Basis-Functions Nonlinear Data-Enabled Predictive Control: Consistent and Computationally Efficient Formulations

This paper considers the extension of data-enabled predictive control (DeePC) to nonlinear systems via general basis functions. Firstly, we formulate a basis-functions DeePC behavioral predictor and identify necessary and sufficient conditions for equivalence with a corresponding basis-functions multi-step identified predictor. The derived conditions yield a dynamic regularization cost function that enables a well-posed (i.e., consistent with the multi-step identified predictor) basis-functions formulation of nonlinear DeePC. Secondly, we develop two alternative, computationally efficient basis-functions DeePC formulations that use a simpler, sparse regularization cost function and ridge regression, respectively. An insightful relation between Koopman DeePC and basis-functions DeePC is also presented. The effectiveness of the developed basis-functions DeePC formulations is shown on a benchmark nonlinear pendulum state-space model, for both noise-free and noisy data, while using only output measurements.