## 4 Simulation Results and Discussion  
The algorithm proposed in this study was tested in MATLAB software. Simulations were conducted on a laptop equipped with an AMD Ryzen 5 4600H processor, 8 GB of RAM, and a 512 GB solid-state drive. To demonstrate the algorithm's feasibility, a platoon of \(N=4\) vehicles was considered with a leader (\(i=0\)), where \(m_{i}=[1200,\ 700,\ 800,\ 900]\) kg, for \(i=1,\dots,4\). The aerodynamic drag profiles for the platoon members were similar to the experimental measurements from [20]. The authors highlight that for inter-vehicular distances below 3m, drag has non-constant and complex behaviour. The measured values used to create the drag profiles are shown in Figure 4. Spline fitting was performed on these values in order to smooth the profile functions and comply with the conditions as stated in Equation (18). Furthermore, we assumed zero wind speed (\(v_{r_{i}}=v_{i}\)), \(\rho=1.293\) kg m\({}^{-3}\) and \(A_{i}=[7,\ 2.5,\ 3,\ 3.5]\) m\({}^{2}\), for \(i=1,\dots,4\). The leading vehicle was set to have a continuously differentiable velocity profile as \(v_{0}=18+0.1\sin(\frac{2\pi t}{100})-0.05\sin(\frac{2\pi t}{50})\). Concerning the PPC design, we set the collision and connectivity constraints as \(\Delta_{Col}=2.5\) m, \(\Delta_{Con}=20\) m, and \(L_{i}=H_{i}=10\) m. To establish predefined transient and steady-state performance, we selected \(l=0.1\), \(\rho_{\infty}=0.07\). Hence, we set the performance functions \(\rho_{p_{i}}(t)=(1-\frac{0.07}{0.95L_{i}})\exp(-0.1t)+\frac{0.07}{0.95L_{i}}\) and \(\rho_{v_{i}}(t)=2|e_{v_{i}}(0)|\exp(-0.1t)+0.3\) for \(i=1,2,3,4\), obeying the initialization restrictions. Finally, the control gains were selected as \(k_{p}=1\) and \(k_{v}=100\). The gains for the observers were set as \(\epsilon_{i}=10^{-4}\) to estimate each vehicle's drag coefficient. For the ESCWAO part, we chose the objective functions \(y_{i}=[-400\hat{C}_{d_{1}}^{2},-500\hat{C}_{d_{2}}^{2},\\ -700\hat{C}_{d_{3}}^{2},-800\hat{C}_{d_{4}}^{2}]\) and the parameters for the extremum seeking controllers were tuned as \(\omega_{h_{1}}=3.2\), \(\omega_{h_{2}}=2.9\), \(\omega_{h_{3}}=\omega_{h_{4}}=2.7\), \(\omega_{l_{1}}=0.645\), \(\omega_{l_{2}}=\omega_{l_{3}}=0.6\), \(\omega_{l_{4}}=0.85\), and \(\omega_{i}=1,k_{i}=0.7\), \(\gamma_{l_{2}}=6\), \(g_{2}(a_{i})=a_{i}\), \(a_{i}(0)  
A long simulation time was chosen \(t=800\) s to allow the ESCWAO to converge to the optimal point and to prove that whereas ESCWAO optimized the distance, PPC works efficiently. The computational time of the algorithm in our hardware was 40.42 s, indicating that the implementation worked sufficiently in our setup. Figure 4 shows that for the first two vehicles in the platoon, the lowest drag coefficient was achieved when the inter-vehicular distances reached 6 m, for the third vehicle at 5 m, and for the fourth vehicle at 4 m; thus, each vehicle's ESC controller was expected to converge around these values, respectively. Although in [20] the authors conclude that for all vehicles in the platoon, the optimal distance is 6m, in that simulation, we slightly changed these values for the third and the fourth vehicle in order to investigate whether the algorithm could correctly track and maintain different optimal distances. Furthermore, the initial distances were intentionally selected far from these values to demonstrate the robustness and efficiency of the controllers. Simulation results are shown in the figures below. Figure 5 shows that the ESCWAO controllers converged correctly to the desired values for all the vehicles in a short time, and for most of the simulation, oscillations at the steady state disappeared, and hence the efficiency was not affected negatively. However, it is clear that in the zoomed plots in the same figure, oscillations in the transient state can be momentarily abrupt.