Practical Fixed-Time Consensus of Discontinuous Multi-Agent Systems: Adaptive Intermittent Control With Time-Varying Gains Approaches

In this paper, the fixed-time (FxT) and practical FxT consensus of discontinuous multi-agent systems (MASs) via adaptive intermittent control strategy are studied. New intermittent FxT stability lemmas incorporating the indefinite function and the unified exponent condition are established, which can include the existing periodically intermittent stability lemmas and aperiodic intermittent lemmas with negative definite derivatives. Considering that the MASs cannot realize the exact consensus under the inevitable external interferences, intermittent-type practical FxT stability lemmas are further obtained. The intermittent controllers and adaptive intermittent controllers are designed, which demonstrates the improvements over the existing control strategies since the chattering phenomenon and singularity do not appear. Notably, the control gains are time-varying, which are also different from the previous time-invariant ones. Based on the established stability lemmas, the FxT consensus and practical FxT consensus are achieved. Clearly, the practical FxT consensus of discontinuous MASs under the discontinuous-time controllers is achieved for the first time. The simulation confirms the applicability of the proposed methods and shows strong support for our theoretical findings.