Generalized Synchronization of Uncertain Chaotic Strict-Feedback Form of Systems via Adaptive Control Method

Lyapunov's stability-based back-stepping approach is commonly used to design controller for systems which are in strict-feedback form. The Strict feedback form refers to the fact that non-linear terms in the system equation depend only on states returning to the system. The above approach is used for non-linear systems which are in recursive form. This paper proposes an adaptive control law and parameter updation laws to design a generalized form of adaptive controller to synchronize the strict feedback class of nonlinear systems with the help of back-stepping approach. Here, drive and response system's parameters are considered to be completely unknown and uncertain. Designed adaptive controller is applied to strict-feedback class of non-linear systems viz. Rossler system and Genesio system separately to validate and visualize the result of the proposed work using MATLAB.