On a Solution of an Optimal Control Problem for a Linear Fractional-Order System

Gomoyunov, Mikhail

doi:10.1007/978-3-030-50936-1_70

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“…that satisfies the equality in (10) and the differential equation in (9) for almost every t ∈ [t * , ϑ]. Then, we put…”

Section: Informational Imagementioning

confidence: 99%

“…Let us note that various optimal control problems in linear fractional-order systems with the Caputo derivatives are studied, e.g., in [1, 14-16, 21, 25] (see also the references therein for possible applications), where suitable variants of the maximum principle, methods of variational calculus and convex analysis, and methods related to the problem of moments are applied to find a solution. Moreover, in [9], a reduction scheme close to that proposed in the paper is developed on the basis of an approximation of fractional-order differential equations with the Caputo derivatives by first-order functional differential equations of a retarded type. However, the present paper follows a different approach that relies on the representation formula for solutions to linear fractional-order differential equations with the Caputo derivatives [8], does not require any approximation as an auxiliary intermediate step, and is more straightforward.…”

Section: Introductionmentioning

confidence: 99%

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Archives of Control Sciences

Gomoyunov¹

2020

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The paper deals with an optimal control problem in a dynamical system described by a linear differential equation with the Caputo fractional derivative. The goal of control is to minimize a Bolza-type cost functional, which consists of two terms: the first one evaluates the state of the system at a fixed terminal time, and the second one is an integral evaluation of the control on the whole time interval. In order to solve this problem, we propose to reduce it to some auxiliary optimal control problem in a dynamical system described by a first-order ordinary differential equation. The reduction is based on the representation formula for solutions to linear fractional differential equations and is performed by some linear transformation, which is called the informational image of a position of the original system and can be treated as a special prediction of a motion of this system at the terminal time. A connection between the original and auxiliary problems is established for both open-loop and feedback (closed-loop) controls. The results obtained in the paper are illustrated by examples.

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“…that satisfies the equality in (10) and the differential equation in (9) for almost every t ∈ [t * , ϑ]. Then, we put…”

Section: Informational Imagementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%