# Difference between revisions of "CDS 101/110 - Dynamic Behavior"

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{{cds101- | {{cds101-fa08 lecture|prev=Introduction and Review|next=Linear Systems}} | ||

{{righttoc}} | {{righttoc}} | ||

== Overview == | == Overview == | ||

The learning objectives for this week are: | |||

* Students should be able to use a phase portraits to describe the behavior of dynamical systems and determine the stability of an equilibrium point | |||

* Students should be able to find equilibrium points for a nonlinear system and determine whether they are stable using linearizations (all) and Lyapunov functions (CDS 110/210) | |||

* Students should be able to explain the difference between stability, asymptotic stability, and global stability | |||

'''Monday:''' Qualitative Analysis and Stability ({{cds101 | '''Monday:''' Qualitative Analysis and Stability ({{cds101 handouts|L2-1_stability.pdf|Slides}}, [http://www.cds.caltech.edu/~murray/courses/cds101/fa07/mp3/cds101-2007-10-15.mp3 MP3]- due to technical difficulties, this is last year's lecture) | ||

<p> | |||

:This lecture provides an introduction to stability of (nonlinear) control systems. Formal definitions of stability are given and phase portraits are introduced to help visualize the concepts. Local and global behavior of nonlinear systems is discussed, using a damped pendulum and the predator-prey problem as examples. | |||

:* {{cds101 handouts|L2-1_stability_h.pdf|Lecture handout}} | |||

:* MATLAB code: {{cds101 matlab|phaseplot.m}}, {{cds101 matlab|boxgrid.m}}, {{cds101 matlab|L2_1_stability.m}}, {{cds101 matlab|oscillator.m}}, {{cds101 matlab|invpend.m}}, {{cds101 matlab|predprey.m}} | |||

</p> | |||

'''Wednesday:''' Stability Analysis using Lyapunov Functions ({{cds101 handouts|L2-2_lyapunov.pdf|Notes}}, [http://www.cds.caltech.edu/~murray/courses/cds101/fa07/mp3/cds101-2007-10-17.mp3 MP3]- due to technical difficulties, this is last year's lecture) | |||

:Lyapunov functions are introduced as a method of proving stability for nonlinear systems. Simple examples are used to explain the concepts. | |||

:* {{cds101 handouts|L2-2_lyapunov.pdf|Lecture notes}} | |||

'''Friday:''' [[CDS 101/110a, Fall 2008 - Recitation Schedule|Recitations]] | |||

:* [[CDS 210 - Stability Analysis]] | |||

'''Friday:''' | |||

* | |||

== Reading == | == Reading == | ||

* {{ | * {{AM08|Chapter 4 - Dynamic Behavior}} | ||

** CDS 101: Read sections 4.1-4.3 [30 min] | |||

** CDS 110: Read sections 4.1-4.4, up to Krasolvski-Lasalle (p 118) [60 min] | |||

** CDS 210: Review sections 4.1-4.3, read sections 4.4-4.5 [60 min] | |||

== Homework == | == Homework == | ||

* {{cds101 handouts|hw2-fa08.pdf|Homework #2}} | |||

== FAQ == | == FAQ == | ||

'''Monday''' | '''Monday''' | ||

<ncl>CDS 101/110 FAQ - Lecture | <ncl>CDS 101/110 FAQ - Lecture 2-1, Fall 2008</ncl> | ||

'''Wednesday''' | '''Wednesday''' | ||

<ncl>CDS 101/110 FAQ - Lecture | <ncl>CDS 101/110 FAQ - Lecture 2-2, Fall 2008</ncl> | ||

'''Homework''' | '''Homework''' | ||

<ncl>CDS 101/110 FAQ - Homework | <ncl>CDS 101/110 FAQ - Homework 2, Fall 2008</ncl> |

## Latest revision as of 05:56, 9 December 2008

CDS 101/110a | ← Schedule → | Recitations | FAQ | AM08 (errata) |

## Overview

The learning objectives for this week are:

- Students should be able to use a phase portraits to describe the behavior of dynamical systems and determine the stability of an equilibrium point
- Students should be able to find equilibrium points for a nonlinear system and determine whether they are stable using linearizations (all) and Lyapunov functions (CDS 110/210)
- Students should be able to explain the difference between stability, asymptotic stability, and global stability

**Monday:** Qualitative Analysis and Stability (Slides, MP3- due to technical difficulties, this is last year's lecture)

- This lecture provides an introduction to stability of (nonlinear) control systems. Formal definitions of stability are given and phase portraits are introduced to help visualize the concepts. Local and global behavior of nonlinear systems is discussed, using a damped pendulum and the predator-prey problem as examples.

- Lecture handout
- MATLAB code: phaseplot.m, boxgrid.m, L2_1_stability.m, oscillator.m, invpend.m, predprey.m

**Wednesday:** Stability Analysis using Lyapunov Functions (Notes, MP3- due to technical difficulties, this is last year's lecture)

- Lyapunov functions are introduced as a method of proving stability for nonlinear systems. Simple examples are used to explain the concepts.

**Friday:** Recitations

## Reading

- K. J. Åström and R. M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, Princeton University Press, 2008. Chapter 4 - Dynamic Behavior.
- CDS 101: Read sections 4.1-4.3 [30 min]
- CDS 110: Read sections 4.1-4.4, up to Krasolvski-Lasalle (p 118) [60 min]
- CDS 210: Review sections 4.1-4.3, read sections 4.4-4.5 [60 min]

## Homework

## FAQ

**Monday**
<ncl>CDS 101/110 FAQ - Lecture 2-1, Fall 2008</ncl>
**Wednesday**
<ncl>CDS 101/110 FAQ - Lecture 2-2, Fall 2008</ncl>
**Homework**
<ncl>CDS 101/110 FAQ - Homework 2, Fall 2008</ncl>