Preview
Unable to display preview. Download preview PDF.
References
I. BABUSKA and A.K. AZIZ, Survey lecture on the mathematical foundations of the finite element method, in The mathematical foundations of the finite element method with applications to partial differential equations, ed. A.K. Aziz, Academic Press, New York 1972.
A. BENSOUSSAN, M.C. DELFOUR and S.K. MITTER, Optimal filtering for linear stochastic hereditary differential systems, Proc. 1972 IEEE Conference on Decision and Control, New Orleans, 378–380.
V. COMINCIOLI, Problemi periodici relativi a equazioni d'evoluzione paraboliche contermini di ritardo. Risoluzione e approssimazione delle soluzioni mediante uno schema alle differenze finite. Instituto Lombardo (Rend. Sc.) A 104 (1970), 356–381.
V. COMINCIOLI and G. FAUSTI, Esperienze numeriche relative all'approssimazione delle soluzioni di disequazioni variazionali d'evoluzione con termini di ritardo. Laboratorio di analisi numerica del Consiglio Nazionale delle Ricerche, Publ. N. 12, Pavia 1971. (69 pages).
M. CROUZEIX, Approximation des équations hyperboliques du second ordre par des méthodes de Runge-Kutta, Séminaire Ciarlet-Glowinski-Raviart 1974–1975.
[2]M. CROUZEIX, Sur l'approximation des équations différentielles opérationnelles linéaires par des méthodes de RUNGE-KUTTA. Thèse de doctorat d'état ès-sciences mathématiques, Université de Paris VI, mars 1975.
R.T. CURTAIN, A. Kalman-Bucy theory for affine hereditary differential equations, in “Control theory, numerical methods and computer systems modelling”, eds. A. BENSOUSSAN and J.L. LIONS, Springer-Verlag, New York 1975, 22–43.
M.C. DELFOUR, Solution numérique de l'équation différentielle de Riccati rencontrée en théorie de la commande optimale de systèmes héréditaires linéaires, in Control theory, numerical methods and computer systems modelling, eds. A. BENSOUSSAN and J.L. LIONS, Springer-Verlag, New York 1975, 362–383.
M.C.DELFOUR S.K. MITTER, Numerical solution of the operational Riccati differential equation in the optimal control theory of linear hereditary differential systems with a linear-quadratic cost function, Proc. 1974 IEEE Conference on Decision and Control, Phoenix, 784–790.
M.C.DELFOUR S.K. MITTER, Numerical solution of the operator Riccati equation for the filtering of linear stochastic hereditary differential systems, in “Proceedings of the 7th IFIP Conference on Optimization Techniques”, to be published by Springer-Verlag.
M.C.DELFOUR S.K. MITTER, The linear quadratic optimal control problem for hereditary differential systems: theory and numerical solution, to appear in Journal of Applied Mathematics and Optimization.
M.C.DELFOUR S.K. MITTER, The state theory of linear hereditary differential systems, CRM-Report 395, to appear in J. Math. Anal. and Appl.
M.C. DELFOUR and S.K. MITTER, Hereditary differential systems with constant delays, I-General case. J. Differential Equations, 12 (1972), 213–235.
, Hereditary differential systems with constant delays, II-A class of affine systems and the adjoint problem, J. Differential Equations, 18 (1975), 18–28.
, Controllability, observability and optimal feedback control of hereditary differential systems, SIAM J. Control, 10 (1972), 298–328.
M.C. DELFOUR, C. McCALLA and S.K. MITTER, Stability and the infinite-time quadratic cost problem for linear hereditary differential systems, SIAM J. Control 13 (1975), 48–88.
R. KWONG, Structural properties and estimation of delay systems, doctoral dissertation, Massachusetts Institute of Technology, Cambridge, Mass. 02139, September 1975.
P. LESAINT and P.A. RAVIART, On a finite element method for solving the neutron transport equation, Proc. Symposium on Mathematical Aspects of Finite Elements in Partial Differential Equations, Mathematics Research Center, Univ. of Wisconsin, Madison, April 1–3, 1974.
J.L. LIONS, Some aspects of the optimal control of distributed parameter systems, SIAM, Philadelphia, 1972.
L.D. MARINI, Esperienze numeriche relative all'approssimazione delle soluzioni periodiche dei problemi d'evoluzione con termini di ritardo, Laboratorio di analisi numerica del Consiglio Nazionale delle Ricerche, Publ. N. 5 Pavia 1971. (14 pages).
J.C. NEDELEC, Schéma d'approximation pour des équations intégro-différentielles de Riccati. Thèse de doctorat d'état ès-sciences mathématiques, 7 octobre 1970, Paris, France.
[2]J.C. NEDELEC, Approximation par éléments finis des équations de Riccati, Rapport interne, Université de Rennes.
J. REVERDY, Discrétisation d'une équation aux différences-différentielles, comparaison entre différents schémas, Instituto Lombardo (Rend. Sc.) A 107 (1973) 511–527.
[2]J. REVERDY, Approximation d'une équation d'évolution linéaire du premier ordre perturbée par un terme retard. UER Informatique, Université Paul Sabatier, Toulouse, mai 1975.
F. TROCHU and M. DELFOUR, Approximation des systèmes différentiels par éléments finis discontinus, CRM-Report, June 1976 (Centre de Recherches Mathématiques, Université de Montréal).
R.B. VINTER, On the evolution of the state of a linear differential delay equation in M2: properties of the generator, Report ESL-R-541, Electronic Systems Laboratory, Massachusetts Institute of Technology, Cambridge, Mass. 02139, U.S.A.
[2]R.B. VINTER, A representation of solutions to stochastic delay equations, Imperial College of Science and Technology, internal report.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1978 Springer-Verlag
About this paper
Cite this paper
Delfour, M.C., Trochu, F. (1978). Discontinuous finite element methods for the approximation of optimal control problems governed by hereditary differential systems. In: Ruberti, A. (eds) Distributed Parameter Systems: Modelling and Identification. Lecture Notes in Control and Information Sciences, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0003742
Download citation
DOI: https://doi.org/10.1007/BFb0003742
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-08405-1
Online ISBN: 978-3-540-37195-3
eBook Packages: Springer Book Archive