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The Koopman operator approach for data-driven control design of a nonlinearsystem is on the rise because of its capability to capture the behaviours ofglobal dynamics. However, the measurement noises of inputs and outputs willbias the Koopman model identification and cause model mismatch from the actualnonlinear dynamics. The current work evaluates the bounds of the noise-inducedmodel bias of the Koopman operator model and proposes a data-driven robustdual-loop control framework (Koopman based robust control-KROC) for the biasedmodel. First, the model mismatch is found bounded under radial basis functions(RBF) and the bounded noises, and the bound of model mismatch is assessed.Second, the pitfalls of linear quadratic Gaussian (LQG) control based on thebiased Koopman model of Van Der Pol oscillator are shown. Motivated from thepitfalls, the dual-loop control is proposed, which consist of an observer-basedstate-feedback control based on the nominal Koopman model and an additionalrobust loop to compensate model mismatch. A linear matrix inequality (LMI) isderived, which can guarantee robust stability and performance under boundednoises for the finite-dimensional Koopman operator model. Finally, the proposedframework is implemented to a nonlinear Van Der Pol oscillator to demonstrateenhanced control performance by the dual-loop robust control.

Dual-Loop Robust Control of Biased Koopman Operator Model by Noisy Data of Nonlinear Systems