Data-Driven Control Synthesis Using Koopman Operator: A Robust Approach

This paper presents a data-driven control design method for nonlinear systems using the Koopman operator framework.The Koopman operator lifts nonlinear dynamics to a higher-dimensional space, where observable functions evolve linearly.We initially consider an approximate linear timeinvariant (LTI) lifted representation of the nonlinear system.To address residual errors, we calculate an approximation of the ℓ2-gain of the error system based on data.Subsequently, we synthesize a robust dynamic feedback controller, relying solely on the LTI frequency response, providing closed-loop guarantees.Additionally, we consider linear parameter-varying (LPV) lifted models to further minimize the error systems ℓ2-gain.In that case, we propose control design based on robustly stabilising the LTI dynamics and compensating for the parameter-varying part.The proposed strategy ensures internal stability under the assumption that the parametervarying dynamics are open-loop BIBO stable.Moreover, it provides nominal performance guarantees for specific inputoutput channels for which the parameter-varying dynamics are fully cancelled.