Acta mathematica scientia, Series B >
EXACT CONTROLLABILITY FOR FIRST ORDER QUASILINEAR HYPERBOLIC SYSTEMS WITH VERTICAL CHARACTERISTICS
Received date: 2009-01-14
Online published: 2009-07-20
We consider first order quasilinear hyperbolic systems with vertical charac-teristics. It was shown in [4] that such systems can be exactly controllable with the help of internal controls applied to the equations corresponding to zero eigenvalues. However, it is possible that, for physical or engineering reasons, we can not put any control on
the equations corresponding to zero eigenvalues. In this paper, we will establish the ex-act controllability only by means of physically meaningful internal controls applied to the equations corresponding to non-zero eigenvalues. We also show the exact controllability for a very simplified model by means of switching controls.
LI Da-Qian , RAO Ba-Feng . EXACT CONTROLLABILITY FOR FIRST ORDER QUASILINEAR HYPERBOLIC SYSTEMS WITH VERTICAL CHARACTERISTICS[J]. Acta mathematica scientia, Series B, 2009 , 29(4) : 980 -990 . DOI: 10.1016/S0252-9602(09)60082-5
[1] Lee E B, Markus L. Foundations of optimal control theory. Melbourne, FL: Robert E Krieger Publishing
Co Inc, 1986
[2] Li Tatsien, Rao Bopeng. Local exact boundary controllability for a class of quasilinear hyperbolic systems.
Chin Ann Math, Ser B, 2002, 23: 209–218
[3] Li Tatsien, Rao Bopeng. Exact boundary controllability for quasilinear hyperbolic systems. SIAM J Control Optim, 2003, 41: 1748–1755
[4] Li Tatsien, Yu Lixin. Exact controllability for first order quasilinear hyperbolic systems with zero eigen-
values. Chin Ann Math, Ser B, 2003, 24: 415–422
[5] Li Tatsien, Yu Lixin. Exact boundary controllability for 1-D quasilinear wave equations. SIAM J Control
Optim, 2006, 45: 1074–1083
[6] Russell D L. Controllability and stabilizability theory for linear partial differential equations: recent
progress and open questions. SIAM Rev, 1978, 20: 639–739
[7] Wang Zhiqiang, Yu Lixin. Exact boundary controllability for a one-dimensional adiabatic flow system (in
Chinese). Appl Math J Chinese Univ, Ser A, 2008, 23: 35–40
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