference. Australia, Gold Coast, Queensland
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Vazquez R, Krstić M (2014) Marcum Q-functions and explicit kernels for stabilization of $ 2 \times 2 $ linear hyperbolic systems with constant coefficients. Syst Control Lett 68:33–42
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Authors and Affiliations

Department of Engineering Cybernetics, Norwegian University of Science and Technology, Trondheim, Norway
Henrik Anfinsen & Ole Morten Aamo

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Henrik Anfinsen
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Ole Morten Aamo
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Correspondence to Henrik Anfinsen .

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Anfinsen, H., Aamo, O.M. (2019). Adaptive State Feedback Controllers. In: Adaptive Control of Hyperbolic PDEs. Communications and Control Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-05879-1_9

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DOI: https://doi.org/10.1007/978-3-030-05879-1_9
Published: 22 February 2019
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-05878-4
Online ISBN: 978-3-030-05879-1
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