# Supplement: Optimization-Based Control

From FBSwiki

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*.

- Chapter 1: Trajectory Generation and Tracking (pdf, 02Jun08)
- Chapter 2: Optimal Control (pdf, 26Jan08)
- Chapter 3: Receding Horizon Control (pdf, 30Jan08)
- Chapter 4: Stochastic Systems (pdf, 19Feb08)
- Chapter 5: Kalman Filtering (pdf, 23Feb08) (pretty rough)
- Chapter 6: Sensor Fusion (pdf, 28Feb08) (bare bones)

### Summary of Changes

- 1 Jun 08: Version 2.0a - fixes and updates throughout; posting individual chapters as they are done. Significant changes:
- Changed Section 2.1 (review of optimization) to refer to minimum instead of maximum (more compatible with later usage)

- 27 Feb 08: Version 1.8a - initial cut at discrete-time/sensor fusion chapter; bare bones derivations
- 23 Feb 08: Version 1.7b - fixed up the Kalman filtering notes a bit, but they still need more work. Inserted MATLAB code as an example of how to apply everything
- 21 Feb 08: Version 1.7a - first version of Kalman filtering notes; still pretty rough (bullets instead of paragraphs)
- 15 Feb 08: Version 1.6d - added references for further reading + summary figure
- 13 Feb 08: Version 1.6c - use R_V instead of Q_V (consistent with main text)
- 12 Feb 08: Version 1.6b posted; updated state space computations for stochastic systems
- 11 Feb 08: Version 1.6a posted; new chapter on stochastic systems
- 30 Jan 08: Version 1.4a posted; new chapter on receding horizon control
- 25 Jan 08: fixed up some bad references; expanded the LQR design example (pvtol); added example of abnormal extremal
- 23 Jan 08: updated Ch 2; more details on LQR
- 14 Jan 08: updated Ch 1 and posted Ch 2. Fixed a couple of small bugs in Ch 1. Changed to .
- 7 Jan 08: first post (Ch 1)