Parameter identification in classes of neutral differential equations with state-dependent delays

Nonlinear Analysis, Theory, Methods and Applications

Volumn 39, Issue 3, 1999, Pages 305-325

  Hartung, Ferenc ^a,b   Herdman, Terry L ^a   Turi, Janos ^c  

^a VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

^b UNIVERSITY OF PANNONIA   (Hungary)

^c UNIVERSITY OF TEXAS AT DALLAS   (United States)

Author keywords

Equations with piecewise constant arguments; Euler method; Neutral equations; Numerical approximation; Parameter identification; State dependent delays

Indexed keywords

EID: 0004407154     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(98)00169-2     Document Type: Article

References (18)

1. H.T. Banks, J.A. Burns, E.M. Cliff, Parameter estimation and identification for systems with delays, SIAM J. Control Optim. 19(6) (1981) 791-828.
2. H.T. Banks, K. Kunisch, Estimation Techniques for Distributed Parameter Systems, Birkhäuser, Basa, 1989.
3. H.T. Banks, P.K. Daniel Lamm, Estimation of delays and other parameters in nonlinear functional differential equations, SIAM J. Control Optim. 21(6) (1983) 895-915.
4. J.A. Burns, P.D. Hirsch, A difference equation approach to parameter estimation for differential-delay equations, Appl. Math. Comput. 7 (1980) 281-311.
5. J.E. Dennis, R.B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, NJ, 1983.
6. R.D. Driver, A neutral system with state-dependent delay, J. Diff. Eqns. 54 (1984) 73-86.
7. L.J. Grimm, Existence and continuous dependence for a class of nonlinear neutral-differential equations, Proc. Amer. Math. Soc. 29(3) (1971) 467-473.
8. I. Györi, On approximation of the solutions of delay differential equations by using piecewise constant arguments, Internat. J. Math. Math. Sci. 14(1) (1991) 111-126.
9. I. Györi, F. Hartung, J. Turi, On numerical approximations for a class of differential equations with time- and state-dependent delays, Appl. Math. Lett. 8(6) (1995) 19-24.
10. J.K. Hale, M.A. Cruz, Existence, uniqueness and continuous dependence for hereditary systems, Ann. Mat. Pura Appl. 85 (1970) 63-81.
11. F. Hartung, T.L. Herdman, J. Turi, Identifications of parameters in hereditary systems, Proc. ASME 15th Biennial Conf. on Mechanical Vibration and Noise, Boston, Massachusetts, September 1995, DE-Vol. 84-3, vol. 3, Part C, pp. 1061-1066.
12. F. Hartung, T.L. Herdman, J. Turi, Identifications of parameters in hereditary systems: a numerical study, Proc. 3rd IEEE Mediterranean Symp. on New Directions in Control and Automation, Cyprus, July 1995, pp. 291-298.
13. F. Hartung, T.L. Herdman, J. Turi, Parameter identification in classes of hereditary systems of neutral type, Appl. Math. Comput. 24 (1997) 393-409.
14. F. Hartung, J. Turi, Identification of parameters in delay equations with state dependent delays, J. Nonlinear Analysis 29(11) (1997) 1303-1318.
15. F. Hartung, T.L. Herdman, J. Turi, On existence, uniqueness and numerical approximation for neutral equations with state-dependent delays, Appl. Numer. Math. 24 (1997) 393-409.
16. Z. Jackiewicz, Existence and uniqueness of neutral delay-differential equations with state dependent delays, Funkcialaj Ekvacioj 30 (1987) 9-17.
17. K.A. Murphy, Estimation of time- and state-dependent delays and other parameters in functional differential equations, SIAM J. Appl. Math. 50(4) (1990) 972-1000.
18. S. Nakagiri, M. Yamamoto, Identifiability of linear retarded systems in Banach spaces, Funkcialaj Ekvacioj 31 (1988) 315-329.