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Punctual control of a vibrating string: Numerical analysis. (English) Zbl 0414.93036


MSC:

93D15 Stabilization of systems by feedback
93B40 Computational methods in systems theory (MSC2010)
93C20 Control/observation systems governed by partial differential equations
35L05 Wave equation
70J25 Stability for problems in linear vibration theory
Full Text: DOI

References:

[1] A. Bamberger, J. Jaffre and J. P. Yvon, Contrôle et Stabilisation d’une Corde Vibrante par une Masse Ponctuelle, Rapport de Recherche Laboria (1978, to be published). Racquencourt, France.; A. Bamberger, J. Jaffre and J. P. Yvon, Contrôle et Stabilisation d’une Corde Vibrante par une Masse Ponctuelle, Rapport de Recherche Laboria (1978, to be published). Racquencourt, France.
[2] Heller, W. G., Feedback stabilization of a distributed parameter system by scanning, Proc. IFAC Symp. (1971), Banff, Canada
[3] Jaffre, J., Analyse Numérique de Deux Problèmes de Domaine Optimal et de contrôle Pontuel, Thèse de \(3^{ème}\) Cycle (1974), Université de Paris VI
[4] Lions, J. L., Contrôle Optimal de Systèmes Gouvernés par des Equations aux Dérivées Partielles (1968), Dunod · Zbl 0179.41801
[5] Lions, J. L.; Magenes, P., Problèmes aux Limites non Homogènes (1969), Dunod: Dunod Paris, Tome 1 · Zbl 0115.31302
[6] Melcher, J. R., Control of a continuum electromechanical instability, Proc. IEEE, 53, 460-473 (May 1965)
[7] Melcher, J. R., An experiment to stabilize an electromechanical continuum, IEEE Transactions on Automatic Control, AC-10, No. 4, 466-469 (October 1965)
[8] Raviart, P. A., Sur l’approximation de certaines equations d’evolution linéaires et non-linéaires, J. Math. Pures et Appliqueés, 46, 11-107 (1967) · Zbl 0198.49803
[9] Richtmyer, R. D.; Morton, K. W., Difference Methods for Initial Value Problems (1967), Interscience Publishers · Zbl 0155.47502
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