Data-driven Nonlinear Model Predictive Control Using NARX Models : An Application of Takens’ Embedding Theorem

Sammanfattning

Data-driven control offers a solution in situations where control based on first-principles modeling is difficult or infeasible. This master thesis investigates the use of Takens’ embedding theorem to enable nonlinear, data-driven model predictive control (MPC). The proposed method involves learning time-delay embedded system dynamics using a nonlinear autoregressive model with exogenous inputs (NARX), which is then integrated into an MPC framework. The results show that increasing the number of past inputs and outputs used in prediction improves model accuracy; however, the selection of feature types is found to be even more critical for achieving strong performance in complex control tasks. Furthermore, the proposed controller demonstrates tracking performance comparable to that of standard model-based MPC and outperforms the regularized Data-enabled Predictive Control (DeePC) method, while significantly reducing computational complexity. To address the computational demands associated with optimizing nonlinear problems, several strategies are employed: model complexity is reduced through lasso regularization, nonlinear optimization problems are approximated as quadratic programs via linearization in a real-time iterative (RTI) approach, and convexity is enforced through structural constraints. A key limitation of the current approach is its restriction to single-input single-output systems. Future work may extend the methodology to multi-input multi-output systems and explore richer feature sets to enhance model expressiveness.