Mounier, H.; Rudolph, J.; Fliess, M.; Rouchon, P. Tracking control of a vibrating string with an interior mass viewed as delay system. (English, French) Zbl 0906.73046 ESAIM, Control Optim. Calc. Var. 3, 315-321 (1998). Summary: A vibrating string, modelled by the wave equation, with an interior mass is considered. It is viewed as a linear delay system. A trajectory tracking problem is solved using a new type of controllability. Cited in 16 Documents MSC: 74M05 Control, switches and devices (“smart materials”) in solid mechanics 74H45 Vibrations in dynamical problems in solid mechanics 74K05 Strings Keywords:wave equation; trajectory tracking problem × Cite Format Result Cite Review PDF Full Text: DOI EuDML References: [1] K.L. Cooke, D.W. Krumme: Differential-difference equations and nonlinear initial-boundary value problems for linear hyperbolic partial differential equations, J. Math. Anal. Appl., 24, 1968, 372-387. Zbl0186.16902 MR232089 · Zbl 0186.16902 · doi:10.1016/0022-247X(68)90038-3 [2] M. Fliess, J. Levine, P. Martin, P. Rouchon: Flatness and defect of nonlinear systems: introductory theory and examples, Internat. J. Control, 61, 1995, 1327-1361. Zbl0838.93022 MR1613557 · Zbl 0838.93022 · doi:10.1080/00207179508921959 [3] M. Fliess, H. Mounier: Controllability and observability of linear delay systems: an algebraic approach, ESAIM: Control Optimisation and Calculus of Variations, http://www.emath.fr/cocv/, 3, 1998, 301-314. Zbl0908.93013 MR1644427 · Zbl 0908.93013 · doi:10.1051/cocv:1998111 [4] M. Fliess, H. Mounier, P. Rouchon, J. Rudolph: Controllability and motion planning for linear delay systems with an application to a flexible rod, In 34th Conf. Decision Contr. Proc., New Orleans, Lousiana, 1995, 2046-2051. [5] M. Fliess, H. Mounier, P. Rouchon, J. Rudolph: Systèmes linéaires sur les opérateurs de Mikusiński, ESAIM: Proceedings, http://www.emath.fr/proc/, 2, 1997, 183-193. Zbl0898.93018 MR1486080 · Zbl 0898.93018 · doi:10.1051/proc:1997012 [6] S. Hansen, E. Zuazua: Exact controllability and stabilization of a vibrating string with an interior point mass, SIAM J. Contr. Opt., 33, 1995, 1357-1391. Zbl0853.93018 MR1348113 · Zbl 0853.93018 · doi:10.1137/S0363012993248347 [7] J.L. Lions: Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués, 1, Masson, Paris, 1988. [8] J.L. Lions: Exact controlability, stabilization and perturbations for distributed systems, SIAM Rev., 30, 1988, 1-68. Zbl0644.49028 MR931277 · Zbl 0644.49028 · doi:10.1137/1030001 [9] H. Mounier: Propriétés structurelles des systèmes linéaires à retards: aspects théoriques et pratiques, Thèse, Université Paris-Sud, Orsay, 1995. [10] H. Mounier: Algebraic interpretations of the spectral controllability of a linear delay system, Forum Math., 10, 1998, 39-58. Zbl0891.93014 MR1490137 · Zbl 0891.93014 · doi:10.1515/form.10.1.39 [11] H. Mounier, P. Rouchon, J. Rudolph: Some examples of linear systems with delay, RAIRO-APII-JESA, 31, 1997, 911-925. [12] H. Mounier, J. Rudolph, M. Petitot, M. Fliess: A flexible rod as a linear delay system, In European Control Conference Proc., Rome, 1995, 3676-3681. [13] D.L. Russel: Controllability and stabilizability theory for partial differential equations, recent progress and open question, SIAM Rev., 20, 1978, 639-739. Zbl0397.93001 MR508380 · Zbl 0397.93001 · doi:10.1137/1020095 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.