Find out how to access previewonly content
A numerical approach to the infinite horizon problem of deterministic control theory
 M. Falcone
 … show all 1 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
We are concerned with the HamiltonJacobi equation related to the infinite horizon problem of deterministic control theory. Approximate solutions are constructed by means of a discretization in time as well as in the state variable and we prove that their rate of convergence to the viscosity solution is of order 1, provided a semiconcavity assumption is satisfied. A computational algorithm, originally due to R. Gonzales and E. Rofman, is adapted and reformulated for the problem at hand in order to obtain an error estimate for the numerical approximate solutions.
This work has been partially supported by CNRGNAFA.
Communicated by W. Fleming
 Aubin JP, Cellina A (1984) Differential Inclusions. SpringerVerlag, Berlin, Heidelberg, New York
 Capuzzo Dolcetta I (1983) On a discrete approximation of the HamiltonJacobi equation of dynamic programming. Appl Math Optim 10:367–377
 Capuzzo Dolcetta I, Ishii H (1984) Approximate solutions of the Bellman equation of deterministic control theory. Appl Math Optim 11:161–181
 Crandall MG, Lions PL (1983) Viscosity solutions of HamiltonJacobi equations. Trans Amer Math Soc 277:1–42
 Crandall MG, Lions PL (1984) Two approximations of solutions of HamiltonJacobi equations. Math Comp 43:1–19
 Crandall MG, Evans LC, Lions PL (1984) Some properties of viscosity solutions of HamiltonJacobi equations. Trans Amer Math Soc 282:487–502
 Falcone M (1985) Numerical solution of deterministic continuous control problems. Proceedings of the International Symposium on Numerical Analysis, Madrid, September 1985
 Falcone M (1986) (forthcoming)
 Fleming WH, Rishel RW (1975) Deterministic and Stochastic Optimal Control. SpringerVerlag, Berlin, Heidelberg, New York
 Glowinski R, Lions JL, Trémolières R (1976) Analyse Numerique des Inéquations Variationnelles, vols 1 and 2. Dunod, Paris
 Gonzales R, Rofman E (1985) On deterministic control problems: an approximation procedure for the optimal cost, I and II. SIAM J Control Optim 23:242–285
 Lions PL (1982) Generalized Solutions of HamiltonJacobi Equations. Pitman, London
 Lions PL, Mercier B (1980) Approximation numerique des equations de HamiltonJacobiBellman. RAIRO Anal Numér 14:369–393
 Quadrat JP (1975) Analyse Numerique de l'Equation de Bellman Stochastique. Rapport INRIA no 140
 Rofman E (1985) Approximation of HamiltonJacobiBellman equation in deterministic control theory. An application to energy production systems. In: Capuzzo Dolcetta I, Fleming WH, Zolezzi T (eds) Recent Mathematical Methods in Dynamic Programming. Lecture Notes in Mathematics 1119. SpringerVerlag, Berlin, Heidelberg, New York
 Souganidis PE (1985) Approximation schemes for viscosity solutions of HamiltonJacobi equations. J. Differential Equations 59:1–43
 Title
 A numerical approach to the infinite horizon problem of deterministic control theory
 Journal

Applied Mathematics and Optimization
Volume 15, Issue 1 , pp 113
 Cover Date
 19870101
 DOI
 10.1007/BF01442644
 Print ISSN
 00954616
 Online ISSN
 14320606
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Authors

 M. Falcone ^{(1)}
 Author Affiliations

 1. Dipartimento di Matematica, Università di Roma, P. A. Moro, 2, 00185, Roma, Italy