Novel closed-loop controllers for fractional nonlinear quadratic systems

Abstract

A novel closed-loop optimal controller for fractional nonlinear quadratic optimal control problems is introduced. By using a new idea, the optimality conditions for the fractional nonlinear problems are derived. The linearized Riccati fractional order differential equation is derived and a new solution method is given for the first time, which can be applied to integer order nonlinear optimal control problems. The proposed closed-loop controller is applied to illustrative examples. Novel unprecedented processes of designing a variable linear controller and of finding the optimal performance index for integer order nonlinear systems are presented.

Keywords

• fractional nonlinear optimal control
• closed-loop controller
• fractional riccati equation for nonlinear systems
• fractional nonlinear system
• linear controller for nonlinear systems
• highly nonlinear system