Murray Wiki - User contributions [en]

Ncsbook/markjls

2009-06-25T15:57:19Z

Vijay:

{{ncsbook menu|infothy|ratelim}}
This page is intended to be used for comments on Chapter 4 - Markovian Jump Linear Systems. To enter a new comment, create a new third level heading with your name and date. Then enter comments below and people can respond/converse.

=== RMM comments, 15 Jun 09 ===

- Notation differs from Chapter 2 and notation chapter. Using r(k) instead of r_k. OK for now, but eventually we will need to standardize.

As I said in the call, subscripts will lead to subscripts of subscripts and subscripts of superscripts. Of course, if the standard is subscript, I will change my notation.

- Use example environment for examples (this will generate the proper header + end of example marks)

- I would suggest that we don't use the acronym MJLS, but rather write out "Markovian jump linear system". The exception would be if you actually say "MJLS" when you talk about a Markovian jump linear system (like we say "LTI").

I am fine with not using MJLS.

- The form of the theorems in this chapter is a bit awkward. They are very long and have itemized lists. I would remove the latter (use enumerated lists if necessary) and see if we can arrange things so that the proof statements are much shorter (using appropriate definitions, lemmas, etc) if that helps.

- Not sure if we need to include H_infty control, but leave as a placeholderer for now.

I agree.

EECI09: Estimation over networks

2009-03-12T16:20:23Z

Vijay:

{{eeci-sp09 header|prev=Cooperative control|next=Distributed protocols and verification}}

{{righttoc}}
In this lecture we consider some results when a process is being observed by multiple sensors, or when the sensor is transmitting information across a network consisting of multiple communication channels combined in an arbitrary topology. We consider both the analog erasure and digital noiseless channel models. For the digital noiseless channel model, we provide stability conditions. For the analog erasure channel model, we solve the two block design problem for optimal performance.

== Lecture Materials ==
* Lecture slides: [[Media:lecture_est_over_networks.pdf|Lecture Summary]]

== Further Reading ==
* [http://ee.nd.edu/faculty/vgupta/research/gdhmhtac06.pdf "Data Transmission over Networks for Estimation and Control"], V. Gupta, A. F. Dana, J. Hespanha, R. M. Murray and B. Hassibi, IEEE Transactions on Automatic Control, October 2009, To appear. This paper presents results for estimation across networks of erasure channels. 
* [http://ee.nd.edu/faculty/vgupta/research/gmbtac07.pdf "Stabilization over Erasure Channels using Multiple Sensors"], V. Gupta, N. C. Martins and J. S. Baras, IEEE Transactions on Automatic Control, November 2009 To Appear. This paper presents the stability results for the multi-sensor case, and discusses some performance issues that arise.
*[http://pantheon.yale.edu/~sct29/publications.dir/conferences.dir/CDC2003_ScalingControl.pdf "Some Scaling Properties of Large Distributed Control Systems"], S. Tatikonda, 42th IEEE Conference on Decision and Control, December 2003. This paper presents some of the earlier work on the digital noiseless channel case, as discussed in the lecture

== Additional Information ==
* [http://home.cwru.edu/ncs/ Networked Control Systems Repository] (M. Branicky and S. Phillipps)
* [[EECI08: Introduction to Networked Control Systems|2008 lecture page]]
* Additional links to external information

EECI09: Quantization and bandwidth limits

2009-03-12T16:17:08Z

Vijay:

{{eeci-sp09 header|prev=Packet loss|next=Estimation over networks}}

{{righttoc}}
In this lecture, we consider networked control over a digital noiseless channel. The one block design problem is largely unsolved. For the two block design problem, the fundamental result is the data rate theorem, which constrains the data rate required for stabilizing the process. There are interesting issues that arise if further constraints are placed on the memory of the encoder.

== Lecture Materials ==
* Lecture slides: [[Media:lecture_quantization.pdf|Lecture Summary]]

== Further Reading ==
* [http://www.ee.unimelb.edu.au/staff/gnair/nairPIEEE07.pdf "Feedback control under data rate constraints: an overview"], G. N. Nair, F. Fagnani, S. Zampieri, and R. J. Evans, Proceedings of the IEEE, vol. 95, no. 1, pp. 108-37, Jan. 2007. This paper gives a nice overview and provides several references for the general area of control over digital noiseless channels.
* [http://pantheon.yale.edu/~sct29/publications.dir/Tatikonda_Thesis.pdf Control Under Communication Constraints] Sekhar Tatikonda, Ph.D. Thesis, MIT. Some of the performance related issues are discussed in this work.
* Stabilizing a linear system with quantized state feedback, D. F. Delchamps, IEEE Transactions on Automatic Control AC-35: 916-924. This work is one of the earlier works to point out the inadequacy of additive white noise approximation of the quantization error. 

== Additional Information ==
* [http://home.cwru.edu/ncs/ Networked Control Systems Repository] (M. Branicky and S. Phillipps)
* [[EECI08: Introduction to Networked Control Systems|2008 lecture page]]
* Additional links to external information

EECI09: Distributed estimation and sensor fusion

2009-03-12T16:16:02Z

Vijay:

{{eeci-sp09 header|prev=Estimation over networks|next=Review of information theory and communications}}

{{righttoc}}
In this lecture, we introduce the basics of distributed estimation. We consider both static sensor fusion and distributed Kalman filtering. We discuss some existing algorithms, and point out some open problems.

== Lecture Materials ==
* Lecture slides: [[Media:Lecture_dist_estimation.pdf|Lecture Summary]]

== Further Reading ==
* "On Optimal Track-to-Track Fusion," K. C. Chang, R. K. Saha and Y. Bar-Shalom, IEEE Transactions on Aerospace and Electronic Systems, AES-33:1271-1276, 1997. This paper provides a good overview of the correlation introduced by common process noise in dynamic sensor fusion.
* "Architectures and Algorithms for Track Association and Fusion," IEEE Aerospace and Electronic Systems Magazine, 15:5-13, 2000. This paper gives a nice overview of existing results on the track fusion problem.
* [http://engineering.dartmouth.edu/~olfati/papers/cdc07_dkf.pdf "Distributed Kalman Filtering for Sensor Networks,"] R. Olfati-Saber, Proc. of the 46th IEEE Conference on Decision and Control, Dec. 2007. This paper provides the Kalman filter based dynamic sensor fusion algorithm discussed in the lecture.

