Abstract
A Ritz-type parameterization of the control functions is used to simplify the calculation of optimal control functions. From the well-known gradient technique for problems constrained by differential equations, an iteration formula for the parameters is derived. This approach allows the efficient solution of fairly general problems even if only small computers (like desk-top calculators, personal computers or micro/mini computers) are used.
Preview
Unable to display preview. Download preview PDF.
References
H. Tolle: Optimization methods, Springer-Verlag, 1971.
W. Ritz: Über eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physik. J. reine angew. Math., Vol. 135, 1908, p1
A. Bryson, W. Denham, E. Caroll, K. Mikami: Determination of the lift or drag program that minmizes reentry heating with acceleration or range constraints using a steepest descent procedure. JAS-Paper Nr. 61-6.
H. Rosenbrock, C. Storey: Computational techniques for chemical engineers. Pergamon Press, 1966.
G. Hicks, W. Ray: Approximation methods for optimal control synthesis. Can. J. Chem. Eng., Vol. 49, 1971, p. 522.
W. Williamson: Use of polynomial approximations to calculate suboptimal controls. J. Am. Inst. Aero. Astron., Vol. 9, 1971, Nr. 11, p. 2271.
R. Brusch: A nonlinear programming approach to space-shuttle trajectory optimization. J. Opt. Theor. Appl., Vol. 13, 1974, Nr. 1, p. 94.
H. Sirisena, A. Chou: Convergence of the control parameterization Ritz method for nonlinear optimal control problems. J. Opt. Theor. Appl., Vol. 29, 1979, Nr. 3, p. 369.
B. Asselmeyer: A two level optimal final-value control system for nonlinear plants realized with mini/micro computers. J. Opt. Contr. Appl. Meth., Vol. 2, to appear 1982.
J. Rosen: The gradient projection method for nonlinear programming, Part I: Linear constraints. SIAM J., Vol. 8, 1960, Nr. 1, p. 181.
S. Jacoby, J. Kowalik, J. Bozzo: Iterative methods for nonlinear optimization problems. Prentica Hall, Inc., 1972.
B. Asselmeyer: Zur optimalen Endwertregelung nichtlinearer Systeme mit Hilfe Kleiner Rechner, Darmstädter Dissertation, 1980.
J. Douglas: Process dynamics and control, Vol. 1, Analysis of dynamic systems. Prentice Hall, Inc., 1972.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1982 Springer-Verlag
About this paper
Cite this paper
Asselmeyer, B. (1982). A ritz-type approach to the calculation of optimal control for nonlinear, dynamic systems. In: Drenick, R.F., Kozin, F. (eds) System Modeling and Optimization. Lecture Notes in Control and Information Sciences, vol 38. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006130
Download citation
DOI: https://doi.org/10.1007/BFb0006130
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-11691-2
Online ISBN: 978-3-540-39459-4
eBook Packages: Springer Book Archive