Supplement: Optimization-Based Control

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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: 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)
  • Jan-Feb 2023: updated versions of Chapters 2-7 (version 2.3x) posted roughly every week
  • 31 Dec 2022: posted Jupyter notebooks for Chapter 1 (intro to python-control)
  • 29 Dec 2022: added new Chapter 1 (introduction) and starting to post updates for v2.3


  • Ch 5 - Stochastic Systems (PDF, 07 Feb 2022)
    • 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, 13 Feb 2022)
    • Linear Quadratic Estimators
    • Extensions of the Kalman Filter
    • LQG Control
    • Application to a Vectored Thrust Aircraft
  • Ch 7 - Sensor Fusion (PDF, 23 Feb 2022)
    • Discrete-Time Stochastic Systems
    • Kalman Filters in Discrete Time
    • Predictor-Corrector Form
    • Sensor Fusion
    • Information Filters
    • Additional Topics
  • Bibliography and Index (PDF, 03 Jan 2023)