On the Relationship Between the Pontryagin Maximum Principle and the Hamilton–Jacobi–Bellman Equation in Optimal Control Problems for Fractional-Order Systems
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引用次数: 0
Abstract
We consider the optimal control problem of minimizing the terminal cost functional for a
dynamical system whose motion is described by a differential equation with Caputo fractional
derivative. The relationship between the necessary optimality condition in the form of
Pontryagin’s maximum principle and the Hamilton–Jacobi–Bellman equation with so-called
fractional coinvariant derivatives is studied. It is proved that the costate variable in the
Pontryagin maximum principle coincides, up to sign, with the fractional coinvariant gradient of
the optimal result functional calculated along the optimal motion.
期刊介绍：
Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.
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