Taming non-linearity with local data-driven predictive control

Model Predictive Control (MPC) relies on dynamical models to compute optimal control actions in a receding-horizon fashion. When accurate models are unavailable or expensive to obtain, data-driven predictive control (DDPC) offers a viable alternative for optimal control synthesis. While the linear case is now relatively well understood, both the theoretical foundations and practical implementations for nonlinear systems remain less developed. In this paper, we proposed an effective approach toward closing this gap by combining locally linear data-driven approximations that, when iteratively refined, yield a sequential data-driven quadratic programming algorithm for nonlinear DDPC. The proposed DDPC framework is validated through extensive numerical simulations on an inverted pendulum benchmark. In particular, we show that (i) as the amount of data increases, the closed-loop performance approaches that of a model-based MPC, (ii) our method compares favorably with a recently proposed nonlinear variant of Data Enabled Predictive Control (DeePC), and (iii) the algorithm can be effectively deployed online, achieving pendulum swing-up within a handful of trials, starting from small and easily collectable dataset.