Supplement: Optimization-Based Control

Richard M. Murray

These notes serve as a supplement to Feedback Systems by Åström and Murray and expand on some of the topics introduced there. Our focus is on the use of optimization-based methods for control, including optimal control theory, receding horizon control and Kalman filtering. Each chapter is intended to be a standalone reference for advanced topics that are introduced in Feedback Systems.

Note: These notes are in draft form and may contain errors. Permission is granted to download and print a copy for individual use, but this material may not be reproduced, in whole or in part, without written consent from the author.

Quick Links Complete text (PDF, 12 Mar 2023) Errata

News (archive)

• 15 Feb 10: updated version of Chapter 4 (stochastic systems) is posted; multiple fixes + some new material
• 3 Jan 10: posted updated version of Chapters 1 and 2 (mainly small fixes) + working errata link
• 22 Dec 09: updated versions of all chapters posted; working through small fixes over the next few weeks
• 22 Dec 09: updated supplement main page to a new format
• 4 Jan 09: Version 2.0b posted - fixes and error corrections for chapters 1-4

Contents

Contents and Preface (PDF, 03 Jan 2010) Ch 1 - Trajectory Generation and Tracking (PDF, 03 Jan 2010) Two Degree of Freedom Design Trajectory Tracking and Gain Scheduling Trajectory Generation and Differential Flatness Ch 2 - Optimal Control (PDF, 27 Oct 2018) Review: Optimization Optimal Control of Systems Examples Linear Quadratic Regulators Choosing LQR Weights Advanced Topics Ch 3 - Receding Horizon Control (PDF, 22 Dec 2009) Optimization-Based Control Receding Horizon Control with CLF Terminal Cost Receding Horizon Control Using Differential Flatness Implementation on the Caltech Ducted Fan

Ch 4 - Stochastic Systems (PDF, 15 Feb 2010) Review of Random Variables Introduction to Random Processes Continuous-Time, Vector-Valued Random Processes Linear Stochastic Systems Random Processes in the Frequency Domain Ch 5 - Kalman Filtering (PDF, 22 Dec 2009) Linear Quadratic Estimators Extensions of the Kalman Filter LQG Control Application to a Vectored Thrust Aircraft Ch 6 - Sensor Fusion (PDF, 22 Dec 2009) Discrete-Time Stochastic Systems Kalman Filters in Discrete Time Predictor-Corrector Form Sensor Fusion Information Filters Additional Topics Bibliography and Index (PDF, 15 Feb 2010)