New control theory ensures robust synchronization despite disturbances

A team of researchers led by Yongchun Bi has developed a novel control framework for robust synchronization of multi-agent systems described by parabolic partial differential equations. The work, published on arXiv in May 2026, addresses the challenge of coordinating multiple agents in the presence of both observable Dirichlet boundary disturbances and unobservable disturbances within the domain. Using only boundary output measurements, the team designed a disturbance observer that estimates the observable disturbances while ensuring the observer error system remains robust against unobservable ones. They then constructed distributed synchronization controllers that use only reference signals and local output information to enable all agents to track a reference trajectory. The proposed system achieves exponential tracking when no unobservable disturbances are present, and maintains robust performance when such disturbances appear during controller implementation.

The paper further analyzes the impact of unobservable Dirichlet-Robin boundary disturbances on synchronization performance by proving boundedness of solutions to the synchronization error system. To fully characterize the influence of all disturbances, the authors establish input-to-state stability (ISS) for the closed-loop system. Their stability analysis employs a generalized Lyapunov method and recursion technique, while well-posedness is proven using lifting techniques and semigroup theory. Simulation results validate the scheme, demonstrating effective disturbance estimation and rejection, robust synchronization, and the ISS properties under various scenarios. This work has significant implications for real-world applications such as coordinated control of autonomous vehicle platoons, thermal regulation in smart buildings, and distributed robotics where PDE-based models capture spatial dynamics.