Nonlinear Model Predictive Control With Value Function Regression: A Tessellation‐Based Sampling Approach

ABSTRACT Advanced model‐based control strategies, such as Model Predictive Control (MPC), offer powerful solutions for managing complex dynamical systems. Despite its benefits, MPC faces significant computational challenges, particularly when applied to systems with fast dynamics and stringent real‐time constraints. To address these challenges, we leverage offline‐generated value function data to enhance real‐time MPC performance. The main parameter affecting the computational demand of MPC is the length of the prediction horizon. This work aims to reduce the length of the prediction horizon of a model predictive controller (MPC) to reduce computation time while maintaining optimality guarantees. To this end, we propose to approximate the trajectory optimization problem for MPC by learning a finite‐horizon value function. This approximated value function is then integrated into a truncated trajectory optimization problem, allowing the MPC to operate with a shorter prediction horizon and thus, ideally, lower computational demands. To manage the costly creation of the value function dataset, we propose a novel tessellation sampling strategy that directs attention to the important regions of the state space. Through this sampling strategy, we show that an effective and robust value function surrogate can be built, resulting in an accurate approximate MPC. The methodology is then validated experimentally on a Furuta pendulum, where it demonstrates the potential for real‐time MPC through learning methodologies. Here, we extend to a multi‐goal problem formulation. By leveraging the model properties of the Furuta system, we can avoid retraining the value function for multiple goals by applying an affine transformation to the value function domain.