Open Access
Issue |
ESAIM: COCV
Volume 30, 2024
|
|
---|---|---|
Article Number | 71 | |
Number of page(s) | 16 | |
DOI | https://doi.org/10.1051/cocv/2024062 | |
Published online | 07 October 2024 |
- G. Bastin and J.-M. Coron, Stability and boundary stabilization of 1-D hyperbolic systems. Vol. 88 of Progress in Nonlinear Differential Equations and their Applications. Birkhauser/Springer, Cham (2016). [CrossRef] [Google Scholar]
- J.-M. Coron, Control and nonlinearity. Vol. 136 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI (2007). [Google Scholar]
- M. Krstic and A. Smyshlyaev, Boundary control of PDEs. Vol. 16 of Advances in Design and Control. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2008). [Google Scholar]
- T. Li, Controllability and observability for quasilinear hyperbolic systems. Vol. 3 of AIMS Series on Applied Mathematics. American Institute of Mathematical Sciences (AIMS), Springfield, MO; Higher Education Press, Beijing (2010). [Google Scholar]
- M.K. Banda, M. Herty and A. Klar, Gas flow in pipeline networks. Networks Heterogeneous Media 1 (2006) 41–56. [CrossRef] [MathSciNet] [Google Scholar]
- M. Dick, M. Gugat and G. Leugering, Classical solutions and feedback stabilization for the gas flow in a sequence of pipes. Networks Heterogeneous Mmedia 5 (2010) 691–709. [CrossRef] [Google Scholar]
- M. Gugat and M. Herty, Existence of classical solutions and feedback stabilization for the flow in gas networks. ESAIM Control Optim. Calc. Var. 17 (2011) 28–51. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
- M. Gugat, G. Leugering, S. Tamasoiu and K. Wang. H 2-stabilization of the isothermal Euler equations: a Lyapunov function approach. Chin. Ann. Math. 4 (2012) 479–500. [CrossRef] [Google Scholar]
- J.-M. Coron, Local ccontrollability of a 1-d tank containing a fluid modeled by the shallow water equations. ESAIM Control Optim. Calc. Var. 8 (2002) 513–554. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
- J.-M. Coron, G. Bastin and B. D’Andrea-Novel, On Lyapunov stability of linearised Saint-Venant equations for a sloping channel. Networks Heterogeneous Media 4 (2009) 177–187. [CrossRef] [MathSciNet] [Google Scholar]
- J. de Halleux, C. Prieur, J.-M. Coron, B. D’Andrea-Novel and G. Bastin, Boundary feedback control in networks of open channels. Automatica 39 (2003) 1365–1376. [CrossRef] [MathSciNet] [Google Scholar]
- M. Gugat and G. Leugering, Global boundary controllability of the de St. Venant equations between steady states. Ann. Inst. Henri Poincare Anal. Non Linéaire 20 (2003) 1–11. [CrossRef] [MathSciNet] [Google Scholar]
- M. Gugat, G. Leugering and G. Schmidt, Global controllability between steady supercritical flows in channel networks. Math. Methods Appl. Sci. 27 (2004) 781–802. [CrossRef] [MathSciNet] [Google Scholar]
- G. Leugering and G. Schmidt, On the modelling and stabilization of flows in networks of open canals. SIAM J. Control Optim. 41 (2002) 164–180. [CrossRef] [MathSciNet] [Google Scholar]
- J.-M. Coron and G. Bastin, Dissipative boundary conditions for one-dimensional quasilinear hyperbolic systems: Lyapunov stability for the C 1-norm. SIAM J. Control Optim. 53 (2015) 1464–1483. [CrossRef] [MathSciNet] [Google Scholar]
- J.-M. Coron, G. Bastin and B. D’Andrea-Novel, A strict Lyapunov function for boundary control of hyperbolic systems of conservation laws. IEEE Trans. Automatic Control 52 (2007) 2–11. [CrossRef] [MathSciNet] [Google Scholar]
- J.-M. Coron, G. Bastin and B. D’Andrea-Novel, Boundary feedback control and Lyapunov stability analysis for physical networks of 2x2 hyperbolic balance laws. Proceedings of the 47th IEEE Conference on decision and control (2008). [Google Scholar]
- J.-M. Coron, G. Bastin, B. D’Andrea-Novel and B. Haut, Lyapunov stability analysis of networks of scalar conservation laws. Networks Heterogeneous Media 2 (2007) 749–757. [Google Scholar]
- J.-M. Coron, G. Bastin and B. D’Andrea-Novel, Dissipative boundary conditions for one dimensional nonlinear hyperbolic systems. SIAM J. Control Optim. 47 (2008) 1460–1498. [CrossRef] [MathSciNet] [Google Scholar]
- C. Prieur and F. Mazenc, ISS-Lyapunov functions for time-varying hyperbolic systems of balance laws. Math. Control Signals Syst. 24 (2012) 111–134. [CrossRef] [Google Scholar]
- M.K. Banda and M. Herty, Numerical discretization of stabilization problems with boundary controls for systems of hyperbolic conservation laws. Math. Control Relat. Fields 3 (2013) 121–142. [CrossRef] [MathSciNet] [Google Scholar]
- S. Gerster and M. Herty, Discretized feedback control for systems of linearized hyperbolic balance laws. Math. Control Relat. Fields 9 (2019) 517–539. [CrossRef] [MathSciNet] [Google Scholar]
- S. Gottlich and P. Schillen, Numerical discretization of boundary control problems for systems of balance laws: feedback stabilization. Eur. J. Control 35 (2017) 11–18. [CrossRef] [MathSciNet] [Google Scholar]
