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The advantages of adjoint-control transformations when determining optimal trajectories by Pontryagin's Maximum Principle

Published online by Cambridge University Press:  04 July 2016

L. C. W. Dixon  and
M. C. Biggs
L. C. W. Dixon
Affiliation:
Numerical Optimisation Centre, Hatfield Polytechnic
M. C. Biggs
Affiliation:
Numerical Optimisation Centre, Hatfield Polytechnic
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Extract

The many methods by which Pontryagin's Maximum Principle is applied in optimal control problems can be divided into two groups, termed direct and indirect. The indirect methods use the conditions required for mathematical optimality as the starting point and attempt to satisfy the boundary conditions. The direct methods on the other hand satisfy the equations of motion and boundary conditions and then attempt to improve the performance index. It has been reported that the direct methods, while normally converging from very bad initial assumptions, have the inherent disadvantage of very slow convergence in the neighbourhood of the optimal solution and, so, complicated second order methods have recently been devised.

Type
Technical notes
Information
The Aeronautical Journal , Volume 76 , Issue 735 , March 1972 , pp. 169 - 174
Copyright
Copyright © Royal Aeronautical Society 1972 

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