The set of N clients is denoted by 𝒩={1,…,N}. Client i has a local dataset Di of size |Di|, and the total size of the dataset is |D|=∑i=1N|Di|. The global federation’s objective is the weighted average of the local objectives. (1)minwF(w)whereF(w)=∑i=1N|Di||D|Fi(w).

The Eq. (1) defines the global loss to be minimized by federated optimization, where Fi(w) is the local loss at client i. The local model update is performed at client i during ei local epochs with a learning rate η (2)wit+1=wt−η∑k=1ei∇Fi(wit,k),where wit,k denotes the local model after k local mini-batch updates during round t. The Eq. (2) represents standard gradient-based local training. The edge/cloud aggregates client updates using a confidence-weighted average (3)wt+1=∑i∈𝒮tαiTit∑j∈𝒮tαjTjtwit+1,where 𝒮t⊆𝒩 is the set of selected clients at round t, αi=|Di|/|D| is the data size weight, and Tit∈[0,1] is the trust score for client i at round t.

Each client i has a mobility state vector containing position and kinematic features (4)Mi(t)=[pi(t),vi(t),ai(t),θi(t)],where p is position, v is velocity, a is acceleration, and θ is direction. A sequence model is used to predict the next step position or waiting time. Suppose the predictor is fmob(⋅), then the predicted waiting time within the current RSU coverage is, (5)τ^i(t)=fmob(Mi(t−Δt),…,Mi(t)).

The dwell-time predictor estimates how long client i will remain connected, which is used for scheduling feasibility. Determine the connection stability score Si(t)∈[0,1] that decreases with lower estimated distance to RSU or dwell time. (6)Si(t)=exp(−d^i(t)dmax)=exp(−vi(t)⋅τ^i(t)dmax),where d^i(t) is the predicted displacement during the residence time interval and dmax is a normalization constant. A small Si(t) indicates a high risk of disconnection.

The energy consumption per client is modeled as the sum of the computational and communication energy required to participate in one round. The computational (local training) energy for client i executing ei epochs is, (7)Eicomp(ei)=ηi⋅FLOPsper_epoch⋅ei,where ηi (Joules per FLOP) is the device-specific energy coefficient and FLOPs_per_epoch depends on the model and batch size. The communication (upload) energy is, (8)Eitx(Δi,Ri)=Pitx⋅titxwithtitx=ΔiRi,where Pitx is the effective transmit power (W), Δi is the compressed update size (bits), and Ri is the uplink rate (bps). The total expected energy for client i in round t, (9)Ei(t)=Eicomp(ei)+Eitx(Δi,Ri).

The feasibility of computation time and transmission time must comply with the estimated dwell time: (10)Ticomp(ei)+Titx(Δi,Ri)≤τ^i(t),where Ticomp(ei)≈FLOPsper_epoch⋅eiFLOPSi and Titx is from (8). The (10) constraint ensures that the client is most likely to complete local training and upload before disconnection. Remaining battery update after participation: (11)Eirem(t+1)=Eirem(t)−Ei(t)+Hi(t),where Hi(t) models the probability of energy harvesting between rounds. The security constraints are enforced (12)Eirem(t+1)≥Emin,with Emin a predetermined safety threshold (e.g., 10%) battery capacity.

Device-level anomaly detection uses a local autoencoder to reconstruct the telemetry vector xi(t) (energy, loss, gradient norm, and telemetry). The mean-squared reconstruction error is calculated as, (13)𝒜i(t)=1d∑j=1d(xi,j(t)−x^i,j(t))2and the normalized anomaly score for trust weighting is computed as, (14)𝒜inorm(t)=𝒜i(t)−μ𝒜(t)σ𝒜(t)where: xi(t) is the local model update vector of client i at round t, x^i(t) is the reconstructed vector from the autoencoder, d is the dimension of the update vector, μ𝒜(t) and σ𝒜(t) are the mean and std of reconstruction errors across all clients. The Cosine similarity can be given as, (15)simi=⟨Δwi,Δw~⟩‖Δwi‖‖Δw~‖.

