Physics-Informed Observable Selection for EDMDc of Nonlinear Mechanical Systems

The Koopman operator enables nonlinear systems to be represented in an approximately linear form for linear control design. However, Extended Dynamic Mode Decomposition with Control (EDMDc) is often limited by the closure problem when generic observables fail to capture the system dynamics. This paper addresses this issue using physics-informed observables derived from Lie derivatives for nonlinear mechanical systems. The resulting lifted models accurately capture nonlinear dynamics and enable standard LQR design with improved performance over Jacobian-based LQR during large transients. Results further demonstrate that complete physics-informed lifting is essential to minimize closure errors. The main contributions are: (1) analysis of the closure problem, (2) a Lie-derivative-based observable selection framework, and (3) comparison of Koopman-based and Jacobian-based LQR for polynomial nonlinear systems.