Robust output formation control for swarm systems with nonlinear uncertainties in directed networks

In this study, output formation control problems for high-order time-invariant swarm systems with unknown nonlinear uncertainties and directed interaction topologies are studied using a robust controller. First, the dimensions of the observation matrix are extended to be non-singular. Then the output formation problem is transformed into consensus problem. Based on observability decomposition, the consensus problem is transformed into stability problem. Further more, A robust controller which consists of a nominal controller and a robust compensator is applied to achieve formation control. The nominal controller based on the output feedback is designed to achieve desired output formation properties for the nominal system and the robust compensator based on the robust signal compensator technology is to restrain the nonlinear uncertainties. The proposed controller is linear, time invariant and easy to implement. Based on partial stability theory, sufficient and necessary conditions for output formation feasibility are given and the formation errors can be made as small as desired with expected convergence rate.