Adaptive control of a four-dimensional memristor-based Chua's circuit

Abstract

This paper investigates the behavior of a four-dimensional memristor-based Chua circuit. Specifically, we emphasize its chaotic and hyperchaotic behavior using the phase portrait and the Lyapunov spectrum. As chaos is deemed undesirable in numerous scientific disciplines, particularly in fields like robotics and electronic sciences, where the analyzed circuit holds potential applications in electronic device construction, we aim to alleviate such behaviors. To achieve this, we put forth an adaptive control strategy involving unknown parameters. The effectiveness of the suggested adaptive chaos control is established using the Lyapunov stability theory. To further illustrate and confirm our findings, we present numerical simulations, providing a visual representation of the successful application of the proposed adaptive control in managing the circuit's dynamics.

Keywords

• Memristor, hyperchaotic system, Chua’s circuit, stability, Lyapunov function, adaptive control