Global exact boundary controllability for general first-order quasilinear hyperbolic systems

Abstract

For general first-order quasilinear hyperbolic systems, based on the analysis of simple wave solutions along characteristic trajectories, the global two-sided exact boundary controllability is achieved in a relatively short controlling time.

Keywords

Global exact boundary controllability / General quasilinear hyperbolic system / Simple wave solution / Characteristic trajectory / Short controlling time

References

[1] Cirinà M.. Boundary controllability of nonlinear hyperbolic systems. SIAM Journal on Control, 1969, 7(2): 198-212

[2] Gugat M., Leugering G.. Global boundary controllability of the de St. Venant equations between steady states. Annales de l’Institut Henri Poincaré, Analyse Non Linéare, 2003, 20(1): 1-11

[3] Gugat M., Leugering G.. Global boundary controllability of the Saint-Venant system for sloped canals with friction. Annales de l’Institut Henri Poincaré, Analyse Non Linéare, 2009, 26(1): 257-270

[4] Lasiecka I., Triggiani R.. Exact controllability of semilinear abstract systems with application to waves and plates boundary control problems. Applied Mathematics and Optimization, 1991, 23(2): 109-154

[5] Lions J.-L.. Exact controllability, stabilization and perturbations for distributed systems. SIAM Review, 1988, 30(1): 1-68

[6] Li T.-T.. Global Classical Solutions for Quasilinear Hyperbolic Systems, Vol. 32, Research in Applied Mathematics, 1994, John Wiley, Paris: Masson

[7] Li T.-T.. Controllability and Observability for Quasilinear Hyperbolic Systems, Vol. 3, AIMS Series on Applied Mathematics, 2010, Springfield, MO, and Higher Education Press, Beijing: American Institute of Mathematical Sciences

[8] Li T.-T.. Global exact boundary controllability for first order quasilinear hyperbolic systems. Discrete and Continuous Dynamical Systems, Ser. B, 2010, 14(4): 1419-1432

[9] Li T.-T., Rao B.-P.. Local exact boundary controllability for a class of quasilinear hyperbolic systems. Chinese Annals of Mathematics, Ser. B, 2002, 23(2): 209-218

[10] Li T.-T., Rao B.-P.. Exact boundary controllability for quasilinear hyperbolic systems. SIAM Journal on Control and Optimization, 2003, 41(6): 1748-1755

[11] Li T.-T., Wang Z.-Q.. Global exact boundary controllability for first order quasilinear hyperbolic systems of diagonal form. International Journal of Dynamical Systems and Differential Equations, 2007, 1(1): 12-19

[12] Li T.-T., Yu L.-X.. Exact controllability for first order quasilinear hyperbolic systems with zero eigenvalues. Chinese Annals of Mathematics, Ser. B, 2003, 24(4): 415-422

[13] Li T.-T., Yu W.-C.. Boundary Value Problems for Quasilinear Hyperbolic Systems, 1985, Duke University, Durham, N. C.: Duke University Mathematics Series

[14] Russell D. L.. Controllability and stabilizability theory for linear partial differential equations: Recent progress and open questions. SIAM Review, 1978, 20(4): 639-739

[15] Wang K.. Global exact boundary controllability for 1-D quasilinear wave equations. Mathematical Methods in the Applied Sciences, 2011, 34(3): 315-324

[16] Wang Z.-Q.. Exact controllability for nonautonomous quasilinear hyperbolic systems, 2006

[17] Wang Z.-Q.. Exact controllability for nonautonomous first order quasilinear hyperbolic systems. Chinese Annals of Mathematics, Ser. B, 2006, 27(6): 643-656

[18] Wang Z.-Q.. Global exact controllability for quasilinear hyperbolic systems of diagonal form with linearly degenerate characteristics. Nonlinear Analysis: Theory, Methods & Applications, 2008, 69(2): 510-522

[19] Zuazua E.. Exact controllability for the semilinear wave equation. Journal de Mathématiques Pures et Appliquées, 1990, 69(1): 1-31

[20] Zuazua E.. Exact controllability for semilinear wave equations in one space dimension. Annales de l’Institut Henri Poincaré, Analyse Non Linéaire, 1993, 10(1): 109-129