Chapter
2.1.2 Properties of Linear Dynamic Systems
2.3 Time Invariant Systems
2.3.1 Stability of Linear Time Invariant Systems
2.3.2 BIBO Stability of Linear Time Invariant Systems
2.3.3 Observability of Linear Time Invariant Systems
2.4 The Method of Adjoints
2.5 Controllability and Duality
2.6 Summary of Key Results
2.7 Bibliographic Notes for Further Reading
3 Stochastic Systems Theory
3.2 Random Variables and Distributions
3.3 Expected Value and Characteristic Function
3.4 Independence and Correlation
3.5 The Gaussian Distribution
3.7 Gauss--Markov Processes
3.8 Linear Gauss--Markov Models
3.9 Summary of Key Results
3.10 Bibliographic Notes for Further Reading
4.1 Position Fixing: The Ideal Case
4.2 Position Fixing: Error Analysis
4.3 Position Fixing: Redundant Measurements
4.5.1 Inertially Stabilized Inertial Navigation Systems
4.5.2 Strapped Down Inertial Navigation Systems
4.8 The Extended Kalman Filter
4.11 Summary of Key Results
4.12 Bibliographic Notes for Further Reading
5.1 Fundamentals of Homing
5.2.1 Terminal Phase Analysis
5.2.2 Approximate Miss Distance Analysis
5.2.3 Exact Miss Distance Analysis
5.4 Constant Bearing Guidance
5.5 Proportional Navigation
5.6 Linearized Proportional Navigation
5.6.1 Miss due to Launch Error
5.6.2 Miss due to Step Target Acceleration
5.6.3 Miss due to Target Sinusoidal Motion
5.6.5 Use of Power Series Solution
5.8 Summary of Key Results
5.9 Bibliographic Notes for Further Reading
6.1 The Restricted Two-Body Problem
6.2 The Two-Dimensional Hit Equation
6.3 In-Plane Error Analysis
6.4 Three-Dimensional Error Analysis
6.4.1 Actual Flight Time Approximation
6.4.2 Down-Range Miss Distance, M[sub(DR)]
6.4.3 Cross-Range Miss Distance, M[sub(CR)]
6.5 Effects of the Earth's Rotation
6.6 Effects of Earth's Oblateness and Geophysical Uncertainties
6.6.1 Effects of Other Perturbations
6.7 General Solution of Ballistic Guidance Problems
6.7.2 Problem Formulation
6.8 Summary of Key Results
6.9 Bibliographic Notes for Further Reading
7.1 Velocity-to-Be-Gained Guidance
7.1.1 Velocity-to-Be-Gained Guidance with Unlimited Thrust
7.1.2 Velocity-to-Be-Gained Guidance with Limited Thrust
7.2 Guidance by State Feedback
7.3 Combined Navigation and Guidance
7.4 Summary of Key Results
7.5 Bibliographic Notes for Further Reading
8.1 Unconstrained Optimization on R[sup(n)]
8.2 Constrained Optimization on R[sup(n)]
8.2.1 Lagrange Multipliers
8.2.2 Second-Order Conditions
8.3 Inequality Constraints on R[sup(n)]
8.4 Optimal Control of Discrete-Time Systems
8.5 Summary of Key Results
8.6 Bibliographic Notes for Further Reading
9.3 Optimal Control without Control Constraints
9.4 The Maximum Principle
9.4.2 The Transversality Conditions
9.4.4 Time-Optimal Control of Double Integrator
9.4.5 Optimal Evasion through Jinking
9.5.1 Motivational Example: Dynamic Programming
9.5.2 The Principle of Optimality
9.5.3 Backward Dynamic Programming
9.5.4 Continuous-Time Dynamic Programming
9.5.5 The Linear Quadratic Regulator
9.5.6 The Linear Quadratic Gaussian Regulator
9.5.7 Relationship between the Maximum Principle and Dynamic Programming
9.5.8 The Hamilton–Jacobi–Bellman Equation
9.5.9 Dynamic Programming Summary
9.6 The Maximum Principle and Dynamic Programming
9.7 Summary of Key Results
9.8 Bibliographic Notes for Further Reading
10 Introduction to Differential Games
10.1 Taxonomy of Two-Player Games
10.2 Example of a Simple Pursuit Game: Two-Player Football Scrimmage
10.2.3 The Apollonius Circle Theorem
10.2.4 Solution to the Football Two-Player Scrimmage Problem
10.3 The Bellman--Isaacs Equation
10.4 The Homicidal Chauffeur: Modeling
10.5 The Homicidal Chauffeur: Features of the Solution
10.6 A Game-Theoretic View of Proportional Navigation
10.7 Summary of Key Results
10.8 Bibliographic Notes for Further Reading
Appendix A: Useful Definitions and Mathematical Results
A.1 Results from Topology
A.2 Results from Linear Algebra
A.5 The Implicit Function Theorem
Fundamentals of Aerospace Navigation and Guidance
( Cambridge Aerospace Series )
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