Applications to Regular and Bang-Bang Control: Second-Order Necessary and Sufficient Optimality Conditions in Calculus of Variations and Optimal Control (Advances in Design and Control)

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. Contents: List of Figures; Notation; Preface; Introduction; Part I: Second-Order Optimality Conditions for Broken Extremals in the Calculus of Variations; Chapter 1: Abstract Scheme for Obtaining Higher-Order Conditions in Smooth Extremal Problems with Constraints; Chapter 2: Quadratic Conditions in the General Problem of the Calculus of Variations; Chapter 3: Quadratic Conditions for Optimal Control Problems with Mixed Control-State Constraints; Chapter 4: Jacobi-Type Conditions and Riccati Equation for Broken Extremals; Part II: Second-Order Optimality Conditions in Optimal Bang-Bang Control Problems; Chapter 5: Second-Order Optimality Conditions in Optimal Control Problems Linear in a Part of Controls; Chapter 6: Second-Order Optimality Conditions for Bang-Bang Control; Chapter 7: Bang-Bang Control Problem and Its Induced Optimization Problem; Chapter 8: Numerical Methods for Solving the Induced Optimization Problem and Applications; Bibliography; Index Front Matter 1 Introduction 16 Chapter 1: Abstract Scheme for Obtaining Higher-Order Conditions in Smooth Extremal Problems with Constraints 22 Chapter 2: Quadratic Conditions in the General Problem of the Calculus of Variations 39 Chapter 3: Quadratic Conditions for Optimal Control Problems with Mixed Control-State Constraints 139 Chapter 4: Jacobi-Type Conditions and Riccati Equation for Broken Extremals 194 Chapter 5: Second-Order Optimality Conditions in Optimal Control Problems Linear in a Part of Controls 231 Chapter 6: Second-Order Optimality Conditions for Bang-Bang Control 262 Chapter 7: Bang-Bang Control Problem and Its Induced Optimization Problem 306 Chapter 8: Numerical Methods for Solving the Induced Optimization Problem and Applications 346 Back Matter 374 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 both the equality and inequality type and for mixed state-control constraints of the 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 Nikolai P. Osmolovskii, Helmut Maurer. Includes Bibliographical References And Index.