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.

翻译：本文考虑通过一般基函数将数据驱动预测控制（DeePC）扩展到非线性系统。首先，我们构建了一个基函数DeePC行为预测器，并给出了其与相应基函数多步辨识预测器等价的充分必要条件。推导出的条件产生了一种动态正则化代价函数，使得非线性DeePC的基函数公式具有适定性（即一致性）。为优化基函数DeePC的计算效率，我们进一步提出了两种替代公式，分别采用更简单的稀疏正则化代价函数和岭回归。本文还指出了Koopman DeePC的一致性含义以及构建基函数表示的几种方法。通过在基准非线性摆状态空间模型上的无噪声和含噪数据实验，验证了所开发的一致基函数DeePC公式的有效性。