Osmolovskii N.P., Maurer H. Applications to Regular and Bang-Bang Control: Second-Order Necessary and Sufficient Optimality Conditions in Calculus of Variations and Optimal Control

Philadelphia: SIAM, 2012. — 389 p.This book is devoted to the theory and applications of second-order necessary and sufficient optimality conditions in the calculus of variations and optimal control. The authors develop theory for a control problem with ordinary differential equations subject to boundary conditions of equality and inequality type and for mixed state-control constraints of equality type. The book is distinctive in that necessary and sufficient conditions are given in the form of no-gap conditions; the theory covers broken extremals where the control has finitely many points of discontinuity; and a number of numerical examples in various application areas are fully solved.
Audience: This book is suitable for researchers in calculus of variations and optimal control and researchers and engineers in optimal control applications in mechanics; mechatronics; physics; economics; and chemical, electrical, and biological engineering.List of Figures;
Notation;
Preface;
Introduction;Second-Order Optimality Conditions for Broken Extremals in the Calculus of Variations;Abstract Scheme for Obtaining Higher-Order Conditions in Smooth Extremal Problems with Constraints;
Quadratic Conditions in the General Problem of the Calculus of Variations;
Quadratic Conditions for Optimal Control Problems with Mixed Control-State Constraints;
Jacobi-Type Conditions and Riccati Equation for Broken Extremals;Second-Order Optimality Conditions in Optimal Bang-Bang Control Problems;Second-Order Optimality Conditions in Optimal Control Problems Linear in a Part of Controls;
Second-Order Optimality Conditions for Bang-Bang Control;
Bang-Bang Control Problem and Its Induced Optimization Problem;
Numerical Methods for Solving the Induced Optimization Problem and Applications;Bibliography;