Novel closed-loop controllers for fractional nonlinear quadratic systems

Iman Malmir; Iman Malmir

doi:10.3934/mmc.2023028

Mathematical Modelling and Control

2023, Volume 3, Issue 4: 345-354. doi: 10.3934/mmc.2023028

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Research article

Novel closed-loop controllers for fractional nonlinear quadratic systems

Iman Malmir ^,

Aerospace and Mechanical Engineering Group, Ronin Institute, Montclair, NJ 07043, USA

Received: 13 March 2023 Revised: 01 July 2023 Accepted: 01 September 2023 Published: 15 December 2023

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.
Citation: Iman Malmir. Novel closed-loop controllers for fractional nonlinear quadratic systems[J]. Mathematical Modelling and Control, 2023, 3(4): 345-354. doi: 10.3934/mmc.2023028

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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.

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