An Optimal Regulator Design of Fractional Differential Systems

Abstract

This paper considers an optimal control problem for linear fractional differential systems which are described in terms of fractional order derivatives of state variables. The optimal feedback gain matrix is derived by using Lyapunov equation and Lagrange multiplier method. It must satisfy simultaneous matrix equations which are solved by iterative calculations for convergence.
A numerical example is carried out for the optimal regulator design of a viscoelastic damper system which is often said to be a good example of a fractional differential system.