Model Predictive Control: Shortcomings and Resolutions
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Authors
Fuernsinn, Annika
Date
2024-10-07
Type
thesis
Language
eng
Keyword
Model predictive control , Lyapunov methods , asymptotic stabilization , nonholonomic systems
Alternative Title
Abstract
This thesis is concerned with model predictive control (MPC); a method that approximates solutions of an infinite-horizon optimal control problem by considering a sequence of finite-horizon optimal control problems implemented in a receding horizon fashion. In the standard scheme, one control input is implemented in each iteration, and a new initial state is set for the next finite-horizon. One critical issue within the MPC setup is guaranteeing stability, and much of the literature on the topic is devoted to this, mainly by using classical tools from Lyapunov theory. Such results often rely on suitable terminal ingredients, whose design significantly impacts the performance of MPC. As we explore in this thesis, the issue mentioned is more critical than only performance, and leads to major shortcomings. The main objective of this work is to mathematically describe the source of some of these issues, and provide some resolutions. In particular, we present a novel MPC scheme with relaxed stability criteria, based on generalized control Lyapunov functions. Most notably, this scheme allows for implementing a flexible number of control inputs in each iteration, in a computationally attractive manner, while guaranteeing recursive feasibility and stability. The advantages of our flexible-step implementation are demonstrated on nonholonomic systems, switched systems and lastly, in the setting of adaptive control. Specifically, we provide a systematic method for constructing generalized control Lyapunov functions for the novel MPC scheme in the case of linear systems. When the true linear system is unknown, generating terminal conditions is not possible. In fact, even when the estimation of the unknown system matrices is done through solving a least-squares problem, existing results that guarantee stabilizing controls rely on unnatural choices of terminal costs. We present an extension of our MPC scheme to the unknown setting and show convergence to the origin of the closed-loop system.
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Queen's University's Thesis/Dissertation Non-Exclusive License for Deposit to QSpace and Library and Archives Canada
ProQuest PhD and Master's Theses International Dissemination Agreement
Intellectual Property Guidelines at Queen's University
Copying and Preserving Your Thesis
This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.
Attribution 4.0 International
ProQuest PhD and Master's Theses International Dissemination Agreement
Intellectual Property Guidelines at Queen's University
Copying and Preserving Your Thesis
This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.
Attribution 4.0 International