This paper presents a robust ℋ∞ control design method that incorporates learning feature. The goal of the work is to improve the performance level of the robust controller, which is achieved through reinforcement learning (RL) process. The contribution of the presented method is that the design of the ℋ∞ controller and the RL-based controller is structured in a joint optimization. This leads to an iterative design for the controllers. The developed design method is applied to the problem of minimizing lap time in vehicle control design. The presented simulation-based analysis shows that the proposed method is able to provide improved performance level, i.e., reduced lap time, compared to the robust control or the independent design process. The outcome of the joint design is that the lap time achieved with the ℋ∞ controller approaches the lap time achievable with the RL process.