Passivity-based designs for synchronized path-following

We consider a formation control system where individual systems are controlled by a path-following design and the path variables are to be synchronized. We first show a passivity property for the path-following system, and next, combine this with a passivity-based synchronization algorithm developed in Arcak [2007. Passivity as a design tool for group coordination. IEEE Transactions on Automatic Control, in press]. The passivity approach expands the classes of synchronization schemes available to the designer. This generality offers the possibility to optimize controllers to, e.g., improve robustness and performance. Two designs are developed in the proposed passivity framework: the first employs the path error information in the synchronization loop, while the second only uses synchronization errors. A sampled-data design, where the path variables are updated in discrete-time and the path-following controllers are updated in continuous time, is also developed.