Value Approximator-based Learning Model Predictive Control for Iterative Tasks

Maximizing the performance of a system without reference over an infinite horizon is a challenging problem for iterative control tasks. This paper introduces a Value Approximator-based Learning Model Predictive Control (VALMPC) framework that aims to enhance the system's performance by learning from previous trajectories. We introduce a value approximator to recursively reconstruct a terminal cost function and reformulate an infinite time optimization problem to a finite time one. This work proposes a novel controller design approach, and shows its recursive feasibility and stability. Moreover, the convergence of closed-loop trajectory and the optimality of steady trajectory as iterations proceed to the infinity are proven for general nonlinear systems. Simulation and comparison results show the lower storage requirement of the proposed control method than two state-of-the-art methods. Its resulting trajectory is validated to achieve the optimality.