Robust time-varying formation control for uncertain multi-agent systems with communication delays and nonlinear couplings

This paper investigates the robust time-varying formation control problems for a class of higher-order multi-agent systems subject to communication delays and heterogeneous uncertainties accounting for not only the parameter perturbations, nonlinearities and external disturbances occurring in the node local dynamics but also the nonlinear couplings in the interconnections of different nodes. For both cases of partially known and unknown time-varying communication delays, we propose a unified formation control protocol, which incorporates a nominal controller to achieve the desired formation and a compensating signal to restrain the influences of uncertainties. Based on the signal compensation theory and Lyapunov-Krasovskii arguments, sufficient conditions to achieve the desired time-varying formation are derived in terms of LMI. Thereafter, an explicit expression to describe the formation reference dynamics is yielded. Moreover, an algorithm is concluded to design the presented formation protocol in four steps. It is proven that the formation error can be made as small as desired under the designed controller despite the uncertainties and communication delays. Numerical simulation results are shown to demonstrate the effectiveness of our proposed control schemes.