Physics-informed learning-based distributed cooperative tracking control for multiple Euler–Lagrange systems

This article addresses the robust consensus tracking problem of multiple Euler–Lagrange systems subject to unknown dynamics and disturbances, in which only the root agent can access to the prescribed time-varying trajectory. A network structure that integrates the enhanced gate recurrent unit (GRU) and the physical-informed deep neural network (PI-DNN) is first developed to learn unknown dynamics. A distributed leader state estimator is designed and a distributed PI-DNN-GRU controller with weight adaptive law is further proposed. The closed-loop system is proved to achieve robust asymptotic consensus. Finally, numerical simulations demonstrate the effectiveness and advantages of the proposed method over the existing approaches.