Optimality Deviation using the Koopman Operator
This work addresses robustness issues in data-driven optimal control for nonlinear systems, providing quantitative bounds for practitioners, but it is incremental as it builds on existing Koopman operator methods.
The paper tackles the problem of approximation error in data-driven optimal control for nonlinear systems using the Koopman operator, deriving explicit upper bounds for optimality deviations in controllers and value functions, with numerical examples supporting these theoretical results.
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.