Computational Methods in Optimal Control Problems
The purpose of this modest report is to present in a simplified manner some of the computational methods that have been developed in the last ten years for the solution of optimal control problems. Only those methods that are based on the minimum (maximum
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Lecture Notes in Operations Research and Mathematical Systems Economics, Computer Science, Information and Control Edited by M. Beckmann, Providence and H. P. Kunzi, Zurich
27 I. H. Mufti National Research Council Ottawa, Ontario/Canada
Computational Methods in Optimal Control Problems
Springer-Verlag Berlin· Heidelberg· New York 1970
Advisory Board H. Albach A. V. Balakrishnan F. Ferschl W. Krelle . N. Wirth
TSBN-13: 978-3-540-04951-7 e-TSBN-13 978-3-642-85960-1 DOl: 10.1007/978-3-642-85960-1
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PREFACE The purpose of this modest report is to present in a simplified manner some of the computational methods that have been developed in the last ten years for the solution of optimal control problems. Only those methods that are based on the minimum (maximum) principle of Pontriagin are discussed here. The autline of the report is as follows:
In the first two
sections a control problem of Bolza is formulated and the necessary conditions in the form of the minimum principle are given.
The
method of steepest descent and a conjugate gradient-method are discussed in Section 3.
In the remaining sections, the successive sweep
method, the Newton-Raphson method and the generalized Newton-Raphson method (also called quasilinearization method) ar~ presented from a unified approach which is based on the application of NewtonRaphson approximation to the necessary conditio
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