Novel closed-loop controllers for fractional linear quadratic time-varying systems

Abstract

A novel method for finding the closed-loop optimal controllers of the finite-time fractional linear quadratic regulator systems is introduced. The necessary optimality conditions for the fractional optimal control problems are obtained. The matrix fractional differential Riccati equation is presented. A new method for solving the fractional differential Riccati equation is given for the first time which can also be applied to the integer order Riccati equation. Several illustrative examples (including a high order system) are presented to show the applicability and capabilities of the method.