Exact solution of Pontryagin's equations of optimal control?Part 1

Kagiwada, H.; Kalaba, Robert E.; Thomas, Y.

doi:10.1007/bf00928121

Cited by 6 publications

(1 citation statement)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A valuable tactic to deal with these problems is to restrict the candidates to be solution through necessary conditions for optimality, such as those given by Pontryagin's Maximum Principle. This technique is used in a wide range of disciplines, as for instance engineering [28,30,38,55], aerospace [69], robotics [35,37,62], medicine [47], economics [45,57], traffic flow [36]. Nevertheless, it is worth remarking that the Maximum Principle does not give sufficient conditions to compute an optimal trajectory; it only provides necessary conditions.…”

Section: Introductionmentioning

confidence: 99%

Geometric Approach to Pontryagin’s Maximum Principle

Barbero-Lin͂án¹,

Muñoz-Lecanda²

2008

Acta Appl Math

View full text Add to dashboard Cite

Since the second half of the 20th century, Pontryagin's Maximum Principle has been widely discussed and used as a method to solve optimal control problems in medicine, robotics, finance, engineering, astronomy. Here, we focus on the proof and on the understanding of this Principle, using as much geometric ideas and geometric tools as possible. This approach provides a better and clearer understanding of the Principle and, in particular, of the role of the abnormal extremals. These extremals are interesting because they do not depend on the cost function, but only on the control system. Moreover, they were discarded as solutions until the nineties, when examples of strict abnormal optimal curves were found. In order to give a detailed exposition of the proof, the paper is mostly self-contained, which forces us to consider different areas in mathematics such as algebra, analysis, geometry.

show abstract