== Additional Information ==
* [http://home.cwru.edu/ncs/ Networked Control Systems Repository] (M. Branicky and S. Phillipps)
* [[EECI08: Introduction to Networked Control Systems|2008 lecture page]]
* Additional links to external information

EECI09: Distributed estimation and sensor fusion

2009-03-12T16:15:01Z

Vijay:

{{eeci-sp09 header|prev=Estimation over networks|next=Information theoretic tools for networked control}}

{{righttoc}}
In this lecture, we introduce the basics of distributed estimation. We consider both static sensor fusion and distributed Kalman filtering. We discuss some existing algorithms, and point out some open problems.

== Lecture Materials ==
* Lecture slides: [[Media:Lecture_dist_estimation.pdf|Lecture Summary]]

== Further Reading ==
* "On Optimal Track-to-Track Fusion," K. C. Chang, R. K. Saha and Y. Bar-Shalom, IEEE Transactions on Aerospace and Electronic Systems, AES-33:1271-1276, 1997. This paper provides a good overview of the correlation introduced by common process noise in dynamic sensor fusion.
* "Architectures and Algorithms for Track Association and Fusion," IEEE Aerospace and Electronic Systems Magazine, 15:5-13, 2000. This paper gives a nice overview of existing results on the track fusion problem.
* [http://engineering.dartmouth.edu/~olfati/papers/cdc07_dkf.pdf "Distributed Kalman Filtering for Sensor Networks,"] R. Olfati-Saber, Proc. of the 46th IEEE Conference on Decision and Control, Dec. 2007. This paper provides the Kalman filter based dynamic sensor fusion algorithm discussed in the lecture.

== Additional Information ==
* [http://home.cwru.edu/ncs/ Networked Control Systems Repository] (M. Branicky and S. Phillipps)
* [[EECI08: Introduction to Networked Control Systems|2008 lecture page]]
* Additional links to external information

EECI09: Cooperative control

2009-03-12T16:14:03Z

Vijay:

{{eeci-sp09 header|prev=Distributed control|next=Distributed estimation and sensor fusion}}

{{righttoc}}
In this lecture we present a survey of recent research in cooperative control of multivehicle systems, using a common mathematical framework to allow different methods to be described in a unified way. The survey has three primary parts: an overview of current applications of cooperative control, a summary of some of the key technical approaches that have been explored, and a description of some possible future directions for research. Specific technical areas that are discussed include distributed receding horizon control, cooperative tasking and spatiotemporal planning.

== Lecture Materials ==
* Lecture slides: {{eeci-sp09 pdf|Ln_topic.pdf|Title}}
* Links to anything else that is handed out in the lecture

== Further Reading ==
* R. M. Murray, “Recent Research in Cooperative Control of Multi-Vehicle Systems”, ''J. Guidance, Control and Dynamics'', 2007.
* W. B. Dunbar and R. M. Murray, "Distributed receding horizon control for multi-vehicle formation stabilization". ''Automatica'', 42(4):549--558, 2006.

== Additional Information ==
* [[EECI08: Formation Control in Multi-Agent Systems|2008 lecture page]]

HYCON-EECI, Spring 2009

2009-03-12T16:09:21Z

Vijay:

<table width="100%" cellspacing=0>
<tr valign=top>
<td rowspan=3 align=center> [[Image:eecilogo.png|90px]]</td>
<td align=center>An Introduction to Networked Control Systems</td>
<td rowspan=3 align=center"> [[Image:cdslogo.png|90px]]</td></tr>
<tr valign=top><td align=center>Vijay Gupta (Notre Dame)   Richard M. Murray (Caltech)</td></tr>
<tr valign=top><td align=center>16-20 March 2009</td></tr>
</table>


{{righttoc}}
Increases in fast and inexpensive computing and communications have enabled a new generation
information-rich control systems that rely on multi-threaded networked execution, distributed
optimization, adaptation and learning, and contingency management in increasingly sophisticated
ways. This set of lectures will provide an introduction to the theory and tools for building such
systems, focusing on the so-called “networked” control systems in which the components that form
the system are connected through a communication network. These lectures were developed as part of
a [[CDS 270-2, Spring 2006|course at Caltech]] on “Networked Control Systems”, first offered in Spring 2006, and a [[HYCON-EECI, Spring 2008|2008 EECI course]]. The instructors are also working on a new textbook, [[ncsbook|Networked Sensing, Estimation and Control Systems]], co-authored with Ling Shi and Bruno Sinopoli.


=== Course information ===
* Instructors: [http://ee.nd.edu/faculty/vgupta/ Vijay Gupta] (Notre Dame EE) and [[User:Murray|Richard M. Murray]] (Caltech CDS)
* Date and location: 16-20 Mar 09, SUPELEC (South of Paris)
* Sponsor: [http://www.eeci-institute.eu/index.php?p=HYCON-EECI%20Graduate%20School%20on%20Control%202009 HYCON-EECI Graduate School on Control]

=== Lecture Schedule ===
The schedule below lists the lectures that will be given as part of the course. Each lecture will last approximately 90 minutes. The individual lecture pages give an overview of the lecture and links to additional information.

{| border=1
|-
| align=center | Lec
| align=center | Date/time
|   Title
|   Reading
{{hycon-eeci09 entry|1|Introduction to Networked Control Systems| |Murray}}
{{hycon-eeci09 entry|2|Optimization-based control| |Murray}}
{{hycon-eeci09 entry|3| Information patterns| |Gupta}}
{{hycon-eeci09 entry|4| Graph theory| |Murray}}
{{hycon-eeci09 entry|5| Distributed control| |Murray}}
{{hycon-eeci09 entry|6| Cooperative control| |Murray}}
{{hycon-eeci09 entry|7| Distributed estimation and sensor fusion| |Gupta}}
{{hycon-eeci09 entry|8| Review of information theory and communications| |Gupta}}
{{hycon-eeci09 entry|9| Jump linear Markov processes| |Gupta}}
{{hycon-eeci09 entry|10| Packet loss, delays and shock absorbers| |Gupta}}
{{hycon-eeci09 entry|11| Quantization and bandwidth limits| |Gupta}}
{{hycon-eeci09 entry|12| Estimation over networks| |Gupta}}
{{hycon-eeci09 entry|13| Distributed protocols and verification| |Murray}}
{{hycon-eeci09 entry|14| Future directions and open problems| |Murray}}
|}

=== References ===
Notes and references are given in the individual lectures.

