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This paper considers the extension of data-enabled predictive control (DeePC)to nonlinear systems via general basis functions. Firstly, we formulate a basisfunctions DeePC behavioral predictor and we identify necessary and sufficientconditions for equivalence with a corresponding basis functions multi-stepidentified predictor. The derived conditions yield a dynamic regularizationcost function that enables a well-posed (i.e., consistent) basis functionsformulation of nonlinear DeePC. To optimize computational efficiency of basisfunctions DeePC we further develop two alternative formulations that use asimpler, sparse regularization cost function and ridge regression,respectively. Consistency implications for Koopman DeePC as well as severalmethods for constructing the basis functions representation are also indicated.The effectiveness of the developed consistent basis functions DeePCformulations is illustrated on a benchmark nonlinear pendulum state-spacemodel, for both noise free and noisy data.

Basis functions nonlinear data-enabled predictive control: Consistent and computationally efficient formulations