### Motivation and Contributions  
Our inspiration is to discover new innovative and effective control strategies that can enhance the performance of complex systems, such as platoons. The main aim of this work is to develop a solution for optimizing vehicle platoon distance that can be implemented in real-world transportation systems. The proposed control algorithm should allow the platoon to seek and track, throughout the whole road course, the optimal inter-vehicular distance in order to achieve the minimum aerodynamic drag, thus improving the energy consumption of the total system. It is noteworthy that the optimal distance is not always the smaller feasible one; for that reason, the algorithm should be in place to identify online proper factors. In order to estimate the aerodynamic drag and find the optimal distance, an extremum seeking scheme that continuously seeks the extremum of a performance metric is proposed; in particular, the estimation of the drag coefficient, which is extracted by an observer. This approach is integrated with a robust prescribed performance control algorithm [6] that ensures the correct tracking of the desired distance. Prescribed performance is particularly useful when designing control algorithms for platoon systems because it allows the designer to explicitly specify desirable performance specifications. This can lead to more effective and efficient control techniques that can meet the desired performance requirements under various operating conditions and ensure collision avoidance while limiting problems that may occur due to sensor limitations.  
Extremum seeking control is a model-free optimization method that is used to optimize the performance of a system by continuously seeking and tracking the extremum (maximum or minimum) of a performance metric. Studies of the method have been carried out for over half a century now with the most iconic ones [7; 8] where stability proofs and optimization solutions for several complex non-linear problems are presented. The key advantage of ESC is that it does not require a mathematical model of the system being controlled. Instead, it relies on direct measurements of the system's output and input signals to estimate the objective function and adjust the system parameters accordingly. ESC has been successfully applied to a wide range of applications, including power electronics, renewable energy systems, air crafts, and process control. However, like any control method, it has its own set of limitations and challenges that must be carefully considered when designing and implementing an ESC system. Fewer studies can be found for ESC when concerning platoons systems since the idea is still in the early stages. Eventually, the outcome of this work should be a well-set designed novel ESC algorithm that can effectively balance the trade-offs between minimizing drag force, thus improving fuel efficiency and carbon footprint and maintaining the stability and safety of the platoon system.  
Concluding, it is worth mentioning that the ultimate goal of the proposed control algorithm is its future implementation in various types of real-world platooning systems, including semi-autonomous and fully autonomous vehicles. The implementation of such a system can have a significant impact on the transportation sector, reducing greenhouse gas emissions, fuel consumption, and traffic congestion, while improving the safety and efficiency of the system. Additionally, the development of this control algorithm can pave the way for future research and innovation in the field of platooning systems and extremum seeking control.