Data‐Driven Optimal Control of Discrete‐Time Nonlinear Dynamics via Koopman Operator With Norm‐Bounded Uncertainty: An Off‐Policy Approach

ABSTRACT

Model uncertainties arising from unmodeled dynamics and disturbances can degrade controller performance in nonlinear dynamical systems. To effectively address this challenge, this paper presents an optimal data‐driven control framework for discrete‐time nonlinear systems, leveraging the Koopman operator to construct a lifted linear representation. The proposed approach explicitly incorporates both additive and multiplicative uncertainties inherent in the modeling process, treating them as bounded mismatches within the drift and input dynamics. A robust control law is derived for the uncertain lifted model, and rigorous conditions are established to guarantee robust stabilization in the presence of model mismatches. The robust control problem is formulated as an optimal control problem for the nominal lifted model via the design of an appropriate utility function. Furthermore, an off‐policy reinforcement‐learning algorithm is developed specifically for data‐driven scenarios associated with the uncertain Koopman‐based model. The efficacy of the proposed method is validated through simulations on the Van der Pol oscillator and the torsion pendulum, demonstrating robust stabilization and improved control performance under substantial modeling uncertainties.