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	<id>https://murray.cds.caltech.edu/index.php?action=history&amp;feed=atom&amp;title=EECI09%3A_Information_patterns</id>
	<title>EECI09: Information patterns - Revision history</title>
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	<updated>2026-09-08T08:10:50Z</updated>
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	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=EECI09:_Information_patterns&amp;diff=9173&amp;oldid=prev</id>
		<title>Vijay at 20:22, 10 March 2009</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=EECI09:_Information_patterns&amp;diff=9173&amp;oldid=prev"/>
		<updated>2009-03-10T20:22:10Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 20:22, 10 March 2009&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l10&quot;&gt;Line 10:&lt;/td&gt;
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&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Further Reading ==&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Further Reading ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* &amp;lt;p&amp;gt;&amp;quot;Separation of Estimation and Control for Discrete Time Systems&amp;quot;], 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.&amp;lt;/p&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* &amp;lt;p&amp;gt;&amp;quot;Separation of Estimation and Control for Discrete Time Systems&amp;quot;], 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.&amp;lt;/p&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* &amp;lt;p&amp;gt;&quot;A Counterexample in Stochastic Optimum Control,&quot; H. S. Witsenhausen, SIAM Journal of&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* &amp;lt;p&amp;gt;&quot;A Counterexample in Stochastic Optimum Control,&quot; 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.&amp;lt;/p&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;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.&amp;lt;/p&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* &amp;lt;p&amp;gt;&amp;quot;Team Decision Theory and Information Structures in Optimal Control Problems - Part I,&amp;quot; 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. &amp;lt;/p&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* &amp;lt;p&amp;gt;&amp;quot;Team Decision Theory and Information Structures in Optimal Control Problems - Part I,&amp;quot; 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. &amp;lt;/p&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;

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		<author><name>Vijay</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=EECI09:_Information_patterns&amp;diff=9172&amp;oldid=prev</id>
		<title>Vijay at 20:21, 10 March 2009</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=EECI09:_Information_patterns&amp;diff=9172&amp;oldid=prev"/>
		<updated>2009-03-10T20:21:47Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 20:21, 10 March 2009&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l2&quot;&gt;Line 2:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 2:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{righttoc}}&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;{{righttoc}}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;One paragraph overview &lt;/del&gt;of the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;lecture&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;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 &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;information patterns, and identify some patterns that permit simple solutions to &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;optimal control problem.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==  Lecture Materials ==&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==  Lecture Materials ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* Lecture slides: &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{eeci-sp09 pdf|Ln_topic&lt;/del&gt;.pdf|&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Title}}&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* Lecture slides: &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Media:lecture_info_patterns&lt;/ins&gt;.pdf|&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Lecture Summary]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;* Links to anything else that is handed out in the lecture&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Further Reading ==&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Further Reading ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* &amp;lt;p&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[http://www&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;cds&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;caltech&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;edu/~murray/cdspanel Control in an Information Rich World]&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;R&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;M&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Murray (ed)&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; SIAM, 2003&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; &lt;/del&gt;This &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;book provides a high level description &lt;/del&gt;of &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;some of the research challenges &lt;/del&gt;and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;opportunities in &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;field of &lt;/del&gt;control. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; The executive summary (Section 1) and the application sections on &lt;/del&gt;&quot;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Information and Networks&lt;/del&gt;&quot; &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;and &quot;Robotics and Intelligent Machines&quot; (Section 3&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2 &lt;/del&gt;and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3.3) are particularly relevant&lt;/del&gt;.&amp;lt;/p&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* &amp;lt;p&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&quot;Separation of Estimation and Control for Discrete Time Systems&quot;], H&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;S&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Witsenhausen, Proceedings of the IEEE, vol&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;59&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;no&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;11, pp&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;1557-1566, Nov&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;1971&lt;/ins&gt;. This &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;paper covers the concept &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;information patterns &lt;/ins&gt;and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;discusses why non-classical information patterns may turn &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;optimal &lt;/ins&gt;control &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;problem difficult to solve&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;/p&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* &amp;lt;p&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Second &lt;/del&gt;paper&amp;lt;/p&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;* &amp;lt;p&amp;gt;&lt;/ins&gt;&quot;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;A Counterexample in Stochastic Optimum Control,&lt;/ins&gt;&quot; &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;H. S. Witsenhausen, SIAM Journal of&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Control, vol. 6, no. 1, pp. 131-147, 1968&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;This paper introduced the counterexample, &lt;/ins&gt;and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;proved that a non-linear controller will perform better than the optimal affine controller&lt;/ins&gt;.&amp;lt;/p&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* &amp;lt;p&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&quot;Team Decision Theory and Information Structures in Optimal Control Problems - Part I,&quot; Y. C. Ho and K. C. Chu, IEEE Transactions on Automatic Control, vol. AC-17, no. 1, pp. 15-22, Jan. 1972. This &lt;/ins&gt;paper &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;considers the partially nested information structure. &lt;/ins&gt;&amp;lt;/p&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==  Additional Information ==  &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==  Additional Information ==  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;

