Super-Twisting Sliding Mode Distributed Consensus for Nonlinear Multi-Agent Systems with Unknown Bounded External Disturbances

This paper addresses the distributed consensus tracking problem for nonlinear multi-agent systems subject to unknown but bounded external disturbances by leveraging a super-twisting sliding mode (STSM) control framework. Two STSM-based consensus algorithms are proposed—one for first-order and another for second-order multi-agent systems—to achieve finite-time convergence despite disturbances. A disturbance observer is integrated into the consensus control protocols to estimate and compensate for these disturbances, ensuring robust tracking without requiring time-derivative sliding variables or smoothing algorithms. The proposed consensus protocols build upon the concepts of finite-time stability, Lipschitz-bounded functions, relative degree analysis of input-output dynamics, and positive-definite matrix properties. Stability and finite-time convergence are rigorously established using Lyapunov-based proofs, Rayleigh’s inequality, and finite-time settling results. Unstructured disturbances are modelled as zero-mean Gaussian noise and structured disturbances are expressed via a regressor formulation. Numerical simulations confirm that the integrated STSM-based consensus approach and disturbance observer ensure high tracking accuracy, robustness, and smooth control performance under diverse disturbance conditions.