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A VARIANT OF THE MAXIMUM PRINCIPLE FOR LINEAR SYSTEMS WITH AFTEREFFECT

Annotation

An optimal control problem is considered for the linear system with time delay of the general form. A sufficient and necessary condition of optimality is derived using the Cauchy matrix. The representation of an analog to the Hamilton-Pontryagin function is given as applied to the case of nonlocal control input operator.

Keywords

functional differential systems; control problems; optimal control

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UDC

517.929

Pages

1284-1287

References

1. Azbelev N.V., Maksimov V.P., Rahmatullina L.F. Vvedenie v teoriju funkcional'no-differencial'nyh uravnenij. M.: Nauka, 1991. 2. Azbelev N.V., Maksimov V.P., Rahmatullina L.F. Jelementy sovremennoj teorii funkcional'no-differencial'nyh uravnenij. M.: Institut komp'juternyh issledovanij, 2002. 3. Azbelev N.V., Maksimov V.P., Rakhmatullina L.F. Introduction to the theory of functional differential equations: methods and applications. New York; Cairo: Hindawi Publishing Corporation, 2007. 4. Azbelev N.V., Maksimov V.P. Apriornye ocenki reshenij zadachi Koshi i razreshimost' kraevyh zadach dlja uravnenij s zapazdyvajushhim argumentom // Differenc. uravnenija. 1979. T. 15. № 10. C. 1731-1747. 5. Maksimov V.P., Rahmatullina L.F. O predstavlenii reshenij linejnogo funkcional'no-differencial'nogo uravnenija // Differenc. uravnenija. 1973. T. 9. № 6. C. 1026-1036. 6. Maksimov V.P. O formule Koshi dlja funkcional'no-differencial'nogo uravnenija // Differenc. uravnenija. 1977. T. 13. № 4. C. 601-606. 7. Maksimov V.P. Voprosy obshhej teorii funkcional'no-differencial'nyh uravnenij. Perm': Izd-vo PGU, 2003. 8. Gabasov R., Kirillova F.M. Princip maksimuma v teorii optimal'nogo upravlenija. M.: Knizhnyj dom «LIBROKOM», 2011.

Received

2015-04-24

Section of issue

Scientific articles

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