Control Theory and Optimization I.pdf

Control Theory and Optimization I

M-I Zelikin

This book is devoted to geometric methods in the theory of differential equations with quadratic right-hand sides (Riccati-type equations), which are closely related to the calculus of variations and optimal control theory. Connections of the calculus of variations and the Riccati equation with the geometry of Lagrange-Grassmann manifolds and classical Cartan-Siegel homogeneity domains in a space of several complex variables are considered. In the study of the minimization problem for a multiple integral, a quadratic partial differential equation that is an analogue of the Riccati equation in the calculus of variations is studied. This book is based on lectures given by the author over a period of several years in the Department of Mechanics and Mathematics of Moscow State University. The book is addressed to, under-graduate and graduate students, scientific researchers and all specialists interested in the problems of geometry, the calculus of variations, and differential equations.

Control Theory and Optimization I Homogeneous Spaces and the Riccati Equation in the Calculus of Variations. Authors: Zelikin, M.I. Free Preview Control Theory and Optimization - Springer

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9783540667414 ISBN
Control Theory and Optimization I.pdf

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Control methods, however, are used much less in optimization, despite the facts that control is dedicated to the analysis and design of dynamical systems and that optimization algorithms are dynamical systems. Hence, our research idea is to analyze and design optimization algorithms employing methods from systems and control theory. In particular, we study continuous-time (models of Control Theory and Optimization I: Homogeneous …

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Optimal control theory is a branch of applied mathematics that deals with finding a control law for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in both science and engineering. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the Control Theory and Optimization I: Homogeneous …