Mikhail Il'ich Zelikin (Russian: Михаил Ильич Зеликин; born 11 February 1936) is a Russian mathematician, known for his work in differential equations (particularly Riccati equations), optimal control theory, differential games, the theory of fields of extremals for multiple integrals, and the geometry of Grassmannians.
Biography
Zelikin was born in Moscow in 1936. He entered Moscow State University (Faculty of Mechanics and Mathematics) in 1953 and graduated in 1958. He subsequently worked at Moscow State University and the Steklov Institute of Mathematics. He earned his Ph.D. under the supervision of the prominent mathematician Lev S. Pontryagin.
He was awarded the Chebyshev Award in 1987 and the Lyapunov Award in 2010. In 2011, he was elected a corresponding member of the Russian Academy of Sciences. He has served as deputy head of the Department of General Problems of Control at the Faculty of Mechanics and Mathematics of Moscow State University since 1992.
Research Contributions
Zelikin's mathematical work spans several areas:
- Differential equations and Riccati equations: He has made contributions to the theory of Riccati equations and their applications in calculus of variations and control theory.
- Optimal control theory: He is known for his work on chattering control (full- and partial-mode sliding regimes), including the monograph Theory of Chattering Control co-authored with V. F. Borisov.
- Differential games: He has worked on pursuit-evasion problems, including the "Princess and Monster" game.
- Homogeneous spaces and the Riccati equation: His monograph Control Theory and Optimization I (Springer, 2000) treats homogeneous spaces and the Riccati equation in the calculus of variations.
Other Activities
Beyond mathematics, Zelikin has been active in ecological advocacy, notably criticizing the Soviet-era Northern river reversal project. He published a book of memoirs titled History of Evergreen Life (Russian: История вечнозелёной жизни, Moscow, 2001) on this subject. He also proposed an explanation of ball lightning based on a hypothesis of plasma superconductivity.
Selected Monographs
- Zelikin, M. I.; Borisov, V. F. Theory of Chattering Control. With Applications to Astronautics, Robotics, Economics, and Engineering. Systems & Control: Foundations & Applications. Birkhäuser Boston, 1994. ISBN 0-8176-3618-8.
- Zelikin, M. I. Control Theory and Optimization I: Homogeneous Spaces and the Riccati Equation in the Calculus of Variations. Encyclopaedia of Mathematical Sciences, 86. Springer-Verlag, Berlin, 2000. ISBN 3-540-66741-5.
- Zelikin, M. I. Optimal Control and Variational Calculus. Editorial URSS, Moscow, 2004 (in Russian); 2010 (in Spanish).
