Abstract
This paper describes a numerical iterative method for computing the optimal control actions in linear or nonlinear control systems with control appearing linearly (1),(2),(3). The method we propose belongs to the class of direct methods but also makes use of the knowledge of the general form of the optimal control derived by the maximum principle (2).
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
H. Hermes and G. Haynes: “On the Nonlinear Control Problem with Control Appearing Linearly”, J.SIAM Control, Ser. A, Vol. 1, N. 2, 1963.
L.S. Pontryagin et al.: “The Mathematical Theory of Optimal Processes”, Editor L.W.Neustadt, Interscience Publishers, New York, 1962.
E.B. Lee and L. Markus: “Foundations of Optimal Control Theory”, J.Wiley and Sons Inc., New York, 1967.
J.P. La Salle: “The Time Optimal Control Problem”, in “Contributions to the Theory of Nonlinear Oscillations”, Vol. 5, Princeton University Press, Princeton, 1960, PP. 1–24.
R. Courant: “Calculus of Variations and Supplementary Notes and Exercises”, 1945–1946 revised and amended by I. Moser, New York Univ., Inst.of Sciences, New York.
K.Okamura: “Some Mathematical Theory of the Penalty Method for Solving Optimum Control Problems” J. SIAM Control, Ser A, Vol. 2, N. 3, 1964.
E.J. Beltrami: “On Infinite Dimensional Convex Programs”, J. Computer and System Sci., December 1967.
M.G.D. Powell: “An Efficient Method for Finding the Minimum of a Function of Several Variables without Calculating Derivatives, The Computer J. Vol. 7, 1964.
R. Kulikowski: “Optimum Processes and Synthesis of Optimum Automatic Control Systems with Non-linear Invariable Elements” In “Proceedings of the International Federation of Automatic Control Congress, Moscow”, 1960.
E.J. Fadden and E.G. Gilbert: “Computational Aspect of the Time Optimal Control Problem” in “Computing Methods in Optimization Problems” edited by A.V. Balakrishnam and L.W. Neustadt, Academic Press, New York, 1964.
M. Athans, P.L. Falb: “Optimal Control: An Introduction to the Theory and its Applications”, Mc Graw Hill, N.Y., 1966.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1969 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Arienti, G., Daneri, A.C. (1969). Computation of the Switching Times in Optimal Control Problems of Bang-Bang Type. In: Computing Methods in Optimization Problems. Lecture Notes in Operations Research and Mathematical Economics, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-85974-8_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-85974-8_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-04637-0
Online ISBN: 978-3-642-85974-8
eBook Packages: Springer Book Archive