Robust Control Methods for Finite Time Synchronization of Uncertain Nonlinear Systems

Abstract

This chapter addresses the dynamic analysis and two different control strategies for the synchronization of new topology of Colpitts oscillator submitted to uncertainties and external disturbances. The diagrams obtained reveal precisely spirals bifurcation and chaos when for a specific values of the system parameters. Based on the relevant control, the authors have controlled this striking phenomenon in the system. The first (control) deals with the sliding mode control (SMC) method. Some important aspects of the design and implementation are considered to reach a suitable controller for the applications. The second presents an adaptive robust tracking control strategy based on a modified polynomial observer which tends to follow exponentially the chaotic Colpitts circuits brought back to a topology of the Chua oscillator with perturbations. To highlight the contribution, they also present some simulation results with the purpose to compare the proposed method to the classical polynomial observer.