Adaptive Backstepping Controller Design for the Anti-Synchronization of Identical WINDMI Chaotic Systems with Unknown Parameters and its SPICE Implementation

Abstract

This paper derives new results for the adaptive backstepping controller design for the anti-synchronization of identical WINDMI systems (Wind-Magnetosphere-Ionosphere models) with unknown parameters and also details the SPICE implementation of the proposed adaptive backstepping controller. In the anti-synchronization of chaotic systems, the sum of the outputs of master and slave systems is made to converge asymptotically to zero with time. The adaptive controller design for the anti-synchronization of identical WINDMI systems with unknown parameters has been established by applying Lyapunov stability theory. MATLAB simulations have been shown for the illustration of the adaptive anti-synchronizing backstepping controller for identical WINDMI chaotic systems. Finally, the proposed controller has been implemented using SPICE and circuit simulation results have been detailed.

Keywords

• Chaos
• chaotic systems
• anti-synchronization
• WINDMI system
• stability
• SPICE simulation.