Quantization observer-based bipartite fixed-time consensus for nonlinear heterogeneous multiagent systems via event-triggered control.

In the study, we address this distributed observer-based bipartite fixed-time consensus problem for nonlinear heterogeneous multi-agent systems (MASs) under an event-triggered mechanism. A fully distributed observer with a quantizer is proposed for different followers to derive distributed estimations of their leader's state and matrices under the signed communication topology. Additionally, there is an adaptive algorithm to solve the regulator equation efficiently, eliminating the need for repetitive computations. Controllers incorporating observers are developed for both state feedback and output feedback scenarios. We also develop an event-triggered mechanism (ETM) that enables intermittent communication while rigorously excluding Zeno behavior. Notably, the convergence time of the observer and global stability depend solely on system parameters rather than initial states. By leveraging fixed-time stability theory and Lyapunov functions, sufficient conditions are derived to guarantee bipartite consensus in finite time. Ultimately, numerical simulations demonstrate that the proposed scheme achieves bipartite fixed-time consensus within approximately 0.4 s under event-triggered communication (0.26 s without ETM), while the average communication saving rate is 44.67%, validating the effectiveness of the theoretical results.