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Inverse Optimal Control for a New Lü Chaotic System

Tingfang Zhang, Hongxing Yao

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Abstract

A new Lu chaotic system and its basic dynamic behaviors are introduced in the paper.When parameters are suitable,the system can display two 1-scroll chaotic attractors,or two 2-scroll chaotic attractors simultaneously.Based on the theory of Lyapunov stability,by means of the inverse optimal controlling approach,an optimal controller is designed for controlling a new Lu chaotic system.The controller is a linear state feedback controller and is very simple.With the chaotic system orbit can be controlled to its unstable equilibrium.By numerical simulation and theory analysis the effectiveness of the controller is verified.

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What this paper is about

A new Lu chaotic system and its basic dynamic behaviors are introduced in the paper.When parameters are suitable,the system can display two 1-scroll chaotic attractors,or two 2-scroll chaotic attractors simultaneously.Based on the theory of Lyapunov stability,by means of the inverse optimal controlling approach,an optimal controller is designed for controlling a new Lu chaotic system.The controller is a linear state feedback controller and is very simple.With the chaotic system orbit can be controlled to its unstable equilibrium.By numerical simulation and theory analysis the effectiveness of the controller is verified.

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Available abstract

A new Lu chaotic system and its basic dynamic behaviors are introduced in the paper.When parameters are suitable,the system can display two 1-scroll chaotic attractors,or two 2-scroll chaotic attractors simultaneously.Based on the theory of Lyapunov stability,by means of the inverse optimal controlling approach,an optimal controller is designed for controlling a new Lu chaotic system.The controller is a linear state feedback controller and is very simple.With the chaotic system orbit can be controlled to its unstable equilibrium.By numerical simulation and theory analysis the effectiveness of the controller is verified.

Key concepts: Control theory (sociology), Chaotic, Attractor, Controller (irrigation), Computer science, Inverse, Mathematics, Lyapunov function

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