Optimal Impulsive Control explores the class of impulsive dynamic optimization
problems-problems that stem from the fact that many conventional optimal control problems do
not have a solution in the classical setting-which is highly relevant with regard to
engineering applications. The absence of a classical solution naturally invokes the so-called
extension or relaxation of a problem and leads to the notion of generalized solution which
encompasses the notions of generalized control and trajectory in this book several extensions
of optimal control problems are considered within the framework of optimal impulsive control
theory. In this framework the feasible arcs are permitted to have jumps while the
conventional absolutely continuous trajectories may fail to exist. The authors draw together
various types of their own results centered on the necessary conditions of optimality in the
form of Pontryagin's maximum principle and the existence theorems which shape a substantial
body of optimal impulsive control theory. At the same time they present optimal impulsive
control theory in a unified framework introducing the different paradigmatic problems in
increasing order of complexity. The rationale underlying the book involves addressing
extensions increasing in complexity from the simplest case provided by linear control systems
and ending with the most general case of a totally nonlinear differential control system with
state constraints.The mathematical models presented in Optimal Impulsive Control being
encountered in various engineering applications this book will be of interest to both academic
researchers and practising engineers.
