Chaos synchronization and parameter estimation of single-degree-of-freedom oscillators via adaptive control

This paper addresses the problem of synchronizing a class of single-degree-of-freedom oscillators with uncertain parameters. A modified adaptive control scheme is proposed to achieve globally asymptotic stable synchronization between the master and slave oscillators with arbitrary different initial conditions based on the Barbalat's Lemma. One of the advantages of the method is that it requires only a scalar driving signal which may be easily designed in practical applications. On the other hand, the method can ensure that the unknown parameters in the slave oscillator would be completely estimated with an adaptive updating law. Numerical simulations are performed on two examples to verify the analytical results.