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Avtomat. i Telemekh., 2009, Issue 10, Pages 45–74 (Mi at540)  

Deterministic Systems

Integral and integro-differential control plants: Optimality conditions

V. Yu. Tertychny-Dauri

St. Petersburg State University of Information Technologies, Mechanics and Optics, St. Petersburg, Russia

Abstract: For the control systems whose dynamics obeys a nonlinear regular integral Volterra equation with additional constraints in the form of equalities, the necessary optimality conditions were established on the basis of the abstract Yakubovich–Matveev theory of optimal control and, in particular, the abstract principle of maximum. Consideration was given to two kinds of the nonlinear controllable singular integral equations with unrestricted multipliers under the integral – with the power kernel of the Cauchy kernel type and with the logarithmic kernel. Attention was paid mostly to the nonlinear controlled dynamic systems obeying an integro-differential Volterra equation of the first order. As before, the study relied on the abstract theory of optimal control. The necessary optimality conditions were established by deriving the corresponding conjugate equation, transversality conditions, and principle of maximum.

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English version:
Automation and Remote Control, 2009, 70:10, 1635–1661

Bibliographic databases:

PACS: 45.10.Db
Presented by the member of Editorial Board: . . 

Received: 23.09.2008

Citation: V. Yu. Tertychny-Dauri, “Integral and integro-differential control plants: Optimality conditions”, Avtomat. i Telemekh., 2009, no. 10, 45–74; Autom. Remote Control, 70:10 (2009), 1635–1661

Citation in format AMSBIB
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