Synchronization of 4-D Hyperchaotic Rikitake Dynamo System Along With Unknown Parameters Via Adaptive Integral Sliding Mode

An adaptive integral sliding mode control approach is proposed for the synchronization of 4-D identical hyperchaotic Rikitake dynamo system which operates with unknown parameters. The error dynamics are first transformed into a special structure which contains a known nominal part as well as unknown terms. The unknown terms are computed adaptively via an adaptive compensator, and the resulted error dynamics are stabilized asymptotically using integral sliding mode control. This stabilizing controller is an algebraic sum of the nominal control and the compensating control. The dangerous chattering phenomenon is suppressed via the designed compensator control. The closed loop stability of the designed compensator controller and the adapted law are ensured via the Lyapunov stability strategy. It is also worthy to report that the posed problem is handled via a reduced number of control inputs as compared the existing literature. In this case, the proposed design becomes a good candidate for chaotic systems with unknown parameters. The simulation results confirms the made claims.