Comparative analysis of chaos control methods: A mechanical system case study

Chaos may be exploited in order to design dynamical systems that may quickly react to some new situation, changing conditions and their response. In this regard, the idea that chaotic behavior may be controlled by small perturbations allows this kind of behavior to be desirable in different applications. This paper presents an overview of chaos control methods classified as follows: OGY methods – include discrete and semi-continuous approaches; multiparameter methods – also include discrete and semi-continuous approaches; and time-delayed feedback methods that are continuous approaches. These methods are employed in order to stabilize some desired UPOs establishing a comparative analysis of all methods. Essentially, a control rule is of concern and each controller needs to follow this rule. Noisy time series is treated establishing a robustness analysis of control methods. The main goal is to present a comparative analysis of the capability of each chaos control method to stabilize a desired UPO.

► Efficacy and robustness of each method are investigated establishing a critical comparison.
► Semi-continuous methods present better performance, stabilizing more and different UPOs when ideal signals are of concern.
► Continuous methods present greater robustness being associated with better performance when noisy signals are of concern.