Abstract: By using the backstepping design method we formulated a simple controller to control the system to its unstable equilibrium (0,0,0), any point of the form (0,0,1+b+p(1-p))(0<p<1) in phase space, and forced the first state variable to trace arbitrary given function r(t). Suppose one parameter was unknown, we proposed a unidirectional coupled scheme and a parameter update role to assure the new Lorenz-like system to globally synchronize with a copy of itself. We presented a rigorous proof of our design by constructing proper Lyapunov function. Numerical simulations using Matlab were presented to show the feasibility of our design.

Key words: backstepping control, adaptive synchronization, chaos, backstepping control, adaptive synchronization