## 1 Introduction  
With the advancement of edge intelligence and data privacy regulations such as GDPR and HIPAA, achieving cross-device collaborative learning while preserving data locality has become a key challenge in building intelligent systems [1, 2]. Federated learning (FL), with its distributed modeling paradigm of \"keeping data local\", has attracted significant attention in recent years [3, 4]. By performing local training on edge devices and uploading only model parameters, FL effectively reduces the risk of data leakage and improves deployability in sensitive scenarios such as smart terminals, healthcare, and financial risk control, as illustrated in Figure 1.  
Figure 1: Typical application domains of federated learning in edge environments. Nevertheless, the deployment of FL in real-world environments still faces critical challenges, particularly due to heterogeneity in statistical properties, system performance, and client behavior [5; 6], as shown in Figure 2. First, data collected by different clients often come from distinct users, environments, or tasks, leading to highly non-independent and imbalanced distributions, which severely hinder global model convergence and generalization [7; 8]. Second, due to the heterogeneous resource capacities of edge devices, issues such as communication delays, interrupted training, and intermittent connectivity commonly arise, widening performance gaps at the system level. More critically, client behaviors in open environments are uncontrollable and may include strategic participation, perturbed gradient uploads, or even collusive poisoning attacks, potentially destabilizing FL training or crashing the global model [9; 10]. To address these issues, extensive research has been conducted in robust aggregation, security mechanisms, trust management, and incentive design [11; 12]. Robust aggregation algorithms such as the Krum [13] and the Trimmed Mean [14] effectively eliminate outlier updates and enhance system resilience, but most adopt rigid filtering strategies and lack tolerance for weak or high-variance clients. In terms of trust mechanisms, approaches such as FedTrust [15] and TrustFL [16] assess client credibility based on model similarity or behavioral patterns, yet are often decoupled from incentive schemes. Existing incentive mechanisms typically design reward allocation based on static indicators (e.g., data volume, training time), which struggle to detect opportunistic behaviors masked as honesty, and may result in incentive abuse under adversarial strategies [17; 18]. It is particularly noteworthy that most existing works treat trust modeling, robust aggregation, and incentive mechanisms as separate submodules, lacking a systematic integrated modeling approach. Trust scores fail to feed back into resource allocation, and aggregation strategies do not respond adaptively to incentive feedback, leading to persistent internal incentive bias, behavior distortion, and training uncontrollability. Furthermore, due to the inherently dynamic nature of client behaviors, one-shot scoring or static thresholds fail to capture long-term trends and fluctuations, often resulting in misjudgments and misallocated rewards that compromise fairness and stability. To tackle the above challenges, this paper proposes a unified Trust-Aware Incentive Mechanism(TAIM) that integrates client trust modeling, incentive feedback, and robust aggregation. Guided by the principle of \"trust drives participation, incentive motivates resource investment, aggregation ensures robustness\", TAIM achieves deep coupling between strategic and optimization layers to enhance system robustness, fairness, and sustainable participation. The main contributions are as follows:  
Figure 2: Three types of heterogeneity in federated learning: statistical, system, and behavioral. We design a dynamic trust modeling framework that integrates participation frequency, gradient consistency, and contribution effectiveness, capturing client behavioral trajectories and quantifying their stability and reliability;
2.