Optimal control for fractionally damped flexible systems

Abstract

This paper is concerned with the linear-quadratic optimal control of a rod whose damping mechanism is described in terms of fractional derivatives. A state-space representation of the original system is obtained by a suitable transformation. This transformation is based on the description of the heredity of the system through an additional state variable and thereby allows the solution of the quadratic optimal control problem to be simply determined. Some numerical simulations are provided also with the aim of demonstrating the legitimacy of the approach in the experimental field.<>