Dynamic Programming for Impulse Feedback and Fast Controls: The Linear Systems Case

Description

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. Front Matter ....Pages i-xiii Introduction: Why Impulses? (Alexander B. Kurzhanski, Alexander N. Daryin)....Pages 1-12 Front Matter ....Pages 13-13 Open-Loop Impulse Control (Alexander B. Kurzhanski, Alexander N. Daryin)....Pages 15-41 Closed-Loop Impulse Control (Alexander B. Kurzhanski, Alexander N. Daryin)....Pages 43-75 Impulse Control Under Uncertainty (Alexander B. Kurzhanski, Alexander N. Daryin)....Pages 77-102 State-Constrained Impulse Control (Alexander B. Kurzhanski, Alexander N. Daryin)....Pages 103-136 State Estimation Under Ordinary Impulsive Inputs (Alexander B. Kurzhanski, Alexander N. Daryin)....Pages 137-160 Front Matter ....Pages 161-161 The Open-Loop and Closed-Loop Impulse Controls (Alexander B. Kurzhanski, Alexander N. Daryin)....Pages 163-177 State-Constrained Control Under Higher Impulses (Alexander B. Kurzhanski, Alexander N. Daryin)....Pages 179-192 State Estimation and State Constrained Control (Alexander B. Kurzhanski, Alexander N. Daryin)....Pages 193-209 Generalized Duality Theory. The Increasing and Decreasing Lagrangian Scales (Alexander B. Kurzhanski, Alexander N. Daryin)....Pages 211-231 Realistic Controls (Alexander B. Kurzhanski, Alexander N. Daryin)....Pages 233-243 Closed-Loop Fast Controls (Alexander B. Kurzhanski, Alexander N. Daryin)....Pages 245-263 Back Matter ....Pages 265-275