Flatness-based control for generalized synchronization of chaotic systems with large dissipation and dimension mismatch.

A flat control law is based on the structural analysis of a controlled system, allowing optimal placement of sensors and actuators. Once designed, any desired dynamics can be imposed onto the system. When the target dynamics comes from a system structurally different from the controlled one, generalized synchronization can be achieved, provided the control gain is sufficiently large. As the gain increases, various relationships emerge between the drive and response systems, depending on differences in their dimensions and dissipation rates. The principal contribution of this work lies in the exploration of drive-response system pairs with varying dimensions (ranging from 2 to 4) and dissipation levels, including combinations of dissipative and conservative systems. We identify several types of generalized synchronization, using a classification based on the thickness of the resulting Lissajous curves and the lack of conjugacy between the first-return maps of the drive and response systems.