Arbitrary Time Spherical Synchronization of a Class of Uncertain Nonlinear Systems via Adaptive Control

ABSTRACT This paper addresses the arbitrary time spherical synchronization problem for a class of uncertain nonlinear systems. Firstly, a novel synchronization paradigm, termed spherical synchronization, is introduced. This paradigm requires the state trajectory of the response system to converge and remain on a hypersphere centered on the state trajectory of the drive system with a prescribed radius . It is crucial that when , this mechanism fundamentally eliminates the collision risk inherent in traditional synchronization scheme (e.g., guaranteeing a minimum safety distance in the unmanned aerial vehicle formations). Secondly, a new sufficient criterion for arbitrary‐time stability is proposed. This criterion is deliberately constructed without exponential terms (e.g., ), significantly reducing computational complexity and enhancing its applicability in controlling nonlinear systems. Thirdly, utilizing this novel stability criterion and adaptive control techniques, sufficient conditions for achieving spherical synchronization in the target class of uncertain nonlinear systems are derived. Finally, the effectiveness and feasibility of the proposed approach are demonstrated through numerical simulations based on a new financial system. Simulation results conclusively validate the performance of the method.