Model Uncertainty-aware Adaptive Controller Design with Online Parameter Identification

Model-based approaches have a notable advantage over model-free methods because they do not necessitate extensive data collection. This might be especially limited for the physical systems, e.g., aircraft, as the data collection over the full state-space brings high-level costs. In this paper, we have focused on integrating online parameter estimation and adaptive optimal controller. Specifically, the paper utilizes Set Membership Identification to quantify the unknown parameters and update the corresponding system matrices. Then the process exploits the size of the polytopes over the parameters to provide adaptive Q and R gains selection for the Linear Quadratic Regulator-based controller. In order to evade singularities due to frequent updates, the Dual Heuristic Programming (DHP) method evaluates the controller gains by approximating the derivative of the value function of the LQR.We have shown the performance of the proposed methodology through various mass uncertainty or sudden mass change scenarios for a quadrotor model.