This paper addresses the challenge of managing state constraints in vehicle platoons, including maintaining safe distances and aligning velocities, which are key factors that contribute to performance degradation in platoon control. Traditional platoon control strategies, which rely on a constant time-headway policy, often lead to deteriorated performance and even instability, primarily during dynamic traffic conditions involving vehicle acceleration and deceleration. The underlying issue is the inadequacy of these methods to adapt to variable time-delays and to accurately modulate the spacing and speed among vehicles. To address these challenges, we propose a dynamic adjustment neural network (DANN) based cooperative control scheme. The proposed strategy employs neural networks to continuously learn and adjust to time varying conditions, thus enabling precise control of each vehicle's state within the platoon. By integrating a DANN into the platoon control system, we ensure that both velocity and inter-vehicular spacing adapt in response to real-time traffic dynamics. The efficacy of our proposed control approach is validated using both Lyapunov stability theory and numeric simulation, which confirms substantial gains in stability and velocity tracking of the vehicle platoon.