Time-Optimal Control of Linear Fractional Systems

TL;DR

This paper develops a convex-analytic method for designing time-optimal controls for linear systems with fractional differential equations, specifically using Riemann-Liouville derivatives, to achieve the shortest possible transition to a target state.

Contribution

It introduces a novel convex-analytic approach to construct control functions for fractional systems, focusing on attainability sets and support functions.

Findings

Method effectively finds shortest-time controls for fractional systems.

Control construction based on attainability sets is feasible and precise.

Provides theoretical foundation for time-optimal control in fractional dynamics.

Abstract

Problem of time-optimal control of linear systems with fractional dynamics is treated in the paper from the convex-analytic standpoint. A linear system of fractional differential equations involving Riemann--Liouville derivatives is considered. A method to construct a control function that brings trajectory of the system to the terminal state in the shortest time is proposed in terms of attainability sets and their support functions.