=== Announcements ===
* 30 Dec 08: course page created for HYCON-EECI
* 1 Mar 09: updated course outline; created all lecture pages

[[Category:Courses]] [[Category:2008-09 Courses]]

HYCON-EECI, Spring 2009

2009-03-12T16:08:32Z

Vijay:

<table width="100%" cellspacing=0>
<tr valign=top>
<td rowspan=3 align=center> [[Image:eecilogo.png|90px]]</td>
<td align=center>An Introduction to Networked Control Systems</td>
<td rowspan=3 align=center"> [[Image:cdslogo.png|90px]]</td></tr>
<tr valign=top><td align=center>Vijay Gupta (Notre Dame)   Richard M. Murray (Caltech)</td></tr>
<tr valign=top><td align=center>16-20 March 2009</td></tr>
</table>


{{righttoc}}
Increases in fast and inexpensive computing and communications have enabled a new generation
information-rich control systems that rely on multi-threaded networked execution, distributed
optimization, adaptation and learning, and contingency management in increasingly sophisticated
ways. This set of lectures will provide an introduction to the theory and tools for building such
systems, focusing on the so-called “networked” control systems in which the components that form
the system are connected through a communication network. These lectures were developed as part of
a [[CDS 270-2, Spring 2006|course at Caltech]] on “Networked Control Systems”, first offered in Spring 2006, and a [[HYCON-EECI, Spring 2008|2008 EECI course]]. The instructors are also working on a new textbook, [[ncsbook|Networked Sensing, Estimation and Control Systems]], co-authored with Ling Shi and Bruno Sinopoli.


=== Course information ===
* Instructors: Vijay Gupta (Notre Dame EE) and [[User:Murray|Richard M. Murray]] (Caltech CDS)
* Date and location: 16-20 Mar 09, SUPELEC (South of Paris)
* Sponsor: [http://www.eeci-institute.eu/index.php?p=HYCON-EECI%20Graduate%20School%20on%20Control%202009 HYCON-EECI Graduate School on Control]

=== Lecture Schedule ===
The schedule below lists the lectures that will be given as part of the course. Each lecture will last approximately 90 minutes. The individual lecture pages give an overview of the lecture and links to additional information.

{| border=1
|-
| align=center | Lec
| align=center | Date/time
|   Title
|   Reading
{{hycon-eeci09 entry|1|Introduction to Networked Control Systems| |Murray}}
{{hycon-eeci09 entry|2|Optimization-based control| |Murray}}
{{hycon-eeci09 entry|3| Information patterns| |Gupta}}
{{hycon-eeci09 entry|4| Graph theory| |Murray}}
{{hycon-eeci09 entry|5| Distributed control| |Murray}}
{{hycon-eeci09 entry|6| Cooperative control| |Murray}}
{{hycon-eeci09 entry|7| Distributed estimation and sensor fusion| |Gupta}}
{{hycon-eeci09 entry|8| Review of information theory and communications| |Gupta}}
{{hycon-eeci09 entry|9| Jump linear Markov processes| |Gupta}}
{{hycon-eeci09 entry|10| Packet loss, delays and shock absorbers| |Gupta}}
{{hycon-eeci09 entry|11| Quantization and bandwidth limits| |Gupta}}
{{hycon-eeci09 entry|12| Estimation over networks| |Gupta}}
{{hycon-eeci09 entry|13| Distributed protocols and verification| |Murray}}
{{hycon-eeci09 entry|14| Future directions and open problems| |Murray}}
|}

=== References ===
Notes and references are given in the individual lectures.

=== Announcements ===
* 30 Dec 08: course page created for HYCON-EECI
* 1 Mar 09: updated course outline; created all lecture pages

[[Category:Courses]] [[Category:2008-09 Courses]]

EECI09: Distributed estimation and sensor fusion

2009-03-12T16:07:40Z

Vijay:

{{eeci-sp09 header|prev=Estimation over networks|next=Distributed protocols}}

{{righttoc}}
In this lecture, we introduce the basics of distributed estimation. We consider both static sensor fusion and distributed Kalman filtering. We discuss some existing algorithms, and point out some open problems.

== Lecture Materials ==
* Lecture slides: [[Media:Lecture_dist_estimation.pdf|Lecture Summary]]

== Further Reading ==
* "On Optimal Track-to-Track Fusion," K. C. Chang, R. K. Saha and Y. Bar-Shalom, IEEE Transactions on Aerospace and Electronic Systems, AES-33:1271-1276, 1997. This paper provides a good overview of the correlation introduced by common process noise in dynamic sensor fusion.
* "Architectures and Algorithms for Track Association and Fusion," IEEE Aerospace and Electronic Systems Magazine, 15:5-13, 2000. This paper gives a nice overview of existing results on the track fusion problem.
* [http://engineering.dartmouth.edu/~olfati/papers/cdc07_dkf.pdf "Distributed Kalman Filtering for Sensor Networks,"] R. Olfati-Saber, Proc. of the 46th IEEE Conference on Decision and Control, Dec. 2007. This paper provides the Kalman filter based dynamic sensor fusion algorithm discussed in the lecture.

== Additional Information ==
* [http://home.cwru.edu/ncs/ Networked Control Systems Repository] (M. Branicky and S. Phillipps)
* [[EECI08: Introduction to Networked Control Systems|2008 lecture page]]
* Additional links to external information

File:Lecture dist estimation.pdf

2009-03-12T14:09:13Z

Vijay:

EECI09: Estimation over networks

2009-03-11T20:26:28Z

Vijay:

{{eeci-sp09 header|prev=Cooperative control|next=Distributed estimation}}

{{righttoc}}
One paragraph overview of the lecture

== Lecture Materials ==
* Lecture slides: [[Media:lecture_est_over_networks.pdf|Lecture Summary]]

== Further Reading ==
* [http://ee.nd.edu/faculty/vgupta/research/gdhmhtac06.pdf "Data Transmission over Networks for Estimation and Control"], V. Gupta, A. F. Dana, J. Hespanha, R. M. Murray and B. Hassibi, IEEE Transactions on Automatic Control, October 2009, To appear. This paper presents results for estimation across networks of erasure channels. 
* [http://ee.nd.edu/faculty/vgupta/research/gmbtac07.pdf "Stabilization over Erasure Channels using Multiple Sensors"], V. Gupta, N. C. Martins and J. S. Baras, IEEE Transactions on Automatic Control, November 2009 To Appear. This paper presents the stability results for the multi-sensor case, and discusses some performance issues that arise.
*[http://pantheon.yale.edu/~sct29/publications.dir/conferences.dir/CDC2003_ScalingControl.pdf "Some Scaling Properties of Large Distributed Control Systems"], S. Tatikonda, 42th IEEE Conference on Decision and Control, December 2003. This paper presents some of the earlier work on the digital noiseless channel case, as discussed in the lecture

