Springer Dynamic Programming for Impulse Feedback and Fast Controls: The Linear Systems Case: 468 (Lecture Notes in Control and Information Sciences, 468)

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 uncertainty in 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. Review “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) From the Back Cover 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 uncertainty in 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. About the Author 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 (199