Distributed cooperative adaptive tracking control for heterogeneous systems with hybrid nonlinear dynamics

The cooperative leader-following tracking for a group of heterogeneous mechanical systems with nonlinear hybrid order dynamics is studied. The controlled systems are considered to be composed of followers (agents) with hybrid first- and second-order time-varying dynamics. The leader is an unknown nonautonomous nonlinear system and can only give the state information of position and velocity to its neighboring followers. The followers are linked by the directed graph with fixed communication topology. And, not all of them have the information path to the leader directly. The directed information topology graph is required to have at least one spanning tree for position and velocity, respectively. Distributed cooperative adaptive control protocols are developed for all followers with first- or second-order dynamics to achieve the ultimate synchronization to the leader. The control protocols are designed based on the neural networks and the adaptive estimation algorithm for unknown time-varying functions and control coefficients. The convergence and boundedness of the synchronization error is proved by the Lyapunov theory. The simulation example verifies the correctness of the developed distributed control protocols.