Abstract
The canonical optimal control problem for a linear time-varying dynamic system in the class of discrete controls is under consideration. Using principles of the adaptive method of linear programming, algorithms of open-loop and close-loop optimization are described. Results are illustrated by a fourth order problem.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and Ye. F. MischenkoMathematical Theory of Optimal ProcessesInterscience Publishers Inc., New York, 1962.
G. B. DantzigLinear Programming and ExtentionsPrinceton University Press, New Jersey, 1963.
R. Bulirsch, F. Montrone, and H. J. PeschAbort Landing in the Presence of Winds-hear as a Minimax Optimal Control Problem, Part 1: Necessary ConditionsJournal of Optimization Theory and Applications70(1) (1991), pp. 1–23.
R. Bulirsch, F. Montrone, and H. J. PeschAbort Landing in the Presence of Winds-hear as a Minimax Optimal Control Problem, Part 2: Multiple Shooting and HomotopyJournal of Optimization Theory and Applications70(2) (1991), pp. 223–254.
H. J. PeschReal-time Computation of Feedback Controls for Constrained Optimal Control Problems. Part 1: Neighbouring ExtremalsOptimal Control Applications and Methods10 (1989), pp. 129–145.
H. J. PeschReal-time Computation of Feedback Controls for Constrained Optimal Control Problems. Part 2: A Correction Method Based on Multiple ShootingOptimal Control Applications and Methods10 (1989), pp. 147–171.
K. ChudejRealistic Modelled Optimal Control Problems in Aerospace Engineering - A Challenge to the Necessary Optimality ConditionsMathematical Modelling of Systems2(4) (1996), pp. 252–261.
O. von StrykUser’s Guide to DIRCOL Version 2.0: A Direct Collocation Method for the Numerical Solution of Optimal Control ProblemsLehrstuhl M2 Höhere Mathematik and Numerische Mathematik, Technische Universität München, 1999, 128 p.
A. I. Tyatushkin, A. I. Zholudev, and N. M. ErinchekThe Program System for Solving Optimal Control Problems with Phase ConstraintsInt. Journal of Software Engineering and Knowledge Engineering3(4) (1993), pp. 487–497.
R. Gabasov, F. M. Kirillova et al.Constructive Methods of Optimization. Part 1: Linear Problems. Part 2: Control Problems. Part 3: Network Problems. Part 4: Convex Problems. Part 5: Nonlinear ProblemsUniversity Publishing House, Minsk, Belarus, 1984, 1984, 1986, 1987, 1998.
R. Gabasov, F. M. Kirillova, and S. V. PrischepovaOptimal Feedback ControlLecture Notes in Control and Information Sciences, M. Thoma, ed., Springer-Verlag2071995.
R. Gabasov, F. M. Kirillova, and N. V. BalashevichOpen-loop and Closed-loop Optimization of Linear Control SystemsAsian Journal of Control2(3) (2000), pp. 155–168.
R. P. FedorenkoApproximate Solution of Optimal Control ProblemsMoscow, Nauka, 1973.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Basel AG
About this paper
Cite this paper
Gabasov, R., Kirillova, F.M. (2001). Fast Algorithms for Positional Optimization of Dynamic Systems. In: Hoffmann, KH., Hoppe, R.H.W., Schulz, V. (eds) Fast Solution of Discretized Optimization Problems. ISNM International Series of Numerical Mathematics, vol 138. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8233-0_9
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8233-0_9
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9484-5
Online ISBN: 978-3-0348-8233-0
eBook Packages: Springer Book Archive