== Additional Information ==
* [http://home.cwru.edu/ncs/ Networked Control Systems Repository] (M. Branicky and S. Phillipps)
* [[EECI08: Introduction to Networked Control Systems|2008 lecture page]]
* Additional links to external information

EECI09: Estimation over networks

2009-03-11T17:09:54Z

Vijay:

{{eeci-sp09 header|prev=Cooperative control|next=Distributed estimation}}

{{righttoc}}
One paragraph overview of the lecture

== Lecture Materials ==
* Lecture slides: [[Media:lecture_est_over_networks.pdf|Lecture Summary]]

== Further Reading ==
* [http://ee.nd.edu/faculty/vgupta/research/gdhmhtac06.pdf "Data Transmission over Networks for Estimation and Control"], V. Gupta, A. F. Dana, J. Hespanha, R. M. Murray and B. Hassibi, IEEE Transactions on Automatic Control, October 2009, To appear. This paper presents results for estimation across networks of erasure channels. 
* [http://ee.nd.edu/faculty/vgupta/research/gmbtac07.pdf "Stabilization over Erasure Channels using Multiple Sensors"], V. Gupta, N. C. Martins and J. S. Baras, IEEE Transactions on Automatic Control, November 2009 To Appear. This paper presents the stability results for the multi-sensor case, and discuss some performance issues that 

== Additional Information ==
* [http://home.cwru.edu/ncs/ Networked Control Systems Repository] (M. Branicky and S. Phillipps)
* [[EECI08: Introduction to Networked Control Systems|2008 lecture page]]
* Additional links to external information

File:Lecture est over networks.pdf

2009-03-11T17:01:28Z

Vijay:

EECI09: Quantization and bandwidth limits

2009-03-11T11:26:01Z

Vijay:

{{eeci-sp09 header|prev=Packet loss|next=Information patterns}}

{{righttoc}}
In this lecture, we consider networked control over a digital noiseless channel. The one block design problem is largely unsolved. For the two block design problem, the fundamental result is the data rate theorem, which constrains the data rate required for stabilizing the process. There are interesting issues that arise if further constraints are placed on the memory of the encoder.

== Lecture Materials ==
* Lecture slides: [[Media:lecture_quantization.pdf|Lecture Summary]]

== Further Reading ==
* [http://www.ee.unimelb.edu.au/staff/gnair/nairPIEEE07.pdf "Feedback control under data rate constraints: an overview"], G. N. Nair, F. Fagnani, S. Zampieri, and R. J. Evans, Proceedings of the IEEE, vol. 95, no. 1, pp. 108-37, Jan. 2007. This paper gives a nice overview and provides several references for the general area of control over digital noiseless channels.
* [http://pantheon.yale.edu/~sct29/publications.dir/Tatikonda_Thesis.pdf Control Under Communication Constraints] Sekhar Tatikonda, Ph.D. Thesis, MIT. Some of the performance related issues are discussed in this work.
* Stabilizing a linear system with quantized state feedback, D. F. Delchamps, IEEE Transactions on Automatic Control AC-35: 916-924. This work is one of the earlier works to point out the inadequacy of additive white noise approximation of the quantization error. 

== Additional Information ==
* [http://home.cwru.edu/ncs/ Networked Control Systems Repository] (M. Branicky and S. Phillipps)
* [[EECI08: Introduction to Networked Control Systems|2008 lecture page]]
* Additional links to external information

File:Lecture quantization.pdf

2009-03-11T10:30:51Z

Vijay:

EECI09: Information patterns

2009-03-10T20:22:10Z

Vijay:

{{eeci-sp09 header|prev=Optimization-based control|next=Graph theory}}

{{righttoc}}
In this lecture, we look at one of the reasons why networked control systems problems are difficult. Due to the distributed nature of the problem, different controllers may have access to different information sets at every time. We introduce the concept of information patterns, and identify some patterns that permit simple solutions to the optimal control problem.

== Lecture Materials ==
* Lecture slides: [[Media:lecture_info_patterns.pdf|Lecture Summary]]

== Further Reading ==
* "Separation of Estimation and Control for Discrete Time Systems"], H. S. Witsenhausen, Proceedings of the IEEE, vol. 59, no. 11, pp. 1557-1566, Nov. 1971. This paper covers the concept of information patterns and discusses why non-classical information patterns may turn the optimal control problem difficult to solve.
* "A Counterexample in Stochastic Optimum Control," H. S. Witsenhausen, SIAM Journal of Control, vol. 6, no. 1, pp. 131-147, 1968. This paper introduced the counterexample, and proved that a non-linear controller will perform better than the optimal affine controller.
* "Team Decision Theory and Information Structures in Optimal Control Problems - Part I," Y. C. Ho and K. C. Chu, IEEE Transactions on Automatic Control, vol. AC-17, no. 1, pp. 15-22, Jan. 1972. This paper considers the partially nested information structure. 

== Additional Information ==
* [http://home.cwru.edu/ncs/ Networked Control Systems Repository] (M. Branicky and S. Phillipps)
* [[EECI08: Introduction to Networked Control Systems|2008 lecture page]]
* Additional links to external information

EECI09: Information patterns

2009-03-10T20:21:47Z

Vijay:

{{eeci-sp09 header|prev=Optimization-based control|next=Graph theory}}

{{righttoc}}
In this lecture, we look at one of the reasons why networked control systems problems are difficult. Due to the distributed nature of the problem, different controllers may have access to different information sets at every time. We introduce the concept of information patterns, and identify some patterns that permit simple solutions to the optimal control problem.

== Lecture Materials ==
* Lecture slides: [[Media:lecture_info_patterns.pdf|Lecture Summary]]

== Further Reading ==
* "Separation of Estimation and Control for Discrete Time Systems"], H. S. Witsenhausen, Proceedings of the IEEE, vol. 59, no. 11, pp. 1557-1566, Nov. 1971. This paper covers the concept of information patterns and discusses why non-classical information patterns may turn the optimal control problem difficult to solve.
* "A Counterexample in Stochastic Optimum Control," H. S. Witsenhausen, SIAM Journal of
Control, vol. 6, no. 1, pp. 131-147, 1968. This paper introduced the counterexample, and proved that a non-linear controller will perform better than the optimal affine controller.
* "Team Decision Theory and Information Structures in Optimal Control Problems - Part I," Y. C. Ho and K. C. Chu, IEEE Transactions on Automatic Control, vol. AC-17, no. 1, pp. 15-22, Jan. 1972. This paper considers the partially nested information structure. 