If simi<τsim, the update is suspicious. The confidence score Ti(t)∈[0,1] is updated as a convex combination that penalizes anomalies as, (16)Ti(t+1)=λTTi(t)+(1−λT)(1−min(𝒜i(t),𝒜max)𝒜max)⋅I[simi≥τsim],where λT∈[0,1] is the forgetting factor, 𝒜max normalizes the anomaly score, and the indicator confirms that low-similarity updates reduce trust. Trust-weighted aggregation uses Ti(t) as in (3).

The proposed framework used model poisoning and backdoor injection integrated with the trust evaluation mechanism to identify and suppress malicious contributions. The local gradients are manipulated using a subset of adversarial clients before transmission to the RSU. The poisoning is calculated as, (17)g~i=gi+αδ,where gi is the benign local gradient of client i, δ is a randomly sampled perturbation vector (Gaussian noise), and α controls the severity of the attack. A target backdoor is also injected by the malicious clients, including local training labels. Let x be an input sample and y its correct label, the poisoned labels are generated as (18)y′={t,if x∈𝒟trigger,y,otherwise,where t is a predefined target class and 𝒟trigger denotes samples containing the backdoor trigger. The poisoned updates are detected using gradient direction similarity, energy sufficiency, and mobility stability. Each client’s gradient and the median gradient direction compute the cosine similarity as, (19)𝒮i=cos⁡(∠(g~i,median⁡(g~))),where lower values indicate potential poisoning. The final trust score is then updated as, (20)Ti(t+1)=λT𝒮i+(1−λT)f(Ei,vi),where f(Ei,vi) incorporates energy availability Ei and mobility stability vi of client i, and λT controls the weight of anomaly-based trust adjustment.

This scheduling problem is transformed into an MDP with states St, actions At, and rewards Rt. The state vector at round t is, (21)St={Eirem(t),Ti(t),Si(t),Ri(t),ΔFi(t)}i=1N,where Ri(t) is the uplink rate and ΔFi(t) indicates the current local contribution. The action is client selection and per-client configuration. (22)At={ai(t)=(si(t),ei(t),ρi(t))}i=1N,with selection flags si(t)∈{0,1}, epoch ei(t)∈Z+, and compression ratio ρi(t)∈(0,1]. The reward function is multi-objective. (23)Rt=ωaccΔAcct−ωEE¯(t)−ωDDropt+ωTT¯(t)+ωSS¯(t),where:

ΔAcct = global validation accuracy gain at round t,

The agent learns a policy πθ(A|S) parameterized by θ (a neural network) to maximize the expected discounted return is (24)J(θ)=Eπθ[∑t=0∞γtRt],where γ∈(0,1] is discount factors. Using Proximal Policy Optimization (PPO), the surrogate objective for policy updating is, (25)LPPO(θ)=Et[min(rt(θ)A^t,clip(rt(θ),1−ϵ,1+ϵ)A^t)],where rt(θ)=πθ(At|St)πθold(At|St), A^t is the advantage estimate, and ϵ is the clip parameter.

The combined energy-trust-mobility selection can be posed as a round-by-round constrained optimization problem expressed as, (26)minsi,ei,ρi∑i=1NsiEi(ei,ρi)subject to∑i=1Nsi=K,Ticomp(ei)+Titx(Δi(ρi),Ri)≤τ^i∀i:si=1,Eirem−Ei(ei,ρi)≥Emin∀i:si=1,Ti≥Tth∀i:si=1,si∈{0,1}, ei∈Z+, ρi∈(0,1]where K is the number of selected target clients. Eq. (26) presents a mixed-integer nonlinear program (MINLP); in practice, the DRL policy approximates the solution online. For analysis, relax si∈[0,1] to obtain a solvable convex surrogate for comparison. The total energy consumption is minimized by selecting devices, the number of local computation epochs, and the fraction of local data used. Each device contributes a minimum amount, ensuring devices are selected exactly with respect to latency and energy limits.

