A Distributed Adaptive Observer-Based Approach to Synchronization of Heterogeneous Nonmonotonic Nonlinear Systems for Formation Application

In this article, the challenging problem of distributed adaptive observer design for synchronization and formation control of heterogeneous nonlinear cyber-physical-vehicle systems is addressed. Since the heterogeneous systems contain nonidentical nonlinear dynamics and the leader has unknown dynamics composed of an unknown input bound, the error dynamics of the equilibrium point for the heterogeneous nonmonotonic nonlinear systems will be affected, which has not previously been recognized in the observer design of synchronization literature. To solve this problem, a distributed adaptive observer-based approach is first developed to provide the estimation and compensation of the error dynamics of the equilibrium point for heterogeneous nonmonotonic nonlinear systems. The nonidentical nonlinear dynamics among subsystems and the unknown dynamics of the leader will be handled by the developed distributed estimation laws. Then, by constructing the appropriate error compensation controllers and scheduling the limited information interaction among neighbors, an integrated synchronization control strategy is further proposed by designing a novel class of error dynamic compensation laws to achieve perfect synchronization behaviors. Finally, the mentioned approach is applied to the formation tracking control of heterogeneous nonlinear cyber-physical-vehicle systems, and the effectiveness of our approach is illustrated by case studies.