Learning-Based Model Predictive Control

Abstract

In this thesis, we investigate the convergence behavior of the dual adaptive model predictive controller (MPC). The dual adaptive MPC is a compelling area of research due to its ability to actively explore unknown parameters within the system. The current convergence result using Lyapunov stability analysis depends on two practical challenges: the difference between the current and the previous estimated parameter and the covariance matrix derived from the recursive least squares (RLS) estimation. Our research aims to achieve convergence independent of these factors. By applying logarithmic upper bounds to both the average squared Euclidean distance between consecutive parameter estimates and the terms in the average Lyapunov decrease function, we establish the average convergence of the dual adaptive MPC. We validate our results with detailed mathematical proofs and simulations, which also illustrate limitations. We contribute valuable insights into the convergence behavior of the dual adaptive MPC and provide some assurance of its operational reliability in practical applications.