- J.-M. Coron, A. Keimer and L. Pflug, Nonlocal transport equations - existence and uniqueness of solutions and relation to the corresponding conservation laws. SIAM J. Math. Anal. 52 (2020) 5500–5532. [CrossRef] [MathSciNet] [Google Scholar]
- M. Bambach, M. Gugat, M. Herty and F. Thein, Stabilization of forming processes using multi-dimensional Hamilton-Jacobi equations, in 2022 61th IEEE Conference on Decision and Control (CDC) (2022). [Google Scholar]
- M. Herty and F. Thein, Stabilization of a multi-dimensional system of hyperbolic balance laws. Math. Control Related Fields (2023). [Google Scholar]
- B.M. Dia and J. Oppelstrup, Boundary feedback control of 2-d shallow water equations. Int. J. Dyn. Control 1 (2013) 41–53. [CrossRef] [Google Scholar]
- H. Yang and W.-A. Yong, Feedback boundary control of 2-d hyperbolic systems with relaxation (2023). [Google Scholar]
- M. Herty and F. Thein, Comparison of approaches for boundary feedback control of hyperbolic systems. Eur. J. Control (2024). [Google Scholar]
- D. Serre, L2-type Lyapunov functions for hyperbolic scalar conservation laws. Commun. Part. Diff. Equ. 47 (2022) 401–416. [CrossRef] [Google Scholar]
- K.O. Friedrichs, Symmetric hyperbolic linear differential equations. Commun. Pure Appl. Math. 7 (1954) 345–392. [Google Scholar]
- S.K. Godunov, An interesting class of quasi-linear systems. Dokl. Akad. Nauk SSSR 139 (1961) 521–523. [MathSciNet] [Google Scholar]
- K.O. Friedrichs and P.D. Lax, Systems of conservation equations with a convex extension. Proc. Natl. Acad. Sci. U.S.A. 68 (1971) 1686–1688. [CrossRef] [PubMed] [Google Scholar]
- G. Boillat, Nonlinear hyperbolic fields and waves, in Recent mathematical methods in nonlinear wave propagation (Montecatini Terme, 1994). Vol. 1640 of Lecture Notes in Mathematics. Springer, Berlin (1996) 1–47. [Google Scholar]
- P. Brenner, The Cauchy problem for symmetric hyperbolic systems in Lp. Math. Scand. 19 (1996) 27–37. [Google Scholar]
- T. Kato, The Cauchy problem for quasi-linear symmetric hyperbolic systems. Arch. Rational Mech. Anal. 58 (1975) 181–205. [CrossRef] [MathSciNet] [Google Scholar]
- A. Majda and S. Osher, Initial-boundary value problems for hyperbolic equations with uniformly characteristic boundary. Commun. Pure Appl. Math. 28 (1975) 607–675. [CrossRef] [Google Scholar]
- G. Peyser, Stability of symmetric hyperbolic systems with nonlinear feedback. SIAM J. Math. Anal. 6 (1975) 925–936. [CrossRef] [MathSciNet] [Google Scholar]
- S. Benzoni-Gavage and D. Serre, Multidimensional hyperbolic partial differential equations. Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, Oxford (2007). [Google Scholar]
- C.M. Dafermos, Hyperbolic Conservation Laws in Continuum Physics. Vol. 325 of Grundlehren der mathematischen Wissenschaften, 4th edn. Springer Berlin Heidelberg (2016). [CrossRef] [Google Scholar]
- T. Ruggeri and M. Sugiyama, Classical and Relativistic Rational Extended Thermodynamics of Gases. Springer, Cham (2021). [CrossRef] [Google Scholar]
- S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan, Linear matrix inequalities in system and control theory. Vol. 15 of SIAM Studies in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (1994). [Google Scholar]
- P.D. Lax, Differential equations, difference equations and matrix theory. Commun. Pure Appl. Math. 11 (1958) 175–194. [CrossRef] [Google Scholar]
- J.W. Helton and V. Vinnikov, Linear matrix inequality representation of sets. Commun. Pure Appl. Math. 60 (2007) 654–674. [CrossRef] [Google Scholar]
- V. Vinnikov, LMI representations of convex semialgebraic sets and determinantal representations of algebraic hypersurfaces: past, present, and future, in Mathematical methods in systems, optimization, and control. Vol. 222 of Oper. Theory Adv. Appl., Birkhauser/Springer Basel AG, Basel (2012) 325–349. [Google Scholar]
- M. Lukacova-MedviDova, G. Warnecke and Y. Zahaykah, On the stability of evolution galerkin schemes applied to a two-dimensional wave equation system. SIAM J. Numer. Anal. 44 (2006) 1556–1583. [CrossRef] [MathSciNet] [Google Scholar]
- A. Hayat and P. Shang, Exponential stability of density-velocity systems with boundary conditions and source term for the H2 norm. J. Math. Pures Appl. 153 (2021) 187–212. [CrossRef] [MathSciNet] [Google Scholar]
- E.F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer Berlin Heidelberg (2009). [CrossRef] [Google Scholar]
- G. Warnecke, Analytische Methoden in der Theorie der Erhaltungsgleichung. B.G. Teubner, Stuttgart-Leipzig (1999). [CrossRef] [Google Scholar]
- E. Godlewski and P.-A. Raviart, Numerical approximation of hyperbolic systems of conservation laws. Vol. 118 of Applied Mathematical Sciences. Springer-Verlag, New York (1996). [CrossRef] [Google Scholar]
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