# Control for Autonomous Intersection Management Based on Adaptive Control Barrier Function
## 1 Introduction
### Autonomous Vehicles (Decentralized Control)
#### 1.3.2 Decision-Making  
Autonomous vehicle technology involves making decisions about the driving strategy based on information such as vehicle position, velocity, direction, lane, and obstacles. At intersections, one of the major maneuvers that requires decision-making for autonomous vehicles is lane-changing [26]. To avoid collisions caused by unreasonable lane-changing, researchers have proposed various methods such as an adaptive fuzzy neural network-based predictor to predict steering angle [23] and a Bayesian network to forecast the probability of lane-changing [28]. As human-driven vehicles will continue to coexist with autonomous vehicles on roads in the future, a decision-making framework resembling human behavior was designed in [24] to reduce discomfort arising from differing driving habits between these vehicle types. It should be noted that there are two disadvantages to autonomous vehicle technology: it requires a lot of training data and cannot guarantee collision-free security due to the complexity of system models and surrounding environments. Therefore, collision avoidance algorithms are crucial for ensuring the safe passage of autonomous vehicles through intersections. Collision avoidance algorithms have undergone substantial research and development because of their usefulness in many applications [29; 30; 31; 32; 33; 34; 35]. However, many algorithms have major limits when faced with unexpected challenges. Traditional collision avoidance algorithms include the bug algorithm, potential field algorithm, and vector field algorithm [36; 37; 38; 39; 40]. Intelligent obstacle avoidance algorithms include the genetic algorithm, fuzzy logic algorithm, and neural network algorithm [41; 42; 43]. The bug method is the most basic obstacle avoidance algorithm, which involves locating a barrier and wandering around its outline to eliminate it [36; 37; 38]. The potential field method is a popular approach in robotic motion planning for obstacle avoidance. It represents the environment as a potential field, with the objective exerting an attractive force and impediments exerting repulsive forces [44; 45]. The robot navigates by following the resultant force vector, which is the total of various attractive and repulsive forces, directing it toward its destination while avoiding obstacles. However, it can suffer from local minima, when the robot becomes trapped in non-goal locations with zero resultant force, and may exhibit oscillations around obstacles [39]. Therefore, designing a collision avoidance controller for autonomous vehicles to safely navigate intersections is of great importance. When designing controllers for safety-critical autonomous vehicle operations, such as ensuring that autonomous vehicles pass through intersections without collisions, it is crucial to account for power transmission loss that can significantly impact vehicle performance. These controllers are responsible for dynamically adjusting the vehicle's control inputs, such as steering angles and acceleration, to ensure safety and efficiency during navigation. However, traditional Control Barrier Function (CBF) approaches may not be suitable for uncertain systems due to their reliance on precise model information. To tackle this challenge, recent studies have introduced adaptive CBF techniques [46; 47; 48; 49]. For example, the online parameter adaptation method in [46] ensures safety, while the strategy outlined in [47] enables operation within larger safe sets. Moreover, the controller utilizing a concurrent learning technique as presented in [48] guarantees exponential convergence of parameter estimation. Additionally, ref. [49] introduces a robust adaptive CBF of higher order, specifically tailored for systems with high-relative-degree safety constraints. However, some existing CBF-based techniques focus on addressing power transmission loss safety issues modeled by input matrix uncertainties that could lead to controllability loss problems [50; 51].