Control Theory from the Geometric Viewpoint

This book presents some facts and methods of Mathematical Control Theory treated from the geometric viewpoint. It is devoted to finite-dimensional deterministic control systems governed by smooth ordinary differential equations. The problems of controllability, state and feedback equivalence, and optimal control are studied. Some of the topics treated by the authors are covered in monographic or textbook literature for the first time while others are presented in a more general and flexible setting than elsewhere. Although being fundamentally written for mathematicians, the authors make an attempt to reach both the practitioner and the theoretician by blending the theory with applications. They maintain a good balance between the mathematical integrity of the text and the conceptual simplicity that might be required by engineers. It can be used as a text for graduate courses and will become most valuable as a reference work for graduate students and researchers.

Author Biography

Andrei A. Agrachev Born in Moscow, Russia. Graduated: Moscow State Univ., Applied Math. Dept., 1974. Ph.D.: Moscow State Univ., 1977. Doctor of Sciences (habilitation): Steklov Inst. for Mathematics, Moscow, 1989. Invited speaker at the International Congress of Mathematicians ICM-94 in Zurich. Over 90 research papers on Control Theory, Optimization, Geometry (featured review of Amer. Math. Soc., 2002). Professional Activity: Inst. for Scientific Information, Russian Academy of Sciences, Moscow, 1977-1992; Moscow State Univ., 1989-1997; Steklov Inst. for Mathematics, Moscow, 1992-present; International School for Advanced Studies (SISSA-ISAS), Trieste, 2000-present. Current positions: Professor of SISSA-ISAS, Trieste, Italy and Leading Researcher of the Steklov Ins. for Math., Moscow, Russia Yuri L. Sachkov Born in Dniepropetrovsk, Ukraine. Graduated: Moscow State Univ., Math. Dept., 1986. Ph.D.: Moscow State Univ., 1992. Over 20 research papers on Control Theory. Professional Activity: Program Systems Institute, Russian Academy of Sciences, Pereslavl-Zalessky, 1989-present; University of Pereslavl, 1993-present. Steklov Inst. for Mathematics, Moscow, 1998-1999; International School for Advanced Studies (SISSA-ISAS), Trieste, 1999-2001. Current positions: Senior researcher of Program Systems Institute, Pereslavl-Zalessky, Russia; Associate professor of University of Pereslavl, Russia.