@article{COCV_1999__4__57_0, author = {Dekoninck, Bertrand and Nicaise, Serge}, title = {Control of networks of {Euler-Bernoulli} beams}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {57--81}, publisher = {EDP-Sciences}, volume = {4}, year = {1999}, mrnumber = {1680764}, zbl = {0922.93005}, language = {en}, url = {http://www.numdam.org/item/COCV_1999__4__57_0/} }
TY - JOUR AU - Dekoninck, Bertrand AU - Nicaise, Serge TI - Control of networks of Euler-Bernoulli beams JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 1999 SP - 57 EP - 81 VL - 4 PB - EDP-Sciences UR - http://www.numdam.org/item/COCV_1999__4__57_0/ LA - en ID - COCV_1999__4__57_0 ER -
Dekoninck, Bertrand; Nicaise, Serge. Control of networks of Euler-Bernoulli beams. ESAIM: Control, Optimisation and Calculus of Variations, Tome 4 (1999), pp. 57-81. http://www.numdam.org/item/COCV_1999__4__57_0/
[1] A characterisation of generalized C∞ notion on nets. Int. Eq. and Operator Theory 9 ( 1986) 753-766. | MR | Zbl
,[2] Regular solutions of transmission and interaction problems for wave equations. Math. Meth. Appl. Sci. 11 ( 1989) 665-685. | MR | Zbl
,[3] Nonharmonic Fourier series and the stabilization of distributed semi-linear control systems. Comm. Pure Appl. Math. 32 ( 1979) 555-587. | MR | Zbl
and ,[4] A characteristic equation associated to an eigenvalue problem on c2-networks. Linear Alg. Appl. 71 ( 1985) 309-325. | MR | Zbl
,[5] Classical solvability of linear parabolic equations on networks. J. Diff. Eq. 72 ( 1988) 316-337. | MR | Zbl
,[6] Sturm-Liouville eigenvalue problems on networks. Math. Meth. Appl. Sci. 10 ( 1988) 383-395. | MR | Zbl
,[7] Parabolic Network Equations. Habilitation Thesis, Eberhard-Karls-Universität Tübingen ( 1993).
,[8] Dynamical interface transition with diffusion in ramified media. Comm. Partial Diff. Eq. 21 ( 1996) 255-279. | MR | Zbl
and ,[9] A class of fourth-order differential equations on a spatial net. Doklady Math. 52 ( 1995) 433-435. | Zbl
, , and ,[10] Modelling, stabilization and control of serially connected beams. SIAM J. Control and Opt. 25 ( 1987) 526-546. | MR | Zbl
, , and ,[11] Analysis, design, and behavior of dissipative joints for coupled beams. SIAM J. Appl. Math. 49 ( 1989) 1665-1693. | MR | Zbl
, , , , and ,[12] The wave propagation method for the analysis of boudary stabilization in vibrating structures, SIAM J. Appl. Math. 50 ( 1990) 1254-1283. | MR | Zbl
and ,[13] Junctions between three-dimension and two-dimensional linearly elastic structures. J. Math. Pures Appl. 68 ( 1989) 261-295. | MR | Zbl
, and ,[14] Stabilization of vibrating beams by a specific feedback, A.V. Balakrishnan and J.P. Zolésio Eds., Stabilization of flexible structures, Opt. Software Inc. ( 1988) 36-51. | Zbl
,[15] The eigenvalue problem for networks of beams. Preprint LIMAV 96-9, University of Valenciennes, Linear Alg. Appl. (submitted). | MR | Zbl
and ,[16] Elliptic problems in nonsmooth domains. Monographs and Studies in Mathematics 21 (Pitman, Boston, 1985). | MR | Zbl
,[17] Contrôlabilité exacte des solutions de l'équation des ondes en présence de singularités. J. Math. Pures Appl. 68 ( 1989) 215-259. | MR | Zbl
,[18] Some trigonometrical inequalities with applications in the theory of series. Math. Z. 41 ( 1936) 367-369. | MR | Zbl
,[19] Exact controllability and stabilization. The multiplier method. RM A 36 Masson, Paris ( 1994). | MR | Zbl
,[20] Modeling and controllability of plate-beam systems. J. Math. Systems, Estimation and Control. 5 ( 1995) 141-187. | MR | Zbl
,[21] Modeling of dynamic networks of thin thermoelastic beams. Math. Meth. Appl. Sci. 16 ( 1993) 327-358. | MR | Zbl
, and ,[22] Control of planar networks of Timoshenko beams. SIAM J. Cont. Opt. 31 ( 1993) 780-811. | MR | Zbl
, and ,[23] Modeling, analysis and control of dynamic elastic multi-link structures, Birkhäuser, Boston ( 1994). | MR | Zbl
, and ,[24] Problèmes variationnels dans les multi-domaines. Modélisation des jonctions et applications. RMA 19, Masson, Paris ( 1991). | MR | Zbl
,[25] On the control of networks of vibrating strings and beams, in Proc. of the 28th IEEE Conference on Decision and Control, Vol. 3, IEEE ( 1989) 2287-2290.
and ,[26] Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués. Tome 1, RMA 8, Masson, Paris ( 1988). | MR | Zbl
,[27] Exact controllability of a pluridimensional coupled problem. Rev. Math. Univ. Complutense Madrid 5 ( 1992) 91-135. | MR | Zbl
,[28] About the Lamé system in a polygonal or a polyhedral domain and a coupled problem between the Lamé system and the plate equation II: Exact controllability. Ann. Scuola Normale Sup. Pisa, Series IV 20 ( 1993) 163-191. | Numdam | MR | Zbl
,[29] Boundary exact controllability of interface problems with singularities I: Addition of the coefficients of singularities. SIAM J. Contr. Opt. 34 ( 1996) 1512-1533. | MR | Zbl
,[30] Boundary exact controllability of interface problems with singularities II: Addition of internal controls. SIAM J. Contr. Opt. 35 ( 1997) 585-603. | MR | Zbl
,[31] Exact controllability for a model of multidimensional flexible structure. Proc. Royal Soc. Edinburgh 123 A ( 1993) 323-344. | MR | Zbl
and ,[32] On the modelling and exact controllability of networks of vibrating strings. SIAM J. Contr. Opt.30 ( 1992) 229-245. | MR | Zbl
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