This monograph presents theoretical methods involving the HamiltonJacobiBellman formalism in conjunction with set-valued techniques of nonlinear analysis to solve significant problems in dynamics and control. The emphasis is on issues of reachability, feedback control synthesis under complex state constraints, hard or double bounds on controls, and performance in finite time. Guaranteed state estimation, output feedback control, and hybrid dynamics are also discussed. Although the focus is on systems with linear structure, the authors indicate how to apply each approach to nonlinear and nonconvex systems. The main theoretical results lead to computational schemes based on extensions of ellipsoidal calculus that provide complete solutions to the problems. These computational schemes in turn yield software tools that can be applied effectively to high-dimensional systems. Ellipsoidal Techniques for Problems of Dynamics and Control: Theory and Computation will interest graduate and senior undergraduate students, as well as researchers and practitioners interested in control theory, its applications, and its computational realizations.

Addresses significant control-theoretical problems, with emphasis on feedback control Indicates the appropriate mathematical theory for these problems in terms of set-valued functions (trajectory tubes) Discusses computational schemes that provide complete solutions to the problems and yield software tools that are applicable to systems of high dimension

Autorentext

Alexander B. Kurzhanski was born in 1939. He graduated with honours in electrical engineering at the Technical University of Ural, Sverdlovsk, USSR (1962). He did his graduate studies in mathematics and mechanics at classical University of Ural (1962-1965), having received his PhD-equivalent degree in 1965 and habilitation doctorate in 1971. He became full professor in 1974. In 1967-1984 he was at Institute of Mathematics and Mechanics, Ural Branch, Academy of Sciences of USSR as a Senior Researcher, Head of Department and finally Director. He was Chairman of Systems and Decision Sciences Program, Deputy Director at IIASA (the International Institute for Applied Systems Analysis), Laxenburg, Austria (1984-1992). He is Head of Department of Systems Analysis, Lomonosov Moscow State University (MSU), Faculty of Computational Mathematics and Cybernetics (1992-present) and also a distinguished professor of MSU (1999). He was elected associate member of the Russian (former Soviet)Academy of Sciences in 1981 and Full Member in 1990. He is Chairman of Russian National Committee on Automatic Control (the IFAC NMO, 1998-present). He also holds a visiting research position at UC-Berkeley, USA. His research interests and achievements are in the field of estimation and control under uncertainty and incomplete (realistic) information, feedback control of complex systems, inverse problems of mathematical physics, computational methods in dynamics and control and mathematical modeling for applied systems analysis. Alexander N. Daryin was born in 1979. He graduated with honours from the Faculty of Computational Mathematics and Cybernetics at Lomonosov Moscow State University in 2001. He did his graduate studies in mathematics (pure and applied) at same faculty (2001-2004). He received PhD-equivalent degree in 2004. He worked as an associate professor at same faculty, Department of Systems Analysis (2004-2014). He currently works at Google Research in Zurich. He authored or coauthored more than 25 research journal and conference papers. His interests lie in the theory and applications of feedback control for complex systems, including control under uncertainty, impulse control and computational methods.

Inhalt
Preface.- 1. Linear Control Systems.- 2. The Dynamic Programming Approach.- 3. Ellipsoidal Techniques: Reachability and Control Synthesis.- 4. Solution Examples on Ellipsoidal Methods: Computation in High Dimensions.- 5. The Comparison Principle: Nonlinearity and Nonconvexity.- 6. Impulse Control and Double Constraints.- 7. Dynamics and Control under State Constraints.- 8. Trajectory Tubes: State-Constrained Feedback Control.- 9. Guaranteed State Estimation.- 10. Uncertain Systems: Output Feedback Control.- 11. Verification: Hybrid Systems.