  The selection of a reward function in Reinforcement Learning (RL) has
garnered significant attention because of its impact on system performance.
Issues of significant steady-state errors often manifest when quadratic reward
functions are employed. Although absolute-value-type reward functions alleviate
this problem, they tend to induce substantial fluctuations in specific system
states, leading to abrupt changes. In response to this challenge, this study
proposes an approach that introduces an integral term. By integrating this
integral term into quadratic-type reward functions, the RL algorithm is adeptly
tuned, augmenting the system's consideration of reward history, and
consequently alleviates concerns related to steady-state errors. Through
experiments and performance evaluations on the Adaptive Cruise Control (ACC)
and lane change models, we validate that the proposed method effectively
diminishes steady-state errors and does not cause significant spikes in some
system states.
