Dynamic Programming for Impulse Feedback and Fast Controls

1. Front Matter

   Pages i-xiii

   PDF

2. Introduction: Why Impulses?

   • Alexander B. Kurzhanski, Alexander N. Daryin

   Pages 1-12

3. Ordinary Impulses

   1. Front Matter

      Pages 13-13

      PDF

   2. Open-Loop Impulse Control

      • Alexander B. Kurzhanski, Alexander N. Daryin

      Pages 15-41

   3. Closed-Loop Impulse Control

      • Alexander B. Kurzhanski, Alexander N. Daryin

      Pages 43-75

   4. Impulse Control Under Uncertainty

      • Alexander B. Kurzhanski, Alexander N. Daryin

      Pages 77-102

   5. State-Constrained Impulse Control

      • Alexander B. Kurzhanski, Alexander N. Daryin

      Pages 103-136

   6. State Estimation Under Ordinary Impulsive Inputs

      • Alexander B. Kurzhanski, Alexander N. Daryin

      Pages 137-160

4. Impulses of Higher Order. Realizability and Fast Control

   1. Front Matter

      Pages 161-161

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   2. The Open-Loop and Closed-Loop Impulse Controls

      • Alexander B. Kurzhanski, Alexander N. Daryin

      Pages 163-177

   3. State-Constrained Control Under Higher Impulses

      • Alexander B. Kurzhanski, Alexander N. Daryin

      Pages 179-192

   4. State Estimation and State Constrained Control

      • Alexander B. Kurzhanski, Alexander N. Daryin

      Pages 193-209

   5. Generalized Duality Theory. The Increasing and Decreasing Lagrangian Scales

      • Alexander B. Kurzhanski, Alexander N. Daryin

      Pages 211-231

   6. Realistic Controls

      • Alexander B. Kurzhanski, Alexander N. Daryin

      Pages 233-243

   7. Closed-Loop Fast Controls

      • Alexander B. Kurzhanski, Alexander N. Daryin

      Pages 245-263

5. Back Matter

   Pages 265-275

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Dynamic Programming for Impulse Feedback and Fast Controls offers a description of feedback control in the class of impulsive inputs. This book deals with the problem of closed-loop impulse control based on generalization of dynamic programming techniques in the form of variational inequalities of the Hamilton–Jacobi–Bellman type. It provides exercises and examples in relation to software, such as techniques for regularization of ill-posed problems. It also gives an introduction to applications such as hybrid dynamics, control in arbitrary small time, and discontinuous trajectories.

This book walks the readers through:

• the design and description of feedback solutions for impulse controls;
  
• the explanation of impulses of higher order that are derivatives of delta functions;
  
• the description of their physically realizable approximations - the fast controls and their approximations;
  
• the treatment of uncertaintyin impulse control and the applications of impulse feedback.
  

Of interest to both academics and graduate students in the field of control theory and applications, the book also protects users from common errors , such as inappropriate solution attempts, by indicating Hamiltonian techniques for hybrid systems with resets.

• Impulse Control
• Dynamic Programming
• Generalized Functions
• Fast Feedback Control
• Hybrid Systems

“This is an advanced monograph on impulse control and optimal impulse control theory of linear systems, with a special emphasis on feedback control in the class of impulsive inputs. The book is intended for both academics and graduate students in the field of control theory and applications.” (Monica Motta, Mathematical Reviews, October, 2019)

“I would like to recommend it to students and researchers interested in impulsive models.” (Jin Liang, zbMATH 1425.93004, 2019)

• Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow, Russia

  Alexander B. Kurzhanski

• Google Research, Zürich, Switzerland

  Alexander N. Daryin

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.

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