Sensitivity analysis of value functional of fractional optimal control problem with application to construction of optimal feedback control

TL;DR

This paper investigates the sensitivity of the value functional in fractional optimal control problems and introduces a new method for constructing optimal feedback controls based on directional differentiability properties.

Contribution

It establishes the directional differentiability of the value functional in fractional control problems and proposes a novel approach for feedback control construction.

Findings

Value functional has directional differentiability of order α.

New method for optimal feedback control construction.

Applicable to systems described by Caputo fractional differential equations.

Abstract

We consider an optimal control problem for a dynamical system described by a Caputo fractional differential equation and a terminal cost functional. We prove that, under certain assumptions, the (non-smooth, in general) value functional of this problem has a property of directional differentiability of order $\alpha$. As an application of this result, we propose a new method for constructing an optimal positional (feedback) control strategy.