A Game-based Optimal and Safe Lane Change Control of Autonomous Vehicles in Mixed Traffic Scenario

This paper proposes a game-theoretic trajectory planning scheme for automated lane changing of a connected autonomous vehicle (CAV) in response to the movement of a human-driven vehicle (HDV) in the target lane. The interaction between CAVs and HDVs is modeled as a Stackelberg game, allowing both HDVs and CAVs to change lanes. An optimal control strategy is developed for CAVs, based on the optimal behavior of HDVs, derived from the Hamilton–Jacobi–Bellman equation. These strategies are shown to constitute equilibrium points, and their stability is analyzed. By constructing a zeroing control barrier function, we demonstrate that the designed equilibrium strategy ensures the collision avoidance set remains forward invariant with an appropriate choice of weight matrices for the CAV cost function. Finally, numerical simulations validate the effectiveness of the proposed method.