Differential-cascade framework for consensus of networked Lagrangian systems

Abstract This paper investigates the consensus problem of multiple uncertain Lagrangian systems with switching topologies and time-varying delays. Due to the discontinuity yielded by the switching topologies and the uncertainty of the time-varying delays, it is challenging to ensure consensus in the context of uncertain Lagrangian systems. We propose a differential-cascade framework for developing adaptive controllers to solve this problem and additionally propose new analysis tools for rigorously demonstrating the stability and convergence of the closed-loop system. The new introduced analysis tools are motivated for addressing the input–output/state properties of linear time-varying interconnected systems. It is shown that the consensus errors between the systems converge to zero so long as the union of the graphs in each of an infinite sequence of time intervals contains a directed spanning tree. It is also shown that the proposed approach enjoys the robustness with respect to unknown time-varying communication delays.

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