Chaos Synchronization, Anti-Synchronization, and Parameter Estimation in a Chaotic System with Coexisting Hidden Attractors

This work considers the problem of chaos synchronization and parameter estimation, for the special case where the unknown parameters are linearly injected into the system. This case is of particular interest because scalar parameters often appear in systems with hidden attractors. For this type of system, state and parameter estimation can be achieved simultaneously by appropriately rewriting the system into descriptor form, and designing an observer that estimates the augmented system's state. The design is adapted to achieve anti-synchronization as well, and a unified switching observer is proposed that can achieve both synchronization and anti-synchronization, based on the values of a switching signal. The design is showcased through an example of a modified chaotic system with hidden, coexisting attractors.