This paper introduces a novel model-based adaptive shared control to allow for the identification and design challenge for shared-control systems, in which humans and automation share control tasks. The main challenge is the adaptive behavior of the human in such shared control interactions. Consequently, merely identifying human behavior without considering automation is insufficient and often leads to inadequate automation design. Therefore, this paper proposes a novel solution involving online identification of the human and the adaptation of shared control using Linear-Quadratic differential games. The effectiveness of the proposed online adaptation is analyzed in simulations and compared with a non-adaptive shared control from the state of the art. Finally, the proposed approach is tested through human-in-the-loop experiments, highlighting its suitability for real-time applications.