Basis functions nonlinear data-enabled predictive control: Consistent and computationally efficient formulations
This work addresses the problem of applying DeePC to nonlinear systems for control engineers, offering incremental improvements in consistency and computational efficiency.
The paper tackles the extension of data-enabled predictive control (DeePC) to nonlinear systems using basis functions, developing consistent formulations and dynamic regularization to ensure equivalence with identified predictors, and demonstrates effectiveness on a nonlinear pendulum model with noise-free and noisy data.
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 we 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) basis functions formulation of nonlinear DeePC. To optimize computational efficiency of basis functions DeePC we further develop two alternative formulations that use a simpler, sparse regularization cost function and ridge regression, respectively. Consistency implications for Koopman DeePC as well as several methods for constructing the basis functions representation are also indicated. The effectiveness of the developed consistent basis functions DeePC formulations is illustrated on a benchmark nonlinear pendulum state-space model, for both noise free and noisy data.