  To address the challenges posed by the heterogeneity inherent in federated
learning (FL) and to attract high-quality clients, various incentive mechanisms
have been employed. However, existing incentive mechanisms are typically
utilized in conventional synchronous aggregation, resulting in significant
straggler issues. In this study, we propose a novel asynchronous FL framework
that integrates an incentive mechanism based on contract theory. Within the
incentive mechanism, we strive to maximize the utility of the task publisher by
adaptively adjusting clients' local model training epochs, taking into account
factors such as time delay and test accuracy. In the asynchronous scheme,
considering client quality, we devise aggregation weights and an access control
algorithm to facilitate asynchronous aggregation. Through experiments conducted
on the MNIST dataset, the simulation results demonstrate that the test accuracy
achieved by our framework is 3.12% and 5.84% higher than that achieved by
FedAvg and FedProx without any attacks, respectively. The framework exhibits a
1.35% accuracy improvement over the ideal Local SGD under attacks. Furthermore,
aiming for the same target accuracy, our framework demands notably less
computation time than both FedAvg and FedProx.
