Modified Optimal Energy and Initial Memory of Fractional Continuous-Time Linear Systems

TL;DR

This paper studies fractional continuous-time linear systems with Riemann-Liouville derivatives, focusing on initial memory, and derives explicit control laws and a generalized Gramian for steering system states.

Contribution

It introduces explicit steering laws based on fractional integrals and generalizes the Gramian for systems with initial memory, advancing control of fractional systems.

Findings

Explicit control laws derived for fractional systems

Generalized Gramian characterizes steering functions

Initial memory significantly influences control strategies

Abstract

Fractional systems with Riemann-Liouville derivatives are considered. The initial memory value problem is posed and studied. We obtain explicit steering laws with respect to the values of the fractional integrals of the state variables. The Gramian is generalized and steering functions between memory values are characterized.