A Systematic Approach for Synchronization of Identical Nosé-Hoover Systems with Multiple Number of Thermostats

This paper introduces a systematic approach to synchronize identical Nosé-Hoover systems that can have multiple number of thermostats. Synchronization is achieved via using a Lyapunov-based approach for which both stability and performance satisfaction are investigated. Both modeling and simulation of the system are presented using different scenarios to verify its similarity to chaotic systems that are very sensitive to initial conditions. The proposed design is exemplified by two case studies that correspond to one and two thermostats. The tuning effort of the proposed controller is explored and conflicts between maximum control effort and fast decay rates of the synchronization errors are investigated. The suitability of the proposed synchronization technique to implement secure communication systems is verified and robustness of the design is highlighted due to its capability to utilize a single state for achieving synchronization. Finally a few practical considerations are investigated, along with suggestions for feasible improvements and extensions to the proposed design. MATLAB was used for the simulations.