A Novel Robust-Adaptive Control Methodology for Sign-Consensus of Multi-agent Systems Under Signed Graphs and External Disturbances

The purpose of the consensus control of multi-agent systems is to attain an agreement between agents via a cooperative controller. Sign-consensus allows to attain an agreement between agents with different strengths of their opinions. However, the existing methods lack in developing the robust-adaptive methods to select the control gains as per need and to attain robustness against perturbations. This paper addresses the sign-consensus of multi-agents, modeled as generic linear time-invariant systems, by intruding amplitude-bounded and energy-bounded disturbances by considering the communication network as a signed graph. In a signed graph, both cooperative and competitive interactions coexist between agents, and the aim of this study is to explore fully distributed methods for achieving the sign-consensus (rather than the conventional complete consensus). Mainly, two techniques for attaining the sign-consensus have been addressed: the former is an exponentially uniformly ultimately bounded-based controller for amplitude-bounded disturbances, and the latter is an energy-based controller for the energy-bounded disturbances. To the best of our knowledge, no previous research work is available on achieving an exponentially fully distributed sign-consensus controller by considering disturbances to limit the divergence of adaptive parameters. Numerical simulation results of the proposed two methods for both amplitude-limited and energy-bounded disturbances have been provided. The results have been applied to seven agents over bidirectional signed graphs. The agents in both scenarios achieve coherent behaviors with different magnitudes. In addition, the coupling weights also adapt as per the requirement.