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Control of a novel fractional hyperchaotic system using a located control method. (English) Zbl 1298.34017

Summary: Fractional order dynamics and chaotics systems have been recently combined, yielding interesting behaviours. In this paper, a novel integer order hyperchaotic system is considered. Then, a fractional order hyperchaotic representation of such system is proposed using a natural fractionalization. Two different linear control methodologies to deal with the complexity which introduce such systems are proposed. Those methods are able to modify the hyperchaotic behaviour of the system and force it to move towards a fixed point; i.e. steady state. These approaches give a general framework for taming such complex systems using simple linear controllers. The main tools for analysing the controlled system are Matignon stability criterion and Routh-Hurwitz test. Using a reliable numerical simulation, the designed system is simulated to verify the theoretical analysis.

MSC:

34A08 Fractional ordinary differential equations
34H10 Chaos control for problems involving ordinary differential equations
34H15 Stabilization of solutions to ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
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