The chaotic Dadras–Momeni system: control and hyperchaotification

Abstract

In this paper, a novel three-dimensional autonomous chaotic system, the so-called Dadras–Momeni system, is considered and two different control techniques are employed to realize chaos control and chaos synchronization. First, the optimal control of the chaotic system is discussed and an open loop feedback controller is proposed to stabilize the system states to one of the system equilibria, minimizing the cost function by virtue of the Pontryagin's minimum principle. Then, an adaptive control law and an update rule for uncertain parameters, based on Lyapunov stability theory, are designed both to drive the system trajectories to an equilibrium or to realize a complete synchronization of the system in periodic and chaotic regimes. Numerical simulations are included to show the effectiveness of the designed controllers in realizing the stabilization and the synchronization of the chaotic system. Finally, a new hyperchaotic system is introduced by adding a controller to the second equation of the three-dimensional autonomous Dadras–Momeni chaotic system and the corresponding hyperchaotic attractor is shown via computer simulations.