Control Theory from the Geometric Viewpoint

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.

Aus den Rezensionen: "Der Band ist aus Graduiertenkursen an der International School for Advanced Studies in Triest entstanden ... Mathematisch werden gute Kenntnisse der Analysis, der linearen Algebra und der Funktionalanalysis vorausgesetzt. ... Bekannte und neue Beispiele ... illustrieren hier die Fulle an Aussagen in sehr anschaulicher Weise. Insgesamt ist so ein Band entstanden, der Mathematikern und mathematisch interessierten Anwendern wertvolle Anregungen bei der Auseinandersetzung mit gesteuerten bzw. geregelten nichtlinearen Systemen und deren Optimierung bietet." (l. Troch, in: IMN - Internationale Mathematische Nachrichten, 2006, Issue 202, S. 44 f.)

• 1 Vector Fields and Control Systems on Smooth Manifolds.- 2 Elements of Chronological Calculus.- 3 Linear Systems.- 4 State Linearizability of Nonlinear Systems.- 5 The Orbit Theorem and its Applications.- 6 Rotations of the Rigid Body.- 7 Control of Configurations.- 8 Attainable Sets.- 9 Feedback and State Equivalence of Control Systems.- 10 Optimal Control Problem.- 11 Elements of Exterior Calculus and Symplectic Geometry.- 12 Pontryagin Maximum Principle.- 13 Examples of Optimal Control Problems.- 14 Hamiltonian Systems with Convex Hamiltonians.- 15 Linear Time-Optimal Problem.- 16 Linear-Quadratic Problem.- 17 Sufficient Optimality Conditions, Hamilton-Jacobi Equation, and Dynamic Programming.- 18 Hamiltonian Systems for Geometric Optimal Control Problems.- 19 Examples of Optimal Control Problems on Compact Lie Groups.- 20 Second Order Optimality Conditions.- 21 Jacobi Equation.- 22 Reduction.- 23 Curvature.- 24 Rolling Bodies.- A Appendix.- A.2 Remainder Term of the Chronological Exponential.- References.- List of Figures.