COLLABORATION IN BASIC SCIENCE AND ENGINEERING (COBASE)

This U.S.-Bulgarian COBASE project on the theory and applications of nonsmooth dynamical systems was a true team effort, involving three Americans—Michael Malisoff, Peter Wolenski, and graduate student Vinicio Rios of Louisiana State University—and two Bulgarians, Tzanko Donchev of the University of Architecture and Civil Engineering in Sofia and Mikhail Krastanov of the Bulgarian Academy of Sciences Institute of Mathematics and Informatics. This multifaceted research effort began with a one-month visit by Donchev to Baton Rouge in March-April 2003, when he, Wolenski, and Rios focused on one-sided Lipschitz (OSL) maps. The three mathematicians have already produced two joint papers and continue their work on difficult and important problems regarding optimal control with OSL data. To some extent, these problems are included in a pending NSF proposal submitted by Wolenski.

The second visit on this project took place when Krastanov traveled to Louisiana for a month during July-August 2003. During his stay, he worked with Malisoff and Wolenski on the strong invariance of non-Lipschitz multifunctions. Malisoff reports that “new results were obtained in this portion of the project that substantially advanced the current state of knowledge of sufficient conditions for strong invariance relative to closed state constraint sets.” He and his partners have submitted two joint papers on this line of research and plan to apply to NSF for continued funding to support their collaboration.

All in all, Malisoff notes that “the project provided valuable opportunities for the grantees to synergize their knowledge of control theory and optimization with the nonsmooth analytic techniques that have been developed by Donchev and Krastanov. It also gave Wolenski’s Rios the chance to interact with international scholars, and this significantly enhanced his graduate training in applied mathematics and nonsmooth analysis.”

[from left to right, Vladimir Veliov, Pando Georgiev, Elza Farkhi, Vera Zeidan, Asen Dontchev, and Tzanko Donchev at the Louisiana Conference on Mathematical Control Theory, April 2003]