<p>In this paper, a novel double event-triggered control strategy is proposed for heterogeneous multi-agent systems with unknown agent states and saturated controller outputs. Firstly, a distributed event-triggered fixed-time leader state observer is designed for estimating the leader’s state to avoid state mismatch issues caused by heterogeneous systems. Secondly, we designed a radial basis function neural network-based state observer to estimate the unknown states of nonlinear agents. Then, based on the estimation results from the two observers, a novel fast finite-time adaptive control strategy is proposed, which takes into account the saturation of control outputs. In addition, the leader state observer and controller both employ a dynamic event-triggering mechanism, which can effectively reduce the communication frequency between agents and between the controller and the actuator, thus conserving communication resources. By employing the Lyapunov stability theory, the proposed control strategy has been proven to achieve system consensus in finite time while ensuring that all signals involved in the control process are bounded. Finally, rigorous numerical simulation examples are provided to validate the effectiveness of the proposed strategy.</p>