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Adaptive Control of Hyperbolic PDEs

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

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Abstract

Systems of hyperbolic partial differential equations (PDEs) describe flow and transport phenomena. Typical examples are transmission lines (Curró, Fusco, Manganaro, J Phys A: Math Theor, 44(33):335205, (2011)), road traffic (Amin, Hante, Baye, Hybrid systems computation and control, Springer, pp 602–605, (2008)), heat exchangers (Xu, Sallet, ESAIM: Control Optim Calc Var, 7:421–442, (2010)) , oil wells (Landet, Pavlov, Aamo, IEEE Trans Control Syst Technol, 21(4):1340–1351, (2013)), multiphase flow (Di Meglio, Dynamics and control of slugging in oil production. Ph.D. thesis, MINES ParisTech, (2011)); (Diagne, Diagne, Tang, Krstić, Automatica, 76:345–354, (2017)), time-delays (Krstić, Smyshlyaev, Syst Control Lett, 57(9):750–758, (2008b)) and predator–prey systems ( Wollkind, Math Model, 7:413–428, (1986)), to mention a few. These distributed parameter systems give rise to important estimation and control problems, with methods ranging from the use of control Lyapunov functions (Coron, d’Andréa Novel, Bastin, IEEE Trans Autom Control, 52(1):2–11, (2007)), Riemann invariants (Greenberg, Tsien, J Differ Equ, 52(1):66–75, (1984)), frequency domain approaches (Litrico, Fromion, 45th IEEE conference on decision and control, San Diego, CA, USA, (2006)) and active disturbance rejection control (ADRC) (Gou, Jin, IEEE Trans Autom Control, 60(3):824–830, (2015)). The approach taken in this book makes extensive use of Volterra integral transformations, and is known as the infinite-dimensional backstepping approach.

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Authors and Affiliations

  1. Department of Engineering Cybernetics, Norwegian University of Science and Technology, Trondheim, Norway

    Henrik Anfinsen & Ole Morten Aamo

Authors
  1. Henrik Anfinsen
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  2. Ole Morten Aamo
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Correspondence to Henrik Anfinsen .

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Anfinsen, H., Aamo, O.M. (2019). Background. In: Adaptive Control of Hyperbolic PDEs. Communications and Control Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-05879-1_1

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