Koopman-LQR Controller for Quadrotor UAVs from Data

Quadrotor systems are common and beneficial for many fields, but their intricate behavior often makes it challenging to design effective and optimal control strategies. Some traditional approaches to nonlinear control often rely on local linearizations or complex nonlinear models, which can be inaccurate or computationally expensive. We present a data-driven approach to identify the dynamics of a given quadrotor system using Koopman operator theory. Koopman theory offers a framework for representing nonlinear dynamics as linear operators acting on observable functions of the state space. This allows to approximate nonlinear systems with globally linear models in a higher dimensional space, which can be analyzed and controlled using standard linear optimal control techniques. We leverage the method of extended dynamic mode decomposition (EDMD) to identify Koopman operator from data with total least squares. We demonstrate that the identified model can be stabilized and controllable by designing a controller using linear quadratic regulator (LQR).