The Mathematics of Group (Multiagent) Control

This presentation deals with a systematic mathematical treatment of how to solve the problem of feedback and feed-forward goal-oriented control under obstacle avoidance for a team of controlled motions. This includes related problems of feedback team control and motion planning under obstacles and collision avoidance. It covers topics from basic theoretical problems to recommended computational methods.

The novelty of the approach lies in treating controlled team motions as lying in a reconfigurable virtual container (shell) that moves towards the target set avoiding both external obstacles (static or dynamic) and internal collisions within the container. The suggested solution schemes rely on combining variational methods of nonlinear analysis and analytical mechanics, including Hamiltonian techniques, with those of set-valued calculus and minimax approaches, as well as on progressive modification of earlier developed computational tools.

Prof. Kurzhanski received his "candidat" (PhD equivalent) and his habilitation "doctorate" from the University of Ural, where he became full professor. In 1967-1984 he worked at the Institute of Mathematics and Mechanics of the Ural Branch of the Academy of Sciences of USSR — as Senior Researcher, Head of Department and Director. Within 1984-1992 Professor Kurzhanski was the Chairman of the Systems and Decision Sciences Program and since 1987 also Deputy Director of IIASA (the International Institute of Applied Systems Analysis) , located in Laxenburg, Austria. From 1992 till present — organizer and head of Department of Systems Analysis at the Moscow State (Lomonosov) University (MSU), Faculty of Computational Mathematics and Cybernetics, Distinguished Professor of MSU(1999). Since 1998 also Visiting Research Scholar at the University of California at Berkeley. Kurzhanski was elected Associate Member of the Russian (former Soviet) Academy of Sciences in 1981 and Full Member in 1990.
His research interests and achievements are in the field of estimation and control under incomplete (realistic) information, control of complex systems, new dynamic programming techniques, distributed and multi-agent control, inverse problems of mathematical physics, numerical methods and set-valued techniques in dynamics, control and mathematical modeling for applied systems analysis.