The average energy per round is defined as, (27)E¯round(t)=1|𝒮t|∑i∈𝒮tEi(t).

The equation above calculates the mean energy consumption of all selected devices, given the typical energy cost per device. The energy efficiency (EE) as accuracy per unit energy can be calculated as, (28)EE(t)=Acc(t)E¯round(t),where Acc(t) is the global validation accuracy at round t. The model is considered convergent at round T⋆ if (29)|F(wT⋆)−F(wT⋆−Δ)|≤ϵF

This equation confirms the training convergence by comparing the global model’s loss. Convergence is confirmed if the loss is below the threshold. The detection rate (DR) and false alarm rate (FAR) are calculated from the anomaly detector output as, (30)DR=#{true positives}#{malicious clients},FAR=#{false positives}#{benign clients}.

Algorithmic Framework Overview

The proposed framework consists of three integrated Algorithms 1–3 that collaboratively achieve adaptive, secure, and energy-efficient federated learning for intelligent transportation systems (ITS). Each algorithm corresponds to a specific operational stage in the federated learning (FL) cycle: client-side participation, server-side aggregation, and policy optimization through deep reinforcement learning (DRL). A mobility-aware self-learning system has been developed that optimizes communication, computation, and trust in dynamic IoT-based vehicular environments. A single-tier centralized aggregation has been implemented in the proposed framework. Global model aggregation has been performed at each round using the Roadside Unit (RSU), which acts as the centralized FL coordinator. The local updates from the IoT nodes are sent to the RSU, which aggregates using an averaging rule. The nodes’ participation, along with the energy allocation and trust-aware update, is optimized directly by keeping the communication pipeline simple. Table 3 shows the computational complexity of the proposed algorithms.

A comprehensive simulation framework was developed using Python with TensorFlow Federated (TFF), PyTorch, and Stable-Baselines. Experiments were run on a workstation equipped with an Intel Core i9 CPU, 32 GB of RAM, and an NVIDIA RTX 4070 GPU. Table 4 shows the detailed simulation parameters and their description. The network of 100 IoT vehicle nodes has been created with a single central aggregator. Telemetry, sensor readings, and steering features have been selected using a random waypoint mobility model. The energy range for the local training epoch has been set to 0.5 to 1.2 J, while the energy per data transmission has been set to 0.2 to 0.8 J. Simulations of over 200 communication rounds were performed.

The experimental setup was simulated for 100 IoT nodes that represent a practical and widely adopted configuration as per MoFeL, ESAFL, and FedProx models. It is consistent with a typical fuzzy-logic-based system, which usually considers 50-200 clients. The increasing number of nodes does not affect the algorithm’s trend but increases the computational load. The training analysis covers an average of 200 rounds, which provides sufficient iterations for convergence analysis. Moreover, the model performance saturates after approximately 150–300 rounds. The Udacity Autonomous Vehicle Dataset has been selected, which contains real-world sensor data and driving scenarios. The mobility features, including acceleration, change of direction, and duration, have been considered with the required parameters for energy consumption, power transmission, and latency. The baseline models, including FedAvg, FedProx, MoFeL, and Energy-Aware FL, have been selected for fair comparison.

Fig. 2 illustrates the variation in global model accuracy over 50 communication rounds for the conventional FL and the proposed DRL-based FL models. A gradual increase in accuracy for the conventional FL has been observed, reaching 89% after 50 rounds, while the proposed DRL-FL reached 93%. It shows that mobility-aware optimization affects the learning rate and that faster convergence balances local updates and global aggregation.

Table 5 shows the comparison results for the proposed DRL-FL with the baseline models. DRL-FL outperforms the other models in terms of the highest accuracy (93.4%), lowest energy consumption (160 J), and highest robustness (86.7%).