== Additional Information ==
* [http://home.cwru.edu/ncs/ Networked Control Systems Repository] (M. Branicky and S. Phillipps)
* [[EECI08: Introduction to Networked Control Systems|2008 lecture page]]
* Additional links to external information

File:Lecture info patterns.pdf

2009-03-10T20:09:55Z

Vijay:

EECI09: Packet loss, delays and shock absorbers

2009-03-09T16:41:39Z

Vijay:

{{eeci-sp09 header|prev=Jump linear Markov processes|next=Quantization}}

{{righttoc}}
In this lecture we will consider two effects introduced by the communication channel: stochastic data erasure and random delay in data transfer. We will consider both the one-block and two-block design problems. The one-block design problem can be solved using the Markov jump linear systems introduced in the last lecture. The two-block design problem requires a new framework; however, somewhat surprisingly, the optimal design is recursive.

== Lecture Materials ==
* Lecture slides: [[Media:lecture_loss_delay.pdf|Summary]]

== Further Reading ==
* A good summary of the one block design problem is provided in the paper [http://circuit.ucsd.edu:16080/~massimo/Journal/IEEE-proceedings.pdf "Foundations of control and estimation over lossy networks"], L. Schenato, B. Sinopoli, M. Franceschetti, K. Poolla, S. S. Sastry, Proceedings of the IEEE, 95(1), pp. 163-187, January 2007.
* The two block design problem has been solved in [http://ee.nd.edu/faculty/vgupta/research/thesis/index.html "Distributed Estimation and Control in Networked Systems"], V. Gupta, Ph.D. Dissertation, Division of Engineering and Applied Science, California Institute of Technology.
* Some of the material for the case of a channel between controller and actuator is provided in [http://ee.nd.edu/faculty/vgupta/research/gmcdc08.pdf "On Stability in the Presence of Analog Erasure Channels"], V. Gupta and N. C. Martins, Proceedings of the IEEE Conference on Decision and Control (CDC '08), December 2008.

== Additional Information ==
* [http://home.cwru.edu/ncs/ Networked Control Systems Repository] (M. Branicky and S. Phillipps)
* [[EECI08: Introduction to Networked Control Systems|2008 lecture page]]
* Additional links to external information

File:Lecture loss delay.pdf

2009-03-09T16:26:08Z

Vijay:

EECI09: Jump linear Markov processes

2009-03-05T14:08:01Z

Vijay:

{{eeci-sp09 header|prev=Information systems|next=Packet loss}}

{{righttoc}}
In this lecture, we give a brief overview of Markovian jump linear systems. Such systems display multiple linear modes for the evolution of the state, and the modes are chosen stochastically. Such systems were important in the early development of networked control systems, where the communication channels were modeled as a Markov chain for effects such as delay and packet loss. As we will see in the next chapter, the one-block design problem for such systems can be studied in the framework of Markovian jump linear systems.

== Lecture Materials ==
* Lecture slides: [[Media:lecture_mjls.pdf|Summary]]

== Further Reading ==
* [http://www.amazon.com/Discrete-Time-Markov-Systems-Probability-Applications/dp/1852337613/ref=sr_11_1?ie=UTF8&qid=1236218843&sr=11-1 Discrete-Time Markov Jump Linear Systems (Probability and its Applications)], O.L.V. Costa, M.D. Fragoso, and R.P. Marques. Springer, 2004. This book is a good introduction to Markov jump linear systems.
* [http://ee.nd.edu/faculty/vgupta/research/gchmaut05/publ.pdf On a Stochastic Sensor Selection Algorithm with Applications in Sensor Scheduling and Sensor Coverage], V. Gupta, T. Chung, B. Hassibi and R. M. Murray, Automatica, 42(2):251-260, February 2006. This paper presents the necessary and sufficient stability conditions for the estimation problem. The results for the LQR problem are dual to the results obtained here.
*[http://www.control.lth.se/database/publications/article.pike?artkey=nilj98dis Real-Time Control Systems with Delays], J. Nilsson, Ph.D. Thesis, Department of Automatic Control, Lund University, 1998. This thesis extends the Markovian jump linear system framework to the case when the system mode defines a probability density function for the system matrices.

== Additional Information ==
* [http://home.cwru.edu/ncs/ Networked Control Systems Repository] (M. Branicky and S. Phillipps)
* [[EECI08: Introduction to Networked Control Systems|2008 lecture page]]
* Additional links to external information

EECI09: Review of information theory and communications

2009-03-05T14:07:41Z

Vijay:

{{eeci-sp09 header|prev=Introduction to NCS|next=Jump linear Markov processes}}

{{righttoc}}
In this lecture, we will briefly review some concepts from information theory. While classical control design is a one-block design problem (design controller / estimator), networked control design is a two-block design problem (design encoder and decoder for every channel). Information theory provides sophisticated tools for considering two block design problems for communication. By adapting these tools for feedback control, we will derive some extensions of the classical Bode integral formula for arbitrary causal feedback, that may possibly include finite capacity communication channels.

== Lecture Materials ==
* Lecture slides: [[Media:lecture_info_theory.pdf|Lecture Summary]]

== Further Reading ==
*[http://www.amazon.com/Elements-Information-Theory-Thomas-Cover/dp/0471062596 Elements of Information Theory], T. M. Cover and J. A. Thomas, Wiley Interscience. This is a classic text for information theory.
* [http://ieeexplore.ieee.org/search/srchabstract.jsp?arnumber=4623271&isnumber=4623249&punumber=9&k2dockey=4623271@ieeejrns&query=(martins+n.+c.%3Cin%3Eau)&pos=1&access=no Feedback Control in the Presence of Noisy Channels: “Bode-Like” Fundamental Limitations of Performance], N. C. Martins and M. Dahleh, IEEE Transactions on Automatic Control, 53(7):1604-1615, August 2008. This paper presents some of the extensions of the Bode integral covered in the lecture. 
* [http://ieeexplore.ieee.org/search/srchabstract.jsp?arnumber=4060988&isnumber=4060972&punumber=9&k2dockey=4060988@ieeejrns&query=(martins+n.+c.%3Cin%3Eau)&pos=0&access=no Fundamental Limitations of Disturbance Attenuation in the Presence of Side Information], N. C. Martins, M. Dahleh and J. C. Doyle, IEEE Transactions on Automatic Control, 52(1):56-66, January 2007. This paper considers similar problems when a preview of the disturbance is available.

