Optimality Deviation using the Koopman Operator
arXiv:2512.10270
The paper derives explicit upper bounds on how approximation errors in data‑driven Koopman operator models affect the optimal controller and value function for nonlinear systems.
Abstract
This paper investigates the impact of approximation error in data-driven optimal control problem of nonlinear systems while using the Koopman operator. While the Koopman operator enables a simplified representation of nonlinear dynamics through a lifted state space, the presence of approximation error inevitably leads to deviations in the computed optimal controller and the resulting value function. We derive explicit upper bounds for these optimality deviations, which characterize the worst-case effect of approximation error. Supported by numerical examples, these theoretical findings provide a quantitative foundation for improving the robustness of data-driven optimal controller design.
This version is withdrawn to avoid confusion with subsequent developments of the authors' research on related topics. The results and presentation are being reorganized in a broader context, and this version is no longer maintained as a standalone manuscript