Modern Methods for Solving Nonconvex Optimal Control Problems
The paper presents a few remarks on the evolution of Irkutsk’s school of O. V. Vasiliev on optimal control methods based on Pontryagin principle. Besides, one reviews some features of Pontryagin principle, in particular, its sufficiency and constructive property for linear (on the state) control sys...
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| Format: | Article |
| Language: | English |
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Irkutsk State University
2014-06-01
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| Series: | Известия Иркутского государственного университета: Серия "Математика" |
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| Online Access: | http://isu.ru/journal/downloadArticle?article=_e984c0116bc94002910d374b3244d5f8&lang=rus |
| Summary: | The paper presents a few remarks on the evolution of Irkutsk’s school
of O. V. Vasiliev on optimal control methods based on Pontryagin principle. Besides,
one reviews some features of Pontryagin principle, in particular, its sufficiency and
constructive property for linear (on the state) control systems and convex cost functionals.
Further, some historical notes on the development of optimal control methods based
on Pontryagin principle are considered. In particular, a separated attention has been
paid to the impact of Irkutsk school of O. V. Vasiliev in the theory and method of
optimal control, and the achievements of the former postgraduate student of O. V.
Vasiliev professor V. A. Srochko. The mathematical presentation is concentrated on
the story of the invention and investigations of the convergence and substantiation of
the consecutive approximate’s method based on Pontryagin principle. In addition, one
considers new Global Optimality Conditions in a general nonconvex optimal control
problem with Bolza goal functionals. Moreover, together with the necessity proof of
global optimality conditions we investigate its relations to Pontryagin principle. Besides,
the constructive (algorithmic) property of new optimality conditions is also demonstrated,
and an example of nonconvex optimal control problems has been solved by means of global
optimality conditions. In this example, we performed an improvement of a feasible control
satisfying Pontryagin principle with a corresponding improvement of the cost functional.
Finally, employing Pontryagin principle and new Global Optimality Conditions we give
a demonstration of construction of a optimal control method and provide for new result
on its convergence. |
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| ISSN: | 1997-7670 2541-8785 |