Adaptive Backstepping and Pid Optimized by Genetic Algorithm in Control of Chaotic

In this paper, the robust adaptive control scheme based on adaptive backstepping design is used to control the autonomous second order strict feedback form such as the Lorenz Chaotic system. The design procedure is recursive; at the i step, the i subsystem is stabilized with respect to a Lyapunov function Vi by the design of a stabilizing function αi, tuning function τi, and the update law ̇̂ θi for the unknowns’ adaptive parameters estimates θ̂i, the feedback control u is designed at the final step. This procedure possesses strong properties of global stability and tracking which are built into the nonlinear system in a number of steps, which is never higher than the system order, without any growth restrictions on nonlinearities. The results show the guarantee of all the parameter estimates to converge to their true values. Some simulation results for the chaotic system cited above are shown to illustrate the parameter convergence with adaptive backstepping design.