# Supplement: Optimization-Based Control

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.

##### News (archive)
• 08 Jan 2022: updated version of Chapter 2 (trajectory generation) and full text (v2.2d)
• 21 Dec 2021: added new Chapter 1 (introduction) and starting to post updates for v2.2
• 15 Feb 2010: updated version of Chapter 4 (stochastic systems) is posted; multiple fixes + some new material
• 3 Jan 2010: posted updated version of Chapters 1 and 2 (mainly small fixes) + working errata link
• 22 Dec 2009: updated versions of all chapters posted; working through small fixes over the next few weeks

### Contents

 Contents and Preface (PDF, 29 Dec 2021) Ch 1 - Introduction (PDF, 29 Dec 2021) System and Control Design The Control System “Standard Model” Layered Control Systems The Python Control Systems Library (python-control) Ch 2 - Trajectory Generation and Tracking (PDF, 08 Jan 2022) Two Degree of Freedom Design Trajectory Tracking and Gain Scheduling Trajectory Generation and Differential Flatness Ch 3 - Optimal Control (PDF, 19 Jan 2022) Review: Optimization Optimal Control of Systems Examples Linear Quadratic Regulators Choosing LQR Weights Advanced Topics Ch 4 - Receding Horizon Control (PDF, 31 Jan 2022) Optimization-Based Control Receding Horizon Control with CLF Terminal Cost Receding Horizon Control Using Differential Flatness Implementation on the Caltech Ducted Fan Ch 5 - 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 6 - Kalman Filtering (PDF, 22 Dec 2009) Linear Quadratic Estimators Extensions of the Kalman Filter LQG Control Application to a Vectored Thrust Aircraft Ch 7 - 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)