== Additional Information ==
* [http://home.cwru.edu/ncs/ Networked Control Systems Repository] (M. Branicky and S. Phillipps)
* [[EECI08: Introduction to Networked Control Systems|2008 lecture page]]

EECI09: Jump linear Markov processes

2009-03-05T02:19:48Z

Vijay:

{{eeci-sp09 header|prev=Information systems|next=Packet loss}}

{{righttoc}}
In this lecture, we give a brief overview of Markovian jump linear systems. Such systems display multiple linear modes for the evolution of the state, and the modes are chosen stochastically. Such systems were important in the early development of networked control systems, where the communication channels were modeled as a Markov chain for effects such as delay and packet loss. As we will see in the next chapter, the one-block design problem for such systems can be studied in the framework of Markovian jump linear systems.

== Lecture Materials ==
* Lecture slides: {{eeci-sp09 pdf|lecture_mjls.pdf|lecture_mjls}}

== Further Reading ==
* [http://www.amazon.com/Discrete-Time-Markov-Systems-Probability-Applications/dp/1852337613/ref=sr_11_1?ie=UTF8&qid=1236218843&sr=11-1 Discrete-Time Markov Jump Linear Systems (Probability and its Applications)], O.L.V. Costa, M.D. Fragoso, and R.P. Marques. Springer, 2004. This book is a good introduction to Markov jump linear systems.
* [http://ee.nd.edu/faculty/vgupta/research/gchmaut05/publ.pdf On a Stochastic Sensor Selection Algorithm with Applications in Sensor Scheduling and Sensor Coverage], V. Gupta, T. Chung, B. Hassibi and R. M. Murray, Automatica, 42(2):251-260, February 2006. This paper presents the necessary and sufficient stability conditions for the estimation problem. The results for the LQR problem are dual to the results obtained here.
*[http://www.control.lth.se/database/publications/article.pike?artkey=nilj98dis Real-Time Control Systems with Delays], J. Nilsson, Ph.D. Thesis, Department of Automatic Control, Lund University, 1998. This thesis extends the Markovian jump linear system framework to the case when the system mode defines a probability density function for the system matrices.

== Additional Information ==
* [http://home.cwru.edu/ncs/ Networked Control Systems Repository] (M. Branicky and S. Phillipps)
* [[EECI08: Introduction to Networked Control Systems|2008 lecture page]]
* Additional links to external information

EECI09: Jump linear Markov processes

2009-03-05T02:05:40Z

Vijay:

EECI09: Jump linear Markov processes

2009-03-05T02:05:17Z

Vijay:

EECI09: Jump linear Markov processes

2009-03-05T02:03:18Z

Vijay:

File:Lecture mjls.pdf

2009-03-05T01:57:53Z

Vijay:

EECI09: Review of information theory and communications

2009-03-04T23:43:08Z

Vijay:

{{eeci-sp09 header|prev=Introduction to NCS|next=Jump linear Markov processes}}

{{righttoc}}
In this lecture, we will briefly review some concepts from information theory. While classical control design is a one-block design problem (design controller / estimator), networked control design is a two-block design problem (design encoder and decoder for every channel). Information theory provides sophisticated tools for considering two block design problems for communication. By adapting these tools for feedback control, we will derive some extensions of the classical Bode integral formula for arbitrary causal feedback, that may possibly include finite capacity communication channels.

== Lecture Materials ==
* Lecture slides: {{eeci-sp09 pdf|Lecture_info_theory.pdf}}

== Further Reading ==
*[http://www.amazon.com/Elements-Information-Theory-Thomas-Cover/dp/0471062596 Elements of Information Theory], T. M. Cover and J. A. Thomas, Wiley Interscience. This is a classic text for information theory.
* [http://ieeexplore.ieee.org/search/srchabstract.jsp?arnumber=4623271&isnumber=4623249&punumber=9&k2dockey=4623271@ieeejrns&query=(martins+n.+c.%3Cin%3Eau)&pos=1&access=no Feedback Control in the Presence of Noisy Channels: “Bode-Like” Fundamental Limitations of Performance], N. C. Martins and M. Dahleh, IEEE Transactions on Automatic Control, 53(7):1604-1615, August 2008. This paper presents some of the extensions of the Bode integral covered in the lecture. 
* [http://ieeexplore.ieee.org/search/srchabstract.jsp?arnumber=4060988&isnumber=4060972&punumber=9&k2dockey=4060988@ieeejrns&query=(martins+n.+c.%3Cin%3Eau)&pos=0&access=no Fundamental Limitations of Disturbance Attenuation in the Presence of Side Information], N. C. Martins, M. Dahleh and J. C. Doyle, IEEE Transactions on Automatic Control, 52(1):56-66, January 2007. This paper considers similar problems when a preview of the disturbance is available.

== Additional Information ==
* [http://home.cwru.edu/ncs/ Networked Control Systems Repository] (M. Branicky and S. Phillipps)
* [[EECI08: Introduction to Networked Control Systems|2008 lecture page]]

EECI09: Review of information theory and communications

2009-03-04T23:42:28Z

Vijay:

{{eeci-sp09 header|prev=Introduction to NCS|next=Jump linear Markov processes}}

{{righttoc}}
In this lecture, we will briefly review some concepts from information theory. While classical control design is a one-block design problem (design controller / estimator), networked control design is a two-block design problem (design encoder and decoder for every channel). Information theory provides sophisticated tools for considering two block design problems for communication. By adapting these tools for feedback control, we will derive some extensions of the classical Bode integral formula for arbitrary causal feedback, that may possibly include finite communication channels.

== Lecture Materials ==
* Lecture slides: {{eeci-sp09 pdf|Lecture_info_theory.pdf}}

== Further Reading ==
*[http://www.amazon.com/Elements-Information-Theory-Thomas-Cover/dp/0471062596 Elements of Information Theory], T. M. Cover and J. A. Thomas, Wiley Interscience. This is a classic text for information theory.
* [http://ieeexplore.ieee.org/search/srchabstract.jsp?arnumber=4623271&isnumber=4623249&punumber=9&k2dockey=4623271@ieeejrns&query=(martins+n.+c.%3Cin%3Eau)&pos=1&access=no Feedback Control in the Presence of Noisy Channels: “Bode-Like” Fundamental Limitations of Performance], N. C. Martins and M. Dahleh, IEEE Transactions on Automatic Control, 53(7):1604-1615, August 2008. This paper presents some of the extensions of the Bode integral covered in the lecture. 
* [http://ieeexplore.ieee.org/search/srchabstract.jsp?arnumber=4060988&isnumber=4060972&punumber=9&k2dockey=4060988@ieeejrns&query=(martins+n.+c.%3Cin%3Eau)&pos=0&access=no Fundamental Limitations of Disturbance Attenuation in the Presence of Side Information], N. C. Martins, M. Dahleh and J. C. Doyle, IEEE Transactions on Automatic Control, 52(1):56-66, January 2007. This paper considers similar problems when a preview of the disturbance is available.

