Flatness-based real-time control of experimental analog chaotic oscillators

In the control of non-linear dynamics, the notion of flatness provides a systematic framework for analyzing the observability and controllability of a system. Several successful applications of flatness-based control (in brief, flat control) have been demonstrated, but, to date, the control of chaos using this approach had been obtained only numerically. Here, for the first time, this issue is addressed through a systematic experimental investigation of two chaotic systems, namely, the Rössler system and the Saito circuit, realized in the form of analog electronic oscillators. These differ in the types of non-linearity and associated dynamics, as well as their observability and controllability. The corresponding flat control laws, including a homogeneous law, are derived and implemented, using suitable numerical reconstructions of the high-order derivatives, in real-time on a microcontroller interfaced with the analog circuits. Albeit with some limitations, viable control is attained over a wide range of settings, and the influences of the device non-idealities are analyzed in detail. These initial results suggest that, besides chaos suppression in engineering applications from vehicle stabilization to cardiology, flat chaos control could probably also be applied toward obtaining desired dynamical and synchronization states in large-scale physical models of complex systems.