Adaptive tracking control of a class of uncertain chaotic systems in the presence of random perturbations

Considering the effect of random perturbations on the chaotic system, a new adaptive tracking control is presented for a large class of uncertain chaotic systems using the invariance principle of differential equations, where the bound of random perturbations is not necessarily known in advance and it is estimated through an adaptive control process. It is theoretically proved that this approach can make the perturbed chaotic system track any desired reference signal; in addition, we can see that this method can apply to almost all uncertain chaotic systems and it is simpler and easier to implement in practical application. In the end, we take the perturbed Lorenz system as an example to illustrate that the proposed scheme is effective.