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.
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