Distributed backstepping control for synchronization of networked class of underactuated systems: A passivity approach

This paper considers the cooperative control problem of networked class of underactuated systems. We propose a new set up for synchronization of this type of systems based on the use of passivity as a design tool to solve the problem in hand. First the underactuated system is transformed to a class of nonlinear system with chain structure using a suitable non-linear static feedback. The cooperative control is designed using a combination of the standard backstepping procedure and the passivity theory by which a synchronizing outputs are constructed recursively then shared within the group. The proposed design technique is based on strongly connected digraph communication structures. Numerical simulations are carried out to illustrate the effectiveness of the proposed approach.