== Additional Information ==
* [http://home.cwru.edu/ncs/ Networked Control Systems Repository] (M. Branicky and S. Phillipps)
* [[EECI08: Introduction to Networked Control Systems|2008 lecture page]]

EECI09: Review of information theory and communications

2009-03-04T23:32:02Z

Vijay:

{{eeci-sp09 header|prev=Introduction to NCS|next=Jump linear Markov processes}}

{{righttoc}}
In this lecture, we will briefly review some concepts from information theory. While classical control design is a one-block design problem (design controller / estimator), networked control design is a two-block design problem (design encoder and decoder for every channel). Information theory provides sophisticated tools for considering two block design problems for communication. By adapting these tools for feedback control, we will derive some extensions of the classical Bode integral formula for arbitrary causal feedback, that may possibly include finite communication channels.

== Lecture Materials ==
* Lecture slides: {{eeci-sp09 pdf|Lecture_info_theory.pdf}}
\* Links to anything else that is handed out in the lecture

== Further Reading ==
* [http://www.cds.caltech.edu/~murray/cdspanel Control in an Information Rich World], R. M. Murray (ed). SIAM, 2003. This book provides a high level description of some of the research challenges and opportunities in the field of control. The executive summary (Section 1) and the application sections on "Information and Networks" and "Robotics and Intelligent Machines" (Section 3.2 and 3.3) are particularly relevant.
* Second paper

== Additional Information ==
* [http://home.cwru.edu/ncs/ Networked Control Systems Repository] (M. Branicky and S. Phillipps)
* [[EECI08: Introduction to Networked Control Systems|2008 lecture page]]
* Additional links to external information

EECI09: Review of information theory and communications

2009-03-04T23:31:50Z

Vijay:

{{eeci-sp09 header|prev=Introduction to NCS|next=Jump linear Markov processes}}

{{righttoc}}
In this lecture, we will briefly review some concepts from information theory. While classical control design is a one-block design problem (design controller / estimator), networked control design is a two-block design problem (design encoder and decoder for every channel). Information theory provides sophisticated tools for considering two block design problems for communication. By adapting these tools for feedback control, we will derive some extensions of the classical Bode integral formula for arbitrary causal feedback, that may possibly include finite communication channels.

== Lecture Materials ==
* Lecture slides: {{eeci-sp09 pdf|Lecture_info_theory.pdf}}
%* Links to anything else that is handed out in the lecture

== Further Reading ==
* [http://www.cds.caltech.edu/~murray/cdspanel Control in an Information Rich World], R. M. Murray (ed). SIAM, 2003. This book provides a high level description of some of the research challenges and opportunities in the field of control. The executive summary (Section 1) and the application sections on "Information and Networks" and "Robotics and Intelligent Machines" (Section 3.2 and 3.3) are particularly relevant.
* Second paper

== Additional Information ==
* [http://home.cwru.edu/ncs/ Networked Control Systems Repository] (M. Branicky and S. Phillipps)
* [[EECI08: Introduction to Networked Control Systems|2008 lecture page]]
* Additional links to external information

EECI09: Review of information theory and communications

2009-03-04T23:31:28Z

Vijay:

{{eeci-sp09 header|prev=Introduction to NCS|next=Jump linear Markov processes}}

{{righttoc}}
In this lecture, we will briefly review some concepts from information theory. While classical control design is a one-block design problem (design controller / estimator), networked control design is a two-block design problem (design encoder and decoder for every channel). Information theory provides sophisticated tools for considering two block design problems for communication. By adapting these tools for feedback control, we will derive some extensions of the classical Bode integral formula for arbitrary causal feedback, that may possibly include finite communication channels.

== Lecture Materials ==
* Lecture slides: {{eeci-sp09 pdf|Lecture_info_theory.pdf}}
* Links to anything else that is handed out in the lecture

== Further Reading ==
* [http://www.cds.caltech.edu/~murray/cdspanel Control in an Information Rich World], R. M. Murray (ed). SIAM, 2003. This book provides a high level description of some of the research challenges and opportunities in the field of control. The executive summary (Section 1) and the application sections on "Information and Networks" and "Robotics and Intelligent Machines" (Section 3.2 and 3.3) are particularly relevant.
* Second paper

== Additional Information ==
* [http://home.cwru.edu/ncs/ Networked Control Systems Repository] (M. Branicky and S. Phillipps)
* [[EECI08: Introduction to Networked Control Systems|2008 lecture page]]
* Additional links to external information

EECI09: Review of information theory and communications

2009-03-04T23:31:09Z

Vijay:

{{eeci-sp09 header|prev=Introduction to NCS|next=Jump linear Markov processes}}

{{righttoc}}
In this lecture, we will briefly review some concepts from information theory. While classical control design is a one-block design problem (design controller / estimator), networked control design is a two-block design problem (design encoder and decoder for every channel). Information theory provides sophisticated tools for considering two block design problems for communication. By adapting these tools for feedback control, we will derive some extensions of the classical Bode integral formula for arbitrary causal feedback, that may possibly include finite communication channels.

== Lecture Materials ==
* Lecture slides: {{eeci-sp09|Lecture_info_theory.pdf}}
* Links to anything else that is handed out in the lecture

== Further Reading ==
* [http://www.cds.caltech.edu/~murray/cdspanel Control in an Information Rich World], R. M. Murray (ed). SIAM, 2003. This book provides a high level description of some of the research challenges and opportunities in the field of control. The executive summary (Section 1) and the application sections on "Information and Networks" and "Robotics and Intelligent Machines" (Section 3.2 and 3.3) are particularly relevant.
* Second paper

== Additional Information ==
* [http://home.cwru.edu/ncs/ Networked Control Systems Repository] (M. Branicky and S. Phillipps)
* [[EECI08: Introduction to Networked Control Systems|2008 lecture page]]
* Additional links to external information

EECI09: Review of information theory and communications

2009-03-04T23:30:46Z

Vijay:

{{eeci-sp09 header|prev=Introduction to NCS|next=Jump linear Markov processes}}

{{righttoc}}
In this lecture, we will briefly review some concepts from information theory. While classical control design is a one-block design problem (design controller / estimator), networked control design is a two-block design problem (design encoder and decoder for every channel). Information theory provides sophisticated tools for considering two block design problems for communication. By adapting these tools for feedback control, we will derive some extensions of the classical Bode integral formula for arbitrary causal feedback, that may possibly include finite communication channels.

