Optimality Deviation using the Koopman Operator

TL;DR

This paper analyzes how approximation errors in the Koopman operator affect the optimal control of nonlinear systems, providing bounds to improve robustness.

Contribution

It derives explicit upper bounds for optimality deviations caused by approximation errors in data-driven Koopman-based control.

Findings

Derived explicit bounds for optimality deviations.

Numerical examples demonstrate the theoretical bounds.

Provides a quantitative foundation for robust control design.

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.