Abstract
In this paper we present an approximation framework and theoretical convergence results for a class of parameter estimation problems for general abstract nonlinear hyperbolic systems. These systems include as a special case those modeling a large class of nonlinear elastomers.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
H.T. Banks, D.S. Gilliam, and V.I. Shubov, Global solvability for damped nonlinear hyperbolic systems, CRSC-TR95-25, August, 1995; Differential and Integral Equations 10 (1997), pp. 309–332.
H.T. Banks, K. Ito, and Y. Wang, Well-posedness for damped second order systems with unbounded input operators, CRSC-TR93-10, June 1993; Differential and Integral Equations, 8(1995), pp. 587–606.
H.T. Banks and K. Kunisch, Estimation Techniques for Distributed Parameter Systems, BirkhĂ´user, Boston, 1989.
H.T. Banks and N.J. Lybeck, Modeling methodology for elastomer dynamics, CRSC-TR96-29, September, 1996; Systems and Control in the 21st Century, ed. by C. Byrnes, B. Datta, D. Gilliam and C. Martin, Birkhôuser, Boston, 1996, pp. 37–50.
H.T. Banks, N.J. Lybeck, M.J. Gaitens, B.C. Munoz, and L.C. Yanyo, Modeling the dynamic mechanical behavior of elastomers, CRSC-TR96-26, September, 1996; Rubber Chem and Tech., submitted.
H.T. Banks, N.J. Lybeck, B.C. Munoz, and L.C. Yanyo, Nonlinear elastomers: Modeling and estimation, CRSC-TR95-19, May, 1995; Proc. 3rd IEEE Mediterranean Symp. on New Directions in Control, Limassol, Cyprus, July, 1995, Vol. 1. pp. 1–7.
H.T. Banks and D.A. Rebnord, Analytic semigroups: Applications to inverse problems for flexible structures, in Differential Equations with Applications in Biology, Physics and Engineering, Marcel Dekker Inc., New York, 1991, pp. 21–35.
H.T. Banks, R. C. Smith and Y. Wang, Smart Material Structures, Modeling, Estimation and Control, Masson/Wiley, Paris/Chichester, 1996.
J.L. Lions, Optimal Control of Systems Governed by Partial Differential Equations,Springer-Verlag, New York, 1971.
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.
J. Wloka, Partial Differential Equations, Cambridge Univ. Press, 1992.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Basel AG
About this paper
Cite this paper
Banks, H.T., Pinter, G.A. (1998). Approximation Results for Parameter Estimation in Nonlinear Elastomers. In: Desch, W., Kappel, F., Kunisch, K. (eds) Control and Estimation of Distributed Parameter Systems. International Series of Numerical Mathematics, vol 126. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8849-3_1
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8849-3_1
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9800-3
Online ISBN: 978-3-0348-8849-3
eBook Packages: Springer Book Archive