Cooperative control of high-order nonlinear systems with unknown control directions

In this paper, we investigate output synchronization problem of nonlinear systems that can be transformed into strict feedback form with unknown control direction. To this end, an augmented Laplacian potential function is introduced to construct local level distributed adaptive controllers such that outputs of networked agents can be synchronized while all other states maintain bounded. Moreover, tuning functions are designed to reduce the order of the parameter updater. In contrast to conventional adaptive backstepping procedure, both the parameter updating law and tuning function of the proposed scheme take advantage of information flow among networked agents and thus distributive in nature. It is proved that output synchronization of the entire network can be achieved by properly choosing Nussbaum functions, provided the information graph is undirected and connected. Furthermore, we also proposed a way to define a proper Nussbaum function. Simulation results are presented to verify the effectiveness of the proposed schemes.