Table Of Contents:
Preface xv

Historical Background 1(8)

Scope of the Chapter 1(1)

Calculus-of-Variations Approach 1(1)

Phase-Plane Approaches 2(1)

Maximum Principle 3(2)

Further Developments 5(4)

References 5(4)

Ordinary Minimum Problems---From the Beginning of Calculus to Kuhn-Tucker 9(34)

Nomenclature 9(1)

Unconstrained Minimization over Bounded and Unbounded Domains 10(4)

Constrained Minimization in R2: Problems with Equality Constraints 14(10)

Constrained Minimization in Rn: Problems with Equality Constraints 24(4)

Constrained Minimization: Problems with Inequality Constraints 28(7)

Direct Optimization by Gradient Methods 35(8)

References 40(1)

Problems 41(2)

Calculus of Variations---From Bernoulli to Bliss 43(44)

Nomenclature 43(1)

Euler-Lagrange Necessary Condition 44(9)

Legendre Necessary Condition 53(4)

Weierstrass Necessary Condition 57(4)

Jacobi Necessary Condition 61(5)

Some Sufficiency Conditions to the Simplest Problem 66(1)

Problem of Lagrange 67(8)

Transversality Conditions 75(4)

Problem of Bolza 79(8)

References 83(1)

Problems 84(3)

Minimum Principle of Pontryagin and Hestenes 87(52)

Nomenclature 87(1)

State and Adjoint Systems 88(4)

Calculus-of-Variations Approach 92(2)

Minimum Principle 94(5)

Terminal Manifold 99(4)

Examples Solved by Phase-Plane Approaches 103(4)

Linear Quadratic Regulator 107(2)

Hodograph Perspective 109(3)

Geometric Interpretation 112(4)

Dynamic Programming Perspective 116(3)

Singular Extremals 119(5)

Internal Constraints 124(4)

State-Dependent Control Bounds 128(2)

Constrained Arcs 130(9)

References 135(1)

Problems 136(3)

Application of the Jacobi Test in Optimal Control and Neighboring Extremals 139(22)

Nomenclature 139(1)

Historical Background 140(1)

First-Order Necessary Conditions with Free End Conditions 140(2)

Testing for Conjugate Points 142(4)

Illustrative Examples with Conjugate Points 146(5)

Numerical Procedures for the Conjugate-Point Test 151(2)

Neighboring Solutions 153(8)

References 158(1)

Problems 159(2)

Numerical Techniques for the Optimal Control Problem 161(18)

Nomenclature 161(1)

Direct and Indirect Methods 161(2)

Simple Shooting Method 163(2)

Multiple Shooting Method 165(1)

Continuation and Embedding 165(1)

Optimal Parametric Control 166(1)

Differential Inclusion Method 167(1)

Collocation Method 167(6)

Pseudospectral Methods 173(6)

References 177(1)

Problems 178(1)

Singular Perturbation Technique and Its Application to Air-to-Air Interception 179(22)

Nomenclature 179(1)

Introduction and Scope 180(1)

SPT in an Initial Value Problem 181(2)

SPT in Optimal Control and Two-Point Boundary-Value Problems 183(3)

Case Study: Air-to-Air Interception 186(15)

References 198(1)

Problems 199(2)

Application to Aircraft Performance: Rutowski and Kaiser's Techniques and More 201(16)

Nomenclature 201(1)

Background and Scope 201(1)

Rutowski and Kaiser's Optimal Climb 202(2)

Application of Singular Perturbations Technique to Flight Mechanics 204(2)

Ardema's Approach to Optimal Climb 206(3)

Calise's Approach to Optimal Climb 209(8)

References 215(1)

Problems 216(1)

Application to Rocket Performance: The Goddard Problem 217(14)

Nomenclature 217(1)

Background and Scope 217(1)

Zero-Drag, Flat-Earth Case 218(3)

Nonzero Drag, Spherical-Earth Case with Bounded Thrust 221(4)

Nonzero Drag, Spherical-Earth Case with Unbounded Thrust 225(6)

References 228(1)

Problems 229(2)

Application to Missile Guidance: Proportional Navigation 231(10)

Nomenclature 231(1)

Background and Scope 231(2)

Mathematical Modeling of Terminal Guidance 233(1)

Optimization of Terminal Guidance 234(3)

Numerical Example 237(4)

References 238(1)

Problem 239(2)

Application to Time-Optimal Rotational Maneuvers of Flexible Spacecraft 241(16)

Nomenclature 241(1)

Background and Scope 242(1)

Problem Formulation 243(1)

Problem Analysis 243(8)

Numerical Example 251(6)

References 254(1)

Problems 254(3)
Index 257(6)
Supporting Materials 263