K_∞ Function-Based Consensus Tracking Control for Multi-Agent Systems With Unknown Disturbances

In this paper, consensus tracking is investigated for multi-agent systems (MASs) with unknown disturbances. A K<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> function-based control strategy is proposed to guarantee that the tracking errors between each follower and the leader are converged to a small neighborhood of zero in finite-time. To be more specific, by introducing an error auxiliary considering local interactions, a K<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> function-based adaptive controller is designed such that the error auxiliary is constrained to an adjustable region. Then, through a matrix-based rigorous proof, practical consensus tracking is realized in finite-time for MASs. A distinguished feature of the K<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> function-based control is its independence on the use of the bound information of unknown disturbances. Another advantage of the proposed controller is its capability of alleviating the input chattering issue. Finally, numerical examples are presented to validate the effectiveness of the K<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> function-based controller.