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		<author><name>Vijay</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=EECI09:_Information_patterns&amp;diff=9144&amp;oldid=prev</id>
		<title>Murray at 22:36, 7 March 2009</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=EECI09:_Information_patterns&amp;diff=9144&amp;oldid=prev"/>
		<updated>2009-03-07T22:36:04Z</updated>

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		<author><name>Murray</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=EECI09:_Information_patterns&amp;diff=9143&amp;oldid=prev</id>
		<title>Murray at 22:35, 7 March 2009</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=EECI09:_Information_patterns&amp;diff=9143&amp;oldid=prev"/>
		<updated>2009-03-07T22:35:20Z</updated>

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		<author><name>Murray</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=EECI09:_Information_patterns&amp;diff=9068&amp;oldid=prev</id>
		<title>Murray at 21:04, 1 March 2009</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=EECI09:_Information_patterns&amp;diff=9068&amp;oldid=prev"/>
		<updated>2009-03-01T21:04:11Z</updated>

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		<author><name>Murray</name></author>
	</entry>
	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=EECI09:_Information_patterns&amp;diff=9067&amp;oldid=prev</id>
		<title>Murray at 21:04, 1 March 2009</title>
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		<updated>2009-03-01T21:04:03Z</updated>

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		<author><name>Murray</name></author>
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	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=EECI09:_Information_patterns&amp;diff=9042&amp;oldid=prev</id>
		<title>Murray at 20:53, 1 March 2009</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=EECI09:_Information_patterns&amp;diff=9042&amp;oldid=prev"/>
		<updated>2009-03-01T20:53:45Z</updated>

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&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;{{eeci-sp09 header|prev=Main Page|next=Main Page}}&lt;br /&gt;
&lt;br /&gt;
{{righttoc}}&lt;br /&gt;
One paragraph overview of the lecture&lt;br /&gt;
&lt;br /&gt;
==  Lecture Materials ==&lt;br /&gt;
* Lecture slides: {{eeci-sp09 pdf|Ln_topic.pdf|Title}}&lt;br /&gt;
* Links to anything else that is handed out in the lecture&lt;br /&gt;
&lt;br /&gt;
== Further Reading ==&lt;br /&gt;
* &amp;lt;p&amp;gt;[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 &amp;quot;Information and Networks&amp;quot; and &amp;quot;Robotics and Intelligent Machines&amp;quot; (Section 3.2 and 3.3) are particularly relevant.&amp;lt;/p&amp;gt;&lt;br /&gt;
* &amp;lt;p&amp;gt;Second paper&amp;lt;/p&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==  Additional Information == &lt;br /&gt;
* [http://home.cwru.edu/ncs/ Networked Control Systems Repository] (M. Branicky and S. Phillipps)&lt;br /&gt;
* [[EECI08: Introduction to Networked Control Systems|2008 lecture page]]&lt;br /&gt;
* Additional links to external information&lt;/div&gt;</summary>
		<author><name>Murray</name></author>
	</entry>
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