Abstract
One-dimensional hyperbolic systems are commonly used to describe the evolution of various physical systems. For many of these systems, controls are available on the boundary. There are then two natural questions: controllability (steer the system from a given state to a desired target) and stabilization (construct feedback laws leading to a good behavior of the closed loop system around a given set point).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Bibliography
Ancona F, Marson A (1998) On the attainable set for scalar nonlinear conservation laws with boundary control. SIAM J Control Optim 36(1):290–312 (electronic)
Aw A, Rascle M (2000) Resurrection of “second order” models of traffic flow. SIAM J Appl Math 60(3):916–938 (electronic)
Barré de Saint-Venant A-C (1871) Théorie du mouvement non permanent des eaux, avec application aux crues des rivières et à l’introduction des marées dans leur lit. Comptes rendus de l’Académie des Sciences de Paris, Série 1, Mathématiques, 53:147–154
Bressan A (2000) Hyperbolic systems of conservation laws. Volume 20 of Oxford lecture series in mathematics and its applications. Oxford University Press, Oxford. The one-dimensional Cauchy problem
Bressan A, Coclite GM (2002) On the boundary control of systems of conservation laws. SIAM J Control Optim 41(2):607–622 (electronic)
Coron J-M, Bastin G, d’Andréa Novel B (2008) Dissipative boundary conditions for one-dimensional nonlinear hyperbolic systems. SIAM J Control Optim 47(3):1460–1498
Coron J-M, Vazquez R, Krstic M, Bastin G (2013) Local exponential H2 stabilization of a 2 × 2 quasilinear hyperbolic system using backstepping. SIAM J Control Optim 51(3):2005–2035
Glass O (2007) On the controllability of the 1-D isentropic Euler equation. J Eur Math Soc (JEMS) 9(3):427–486
Heaviside O (1885, 1886 and 1887) Electromagnetic induction and its propagation. The Electrician, reprinted in Electrical Papers, 2 vols, London. Macmillan and co. 1892
Horsin T (1998) On the controllability of the Burgers equation. ESAIM Control Optim Calc Var 3:83–95 (electronic)
Krstic M, Smyshlyaev A (2008) Boundary control of PDEs. Volume 16 of advances in design and control. Society for Industrial and Applied Mathematics (SIAM), Philadelphia. A course on backstepping designs
Langmuir I (1916) The constitution and fundamental properties of solids and liquids. Part I. Solids. J Am Chem Soc 38:2221–2295
Li T (1994) Global classical solutions for quasilinear hyperbolic systems. Volume 32 of RAM: research in applied mathematics. Masson, Paris
Li T (2010) Controllability and observability for quasilinear hyperbolic systems. Volume 3 of AIMS series on applied mathematics. American Institute of Mathematical Sciences (AIMS), Springfield
Li T, Rao B-P (2003) Exact boundary controllability for quasi-linear hyperbolic systems. SIAM J Control Optim 41(6):1748–1755 (electronic)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer-Verlag London
About this entry
Cite this entry
Bastin, G., Coron, JM. (2015). Boundary Control of 1-D Hyperbolic Systems. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5058-9_11
Download citation
DOI: https://doi.org/10.1007/978-1-4471-5058-9_11
Published:
Publisher Name: Springer, London
Print ISBN: 978-1-4471-5057-2
Online ISBN: 978-1-4471-5058-9
eBook Packages: EngineeringReference Module Computer Science and Engineering