Several kinds of exact synchronizations and the generalized exact synchronization are introduced for a coupled system of 1-D wave equations with various boundary conditions and we show that these synchronizations can be realized by means of some boundary controls.
Mots-clés : exact null controllability, exact synchronization, exact synchronization by groups, exact null controllability and synchronization by groups, generalized exact synchronization
@article{COCV_2014__20_2_339_0, author = {Li, Tatsien and Rao, Bopeng and Hu, Long}, title = {Exact boundary synchronization for a coupled system of {1-D} wave equations}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {339--361}, publisher = {EDP-Sciences}, volume = {20}, number = {2}, year = {2014}, doi = {10.1051/cocv/2013066}, mrnumber = {3264207}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv/2013066/} }
TY - JOUR AU - Li, Tatsien AU - Rao, Bopeng AU - Hu, Long TI - Exact boundary synchronization for a coupled system of 1-D wave equations JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2014 SP - 339 EP - 361 VL - 20 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2013066/ DO - 10.1051/cocv/2013066 LA - en ID - COCV_2014__20_2_339_0 ER -
%0 Journal Article %A Li, Tatsien %A Rao, Bopeng %A Hu, Long %T Exact boundary synchronization for a coupled system of 1-D wave equations %J ESAIM: Control, Optimisation and Calculus of Variations %D 2014 %P 339-361 %V 20 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2013066/ %R 10.1051/cocv/2013066 %G en %F COCV_2014__20_2_339_0
Li, Tatsien; Rao, Bopeng; Hu, Long. Exact boundary synchronization for a coupled system of 1-D wave equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 2, pp. 339-361. doi : 10.1051/cocv/2013066. http://www.numdam.org/articles/10.1051/cocv/2013066/
[1] Indirect boundary stabilization of weakly coupled hyperbolic systems. SIAM J. Control Optim. 41 (2002) 511-541. | MR | Zbl
,[2] A two-level energy method for indirect boundary observability and controllability of weakly coupled hyperbolic systems. SIAM J. Control Optim. 42 (2003) 871-906. | MR | Zbl
,[3] Indirect stabilization of locally coupled wave-type systems. ESAIM: COCV 18 (2012) 548-582. | Numdam | MR | Zbl
, ,[4] Stability theory of synchronized motion in coupled-oscillator systems. Progress Theoret. Phys. 69 (1983) 32-47. | MR | Zbl
and ,[5] Optimal boundary control in flood management, Control of Coupled Partial Differential Equations, edited by K. Kunisch, J. Sprekels, G. Leugering and F. Tröltzsch, vol. 155 of Int. Ser. Numer. Math., Birkhäuser Verlag, Basel/Switzerland (2007) 69-94. | MR | Zbl
,[6] Exact boundary controllability and exact boundary observability for a coupled system of quasilinear wave equations. Chin. Ann. Math. B 34 (2013) 479-490. | MR | Zbl
, and ,[7] Ch. Huygens, Œuvres Complètes, vol. 15, edited by S. and B.V. Zeitlinger, Amsterdam (1967).
[8] Semi-global C1 solution to the mixed initial-boundary value problem for quasilinear hyperbolic systems. Chin. Ann. Math. B 22 (2001) 325-336. | MR | Zbl
and ,[9] Exact boundary observability for 1-D quasilinear wave equations. Math. Meth. Appl. Sci. 29 (2006) 1543-1553. | MR | Zbl
,[10] Controllability and Observability for Quasilinear Hyperbolic Systems, vol. 3 of AIMS Ser. Appl. Math. AIMS and Higher Education Press (2010). | MR | Zbl
,[11] Strong (weak) exact controllability and strong (weak) exact observability for quasilinear hyperbolic systems. Chin. Annal. Math. B 31 (2010) 723-742. | MR | Zbl
and ,[12] Asymptotic controllability for linear hyperbolic systems. Asymp. Anal. 72 (2011) 169-187. | MR | Zbl
and ,[13] Exact synchronization for a coupled system of wave equations with Dirichlet boundary controls. Chin. Annal. Math. B 34 (2013) 139-160. | MR | Zbl
and ,[14] Contrôlabilité Exacte, Perturbations et Stabilization de Systèmes Distribués, Vol. 1, Masson (1988). | MR | Zbl
,[15] Exact controllability, stabilization and perturbations for distributed systems. SIAM Review 30 (1988) 1-68. | MR | Zbl
,[16] Controllability and stabilization theory for linear partial differential equations: Recent progress and open questions. SIAM Review 20 (1978) 639-739. | MR | Zbl
,[17] SYNC: The Emerging Science of Spontaneous Order, THEIA, New York (2003).
,[18] Exact boundary controllability for a kind of second-order quasilinear hyperbolic systems. Chin. Ann. Math. B 32 (2011) 803-822. | MR | Zbl
,[19] Synchronization in Complex Networks of Nonlinear Dynamical Systems. World Scientific (2007). | Zbl
,[20] Exact boundary controllability for a kind of second-order quasilinear hyperbolic systems and its applications. Math. Meth. Appl. Sci. 33 (2010) 273-286. | MR | Zbl
,Cité par Sources :