== Lecture Materials ==
* Lecture slides: {{eeci-sp09 pdf|Lecture_info_theory.pdf|Title}}
* Links to anything else that is handed out in the lecture

== Further Reading ==
* [http://www.cds.caltech.edu/~murray/cdspanel Control in an Information Rich World], R. M. Murray (ed). SIAM, 2003. This book provides a high level description of some of the research challenges and opportunities in the field of control. The executive summary (Section 1) and the application sections on "Information and Networks" and "Robotics and Intelligent Machines" (Section 3.2 and 3.3) are particularly relevant.
* Second paper

== Additional Information ==
* [http://home.cwru.edu/ncs/ Networked Control Systems Repository] (M. Branicky and S. Phillipps)
* [[EECI08: Introduction to Networked Control Systems|2008 lecture page]]
* Additional links to external information

EECI09: Review of information theory and communications

2009-03-04T23:28:51Z

Vijay:

{{eeci-sp09 header|prev=Introduction to NCS|next=Jump linear Markov processes}}

{{righttoc}}
In this lecture, we will briefly review some concepts from information theory. While classical control design is a one-block design problem (design controller / estimator), networked control design is a two-block design problem (design encoder and decoder for every channel). Information theory provides sophisticated tools for considering two block design problems for communication. By adapting these tools for feedback control, we will derive some extensions of the classical Bode integral formula for arbitrary causal feedback, that may possibly include finite communication channels.

== Lecture Materials ==
* Lecture slides: {{eeci-sp09 pdf|Image:Lecture_info_theory.pdf|Title}}
* Links to anything else that is handed out in the lecture

== Further Reading ==
* [http://www.cds.caltech.edu/~murray/cdspanel Control in an Information Rich World], R. M. Murray (ed). SIAM, 2003. This book provides a high level description of some of the research challenges and opportunities in the field of control. The executive summary (Section 1) and the application sections on "Information and Networks" and "Robotics and Intelligent Machines" (Section 3.2 and 3.3) are particularly relevant.
* Second paper

== Additional Information ==
* [http://home.cwru.edu/ncs/ Networked Control Systems Repository] (M. Branicky and S. Phillipps)
* [[EECI08: Introduction to Networked Control Systems|2008 lecture page]]
* Additional links to external information

EECI09: Review of information theory and communications

2009-03-04T23:26:45Z

Vijay:

{{eeci-sp09 header|prev=Introduction to NCS|next=Jump linear Markov processes}}

{{righttoc}}
In this lecture, we will briefly review some concepts from information theory. While classical control design is a one-block design problem (design controller / estimator), networked control design is a two-block design problem (design encoder and decoder for every channel). Information theory provides sophisticated tools for considering two block design problems for communication. By adapting these tools for feedback control, we will derive some extensions of the classical Bode integral formula for arbitrary causal feedback, that may possibly include finite communication channels.

== Lecture Materials ==
* Lecture slides: {{eeci-sp09 pdf|Lecture_info_theory.pdf|Title}}
* Links to anything else that is handed out in the lecture

== Further Reading ==
* [http://www.cds.caltech.edu/~murray/cdspanel Control in an Information Rich World], R. M. Murray (ed). SIAM, 2003. This book provides a high level description of some of the research challenges and opportunities in the field of control. The executive summary (Section 1) and the application sections on "Information and Networks" and "Robotics and Intelligent Machines" (Section 3.2 and 3.3) are particularly relevant.
* Second paper

== Additional Information ==
* [http://home.cwru.edu/ncs/ Networked Control Systems Repository] (M. Branicky and S. Phillipps)
* [[EECI08: Introduction to Networked Control Systems|2008 lecture page]]
* Additional links to external information

EECI09: Review of information theory and communications

2009-03-04T23:25:48Z

Vijay:

{{eeci-sp09 header|prev=Introduction to NCS|next=Jump linear Markov processes}}

{{righttoc}}
In this lecture, we will briefly review some concepts from information theory. While classical control design is a one-block design problem (design controller / estimator), networked control design is a two-block design problem (design encoder and decoder for every channel). Information theory provides sophisticated tools for considering two block design problems for communication. By adapting these tools for feedback control, we will derive some extensions of the classical Bode integral formula for arbitrary causal feedback, that may possibly include finite communication channels.

== Lecture Materials ==
* Lecture slides: {{Lecture_info_theory.pdf}}
* Links to anything else that is handed out in the lecture

== Further Reading ==
* [http://www.cds.caltech.edu/~murray/cdspanel Control in an Information Rich World], R. M. Murray (ed). SIAM, 2003. This book provides a high level description of some of the research challenges and opportunities in the field of control. The executive summary (Section 1) and the application sections on "Information and Networks" and "Robotics and Intelligent Machines" (Section 3.2 and 3.3) are particularly relevant.
* Second paper

== Additional Information ==
* [http://home.cwru.edu/ncs/ Networked Control Systems Repository] (M. Branicky and S. Phillipps)
* [[EECI08: Introduction to Networked Control Systems|2008 lecture page]]
* Additional links to external information

File:Lecture info theory.pdf

2009-03-04T23:25:04Z

Vijay: Summary of the lecture on information theory.

Summary of the lecture on information theory.

EECI09: Review of information theory and communications

2009-03-04T23:23:23Z

Vijay:

{{eeci-sp09 header|prev=Introduction to NCS|next=Jump linear Markov processes}}

{{righttoc}}
In this lecture, we will briefly review some concepts from information theory. While classical control design is a one-block design problem (design controller / estimator), networked control design is a two-block design problem (design encoder and decoder for every channel). Information theory provides sophisticated tools for considering two block design problems for communication. By adapting these tools for feedback control, we will derive some extensions of the classical Bode integral formula for arbitrary causal feedback, that may possibly include finite communication channels.

== Lecture Materials ==
* Lecture slides: {{eeci-sp09 pdf|Ln_topic.pdf|Title}}
* Links to anything else that is handed out in the lecture

== Further Reading ==
* [http://www.cds.caltech.edu/~murray/cdspanel Control in an Information Rich World], R. M. Murray (ed). SIAM, 2003. This book provides a high level description of some of the research challenges and opportunities in the field of control. The executive summary (Section 1) and the application sections on "Information and Networks" and "Robotics and Intelligent Machines" (Section 3.2 and 3.3) are particularly relevant.
* Second paper

== Additional Information ==
* [http://home.cwru.edu/ncs/ Networked Control Systems Repository] (M. Branicky and S. Phillipps)
* [[EECI08: Introduction to Networked Control Systems|2008 lecture page]]
* Additional links to external information