Week 5: Reachability and State Feedback
Overview
This lecture introduces the concept of reachability and explores the use of state space feedback for control of linear systems. Reachability is defined as the ability to move the system from one condition to another over finite time. The reachability matrix test is given to check if a linear system is reachable, and the test is applied to several examples. The concept of (linear) state space feedback is introduced and the ability to place eigenvalues of the closed loop system arbitrarily is related to reachability. A cart and pendulum system and the predator prey problem are used as examples.
Reading Material and Handouts
Handouts from lecture
- Monday lecture handout
- MATLAB files: L5_1_reachability.m
- No homework this week due to the midterm exam.
Required reading
-
K. J. Åström and R. M. Murray, Analysis and Design of Feedback Systems, Preprint, 2003. Chapter 5. (Caltech access only).
Supplemental reading
- Packard, Poola and Horowitz, Dynamic Systems and Feedback, Section 25
- B. Friedland, Sections 5.1-5.4 (controllability only)
- Advanced: A. D. Lewis, A Mathematical Introduction to Feedback Control, Chapter 2. [pdf]
Homework Set
There is no homework this week due to the midterm exam.