Higher order numerical schemes for affinely controlled nonlinear systems

Authors
Grune, L Kloeden, PE
Citation
L. Grune et Pe. Kloeden, Higher order numerical schemes for affinely controlled nonlinear systems, NUMER MATH, 89(4), 2001, pp. 669-690
Citations number
15
Categorie Soggetti
Mathematics
Journal title
NUMERISCHE MATHEMATIK
ISSN journal
0029599X → ACNP
Volume
89
Issue
4
Year of publication
2001
Pages
669 - 690
Database
ISI
SICI code
0029-599X(200110)89:4<669:HONSFA>2.0.ZU;2-5
Abstract
A systematic method for the derivation of high order schemes for affinely c ontrolled nonlinear systems is developed. Using an adaptation of the stocha stic Taylor expansion for control systems we construct Taylor schemes of ar bitrary high order and indicate how derivative free Runge-Kutta type scheme s can be obtained. Furthermore an approximation technique for the multiple control integrals appearing in the schemes is proposed.