<HTML><BODY style="word-wrap: break-word; -khtml-nbsp-mode: space; -khtml-line-break: after-white-space; "><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Dear colleague,</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><BR class="khtml-block-placeholder"></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">A number of one-week courses in control theory are being offered in February-March-April by the HYCON European Embedded Control Institute (near Paris). These are described at the following site:</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><BR class="khtml-block-placeholder"></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN><A href="http://www.ist-hycon.org/index.php?p=EECI">http://www.ist-hycon.org/index.php?p=EECI</A></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><BR class="khtml-block-placeholder"></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">They may interest thesis or postdoctoral/young faculty level people you know...please pass on this message to anyone who might wish to attend.</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><BR class="khtml-block-placeholder"></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">As for the course I am giving, it's entitled</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><BR class="khtml-block-placeholder"></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN>"Optimality, Stabilization, and Feedback in Nonlinear Control",</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><BR class="khtml-block-placeholder"></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">and takes place from April 2 to 6. A brief course description appears below.</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><BR class="khtml-block-placeholder"></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">With best regards,</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><BR class="khtml-block-placeholder"></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Francis Clarke</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><BR class="khtml-block-placeholder"></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">___________</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 12px/normal Helvetica; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 12px/normal Helvetica; min-height: 14px; ">"Optimality, Stabilization, and Feedback in Nonlinear Control" April 2-6</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Francis Clarke, Institut universitaire de France et Université de Lyon 1 <<FONT class="Apple-style-span" color="#1919FF"><SPAN class="Apple-style-span" style="text-decoration: underline;"><A href="mailto:clarke@math.univ-lyon1.fr">clarke@math.univ-lyon1.fr</A></SPAN></FONT>></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 12px/normal Helvetica; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">This course presents some modern tools for treating truly nonlinear control problems, including nonsmooth calculus and discontinuous feedback. The need for such tools will be motivated, and applications made to central issues in optimal and stabilizing control. Topics include:</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 12px/normal Helvetica; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN>1. Dynamic optimization: from the calculus of variations to the Pontryagin Maximum Principle</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 12px/normal Helvetica; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN>2. Some constructs of nonsmooth analysis, and why we need them</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 12px/normal Helvetica; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN>3. Lyapunov functions, classical to modern</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 12px/normal Helvetica; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN>4. Discontinuous feedback synthesis for stabilization</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 12px/normal Helvetica; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN>5. Sliding modes and hybrid systems: a new approach</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 12px/normal Helvetica; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">References:</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 12px/normal Helvetica; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">R1. <SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN>"<FONT class="Apple-style-span" face="Geneva">Nonsmooth Analysis and Control Theory", by F. Clarke, Yu. Ledyaev, R. Stern and P. Wolenski,</FONT><FONT class="Apple-style-span" face="Geneva"> </FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN><FONT class="Apple-style-span" face="Geneva">Graduate Texts in Mathematics Vol. 178, Springer-Verlag, New York, 1998.</FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 12px/normal Geneva; min-height: 16px; "><BR style=""></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" face="Geneva">R2. </FONT><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN><FONT class="Apple-style-span" face="Geneva">F. Clarke, "Lyapunov functions and feedback in nonlinear control," in "Optimal Control, Stabilization and </FONT><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN><FONT class="Apple-style-span" face="Geneva">Nonsmooth Analysis", M.S. de Queiroz, M. Malisoff, P. Wolenski (Eds.), Lecture Notes in Control and Information </FONT><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN><FONT class="Apple-style-span" face="Geneva">Sciences Vol. 301, pp. 267-282, Springer-Verlag, 2004.</FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 12px/normal Geneva; min-height: 16px; "><BR style=""></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" face="Geneva">R3. </FONT><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN><FONT class="Apple-style-span" face="Geneva">F. Clarke, "Necessary Conditions in Dynamic Optimization", Memoirs of the Amer. Math. Soc., No. 816,</FONT><FONT class="Apple-style-span" face="Geneva"> </FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN><FONT class="Apple-style-span" face="Geneva">vol. 173 (2005) (113 pages).</FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 12px/normal Geneva; min-height: 16px; "><BR style=""></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" face="Geneva">R4. </FONT><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN><FONT class="Apple-style-span" face="Geneva">F. Clarke, "Nonsmooth analysis in control theory: a survey," European J. of Control 7 (2001) 63-78.</FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 12px/normal Geneva; min-height: 16px; "><BR style=""></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" face="Geneva">R5. </FONT><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN><FONT class="Apple-style-span" face="Geneva">F. Clarke, Yu. Ledyaev, L. Rifford and R. Stern, "Feedback stabilization and Lyapunov functions,"</FONT><FONT class="Apple-style-span" face="Geneva"> </FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><SPAN class="Apple-tab-span" style="white-space:pre"> </SPAN><FONT class="Apple-style-span" face="Geneva">SIAM J. Control and Optim. 39 (2000) 25-48.</FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 12px/normal Geneva; min-height: 16px; "><BR style=""></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Some of these references are available on Francis Clarke's website : <FONT class="Apple-style-span" color="#1919FF"><SPAN class="Apple-style-span" style="text-decoration: underline;"><A href="http://igd.univ-lyon1.fr/~clarke/Clarke-english.html">http://igd.univ-lyon1.fr/~clarke/Clarke-english.html</A></SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><BR class="khtml-block-placeholder"></DIV></BODY></HTML>