Learning Model Predictive Control for Iterative Tasks: A Computationally Efficient Approach for Linear System

A Learning Model Predictive Controller (LMPC) for linear system in presented. The proposed controller is an extension of the LMPC [1] and it aims to decrease the computational burden. The control scheme is reference-free and is able to improve its performance by learning from previous iterations. A convex safe set and a terminal cost function are used in order to guarantee recursive feasibility and non-increasing performance at each iteration. The paper presents the control design approach, and shows how to recursively construct the convex terminal set and the terminal cost from state and input trajectories of previous iterations. Simulation results show the effectiveness of the proposed control logic.