Sliding mode based robustification of consensus and distributed optimization control protocols

This paper proposes a design approach, based on the integral sliding mode control paradigm, devoted to provide robustness on multi-agent systems (MASs) executing arbitrary distributed optimization and consensus protocols which do not take this feature into account. Robustness is understood as the capability of rejecting the effect of exogenous disturbances, parameter uncertainties, and uncertain physical couplings between the agents dynamics, by achieving the same emerging behaviour as that corresponding to a reference MAS tasked to achieve a given coordination objective task for the nominal case. The proposed approach yields a distributed state feedback which can seamlessly be integrated into existing distributed optimization and control protocols which are usually prone against disturbances and uncertainties corrupting the MAS dynamics. Nonsmooth Lyapunov analysis supports the claimed properties. Numerical simulations, showing how popular distributed optimization and consensus protocols can effectively be robustified are discussed.