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. Note to Practitioners—Many studies in multi-agent systems (MASs) rely heavily on continuous information exchange among agents, which can lead to significant communication overhead. In practical applications, however, such continuous communication may be inefficient or even infeasible due to network constraints, high energy consumption, or intermittent connectivity. To overcome these challenges, this paper presents a novel adaptive intermittent control strategy aimed at achieving both fixed-time (FxT) and practical FxT consensus. The key innovation of this strategy lies in the development of adaptive intermittent controllers that dynamically adjust the feedback gain based on system states and external disturbances. This method reduces communication load while ensuring fast and reliable consensus convergence. Moreover, new intermittent stability lemmas are introduced, extending existing stability results by incorporating indefinite functions and unified exponential conditions. These lemmas facilitate the achievement of multi-agent consensus within a fixed-time or practical-time framework. By utilizing these new stability results, the adaptive intermittent control strategy effectively addresses challenges posed by discontinuous dynamics in MASs, such as chattering and singularities, thereby ensuring desired consensus behavior. The proposed strategy and lemmas represent significant advancements over traditional consensus algorithms, with promising applications in systems where communication efficiency and robustness are crucial. Future research will focus on expanding the applicability of this approach to larger and more complex systems.