Synchronization of Frequency-Modulated Multiagent Systems

Oscillation synchronization is a widely observed phenomenon in natural systems through frequency-modulated signals, especially in biological neural networks. Frequency modulation is also one of the most widely used technologies in engineering. However, due to technical difficulties, oscillations have always been simplified as unmodulated sinusoidal-like waves in studying the synchronization mechanism in the bulky literature. The application of mathematical principles, especially systems and control theories, is lacking for frequency modulated multiagent systems (MASs). This article aims to introduce a new formulation of the synchronization of frequency-modulated MASs. It develops new tools to solve the synchronization problem by addressing the following three issues: frequency observation in nonlinear frequency-modulated oscillators subject to network influence, frequency consensus via network interaction subject to observation error, and a well-placed small-gain condition among them. The architecture of this article consists of a novel problem formulation, rigorous theoretical development, and numerical verification.