Parametric convergence and control of chaotic system using adaptive feedback linearization

Adaptive feedback linearization control technique for chaos suppression in a chaotic system is proposed. The dynamics of the system is altered so that the closed loop model matches with a specified linear reference model. The controller parameters are assumed to be unknown and are evolved using an adaptation law that aims to drive these parameters towards their ideal values so as to achieve perfect matching between the reference and the system model. A common external forcing signal to both chaotic Genesio system and reference system is considered and adaptation laws are derived considering Lyapunov function based stability. Simulation results show that the chaotic behavior is suppressed effectively with proposed controller. Analysis of linear and nonlinear parametric convergence is also shown through simulation, both with and without excitation using suitable forcing function.