The mobility evaluation and the scalability comparison have been shown in Table 6. A gradual decrease in model accuracy and an increase in training latency are observed for both models as the number of IoT nodes increases from 10 to 50. DRL- FL also outperforms FL, maintaining 10% higher accuracy and up to 40% lower latency. The learning performance and energy consumption have been illustrated in the mobility analysis as the vehicle speed increases. The increase in vehicle speed reduces accuracy for both models due to the lower communication stability and less connection time. DRL-FL comparatively maintains higher accuracy and also consumes less energy.

The energy consumption per communication round has been shown in Fig. 3 for both approaches. The proposed DRL-FL model converges to approximately 150 J, while the FL model converges to approximately 180 J. It shows that the proposed model consumes less energy than the simple FL model up to 16.7%. It is due to the reduced data transmission overhead that ensures the continuous involvement of the IoT nodes.

The robustness of the proposed framework has been evaluated using parameter sensitivity analysis. Various key design parameters have been assessed, including PPO hyperparameters, trust thresholds, and anomaly-detection parameters. The detailed results are presented in Tables 7–10. Results demonstrated that the proposed model outperforms the baseline models in terms of stability and consistency. A predictable behavior has been observed for PPO in terms of learning rate and discount factor, with aggressive values, while the moderate settings achieved a reasonable balance. The most effective observed parameter is the trust mechanism, with a value range of 0.5–0.7 without increasing the false-positive rate. The anomaly detection parameter demonstrated resilience behavior, avoiding unnecessary exclusion of benign nodes. The overall performance indicates that the framework parameters are not overly sensitive to narrow hyperparameter tuning.

Fig. 4 exhibits the energy efficiency of various learning configurations. Results indicate that the FL achieves an efficiency of 0.62, while DRL-FL achieves 0.89. It highlights an overall improvement of 43.5%, demonstrating the minimization of redundant computation. Moreover, each training round effectively contributes to the overall learning process without the energy loss.

The impact of malicious nodes on accuracy has been shown in Fig. 5. FL accuracy decreases gradually from 93% to 69% as the malicious nodes increase from 0%–40%. A minor decrease in the proposed DRL-FL has been observed, thus maintaining the accuracy around 82%. It shows that the proposed model effectively detects suspicious updates, confirming its robust threat detection.

Fig. 6 demonstrates the learning behavior of the DRL agent for 100 training episodes. In the first few episodes, the cumulative reward increased rapidly and stabilized around episode 80. It specifies that the DRL effectively learns to optimize energy and balances competing goals.

The communication efficiency for the FL and DRL-FL models is shown in Fig. 7. The average communication overhead for the FL has been 6.5 MB, while it has been 4.7 MB for the DRL-FL. The nodes are allowed to transmit the model updates using the adaptive share mechanism, which is useful for ITS. It not only reduces the bandwidth but also maintains low-latency communication.

The inclusion of core design elements, mobility-aware client selection, dynamic energy management, trust-weighted aggregation, and anomaly detection in the proposed framework leads to superior performance. Algorithms, including FedAvg and FedProx, with static connectivity with rapid change in client availability, may lead to unstable convergence. The proposed DRL-FL model continuously evaluates client stability, avoiding wasting computational resources on potentially disconnected nodes. The issue of overly erratic update quality is avoided by the energy-aware DRL policy, which adjusts the local training workload of battery usage. The trust-weighted aggregation reduces the overall number of malicious model updates based on anomaly scores to prevent malicious influence. The PPO-based policy simultaneously balances accuracy, energy consumption, and robustness, achieving faster convergence and lower energy consumption. The computational cost comparison per communication round for the proposed framework and several models is presented in Table 11.

The contribution of each system module for the ablation study has been presented in Table 12. Removing the mobility predictor may increase energy consumption and reduce accuracy by selecting unstable clients. The robustness to adversarial nodes decreases as trust-weighted aggregation is reduced. Convergence can also be delayed by replacing PPO with a heuristic selection strategy, and removing the autoencoder-based anomaly detector increases the exposure to the malicious activities. The analysis confirms that each component in the proposed framework contributes meaningfully to the observed performance metrics.