Longuski J.M., Guzmán J.J., Prussing J.E. Optimal Control with Aerospace Applications

Springer Science+Business Media New York, 2014. XX, 273 p. 91 illus. — ISBN: 978-1-4614-8944-3, ISBN: 978-1-4614-8945-0 (eBook), DOI 10.1007/978-1-4614-8945-0.Begins from scratch to introduce the elementary computational techniques of optimal control in aerospace engineering
Includes concrete examples to demonstrate theories in a way that is understandable to students and researchers in engineering, science, and applied mathematics
Authored by experts in the field and based on over seventy years of collective experience in their careers
Want to know not just what makes rockets go up but how to do it optimally? Optimal control theory has become such an important field in aerospace engineering that no graduate student or practicing engineer can afford to be without a working knowledge of it. This is the first book that begins from scratch to teach the reader the basic principles of the calculus of variations, develop the necessary conditions step-by-step, and introduce the elementary computational techniques of optimal control. This book, with problems and an online solution manual, provides the graduate-level reader with enough introductory knowledge so that he or she can not only read the literature and study the next level textbook but can also apply the theory to find optimal solutions in practice. No more is needed than the usual background of an undergraduate engineering, science, or mathematics program: namely calculus, differential equations, and numerical integration.
Although finding optimal solutions for these problems is a complex process involving the calculus of variations, the authors carefully lay out step-by-step the most important theorems and concepts. Numerous examples are worked to demonstrate how to apply the theories to everything from classical problems (e.g., crossing a river in minimum time) to engineering problems (e.g., minimum-fuel launch of a satellite). Throughout the book use is made of the time-optimal launch of a satellite into orbit as an important case study with detailed analysis of two examples: launch from the Moon and launch from Earth. For launching into the field of optimal solutions, look no further!Content Level » Graduate
Keywords » Calculus of Variations - Constant Specific Impulse - MatLAB Code - Optimal Control Theory - Orbital Satellite Launch - Satellite Launch Into Orbit - Time-optimal Satellite Launch -Trajectory Optimization - Tranversality Condition - Variable Specific Impulse
Related subjects » Applied & Technical Physics - Classical Continuum Physics - Control Engineering - Dynamical Systems & Differential Equations - Mechanical EngineeringюParameter OptimizationParameter Optimization with Constraints
LagrangeMultipliers
Parameter Optimization: The Hohmann Transfer (1925)
Extensions of the Hohmann Transfer (1959)
The Bi-parabolic Transfer
ExercisesOptimal Control TheoryOptimal Launch of a Satellite
General Form of the Problem
The Problems of Bolza, Lagrange, and Mayer
Transformation from Lagrange to Mayer
Transformation from Mayer to Lagrange
A Provocative Example Regarding Admissible FunctionsExercisesThe Euler-Lagrange TheoremThe Variation
The Euler-Lagrange Equation and the Brachistochrone Problem
The Euler-Lagrange Theorem
Proof Outline of the Euler-Lagrange Theorem
Summary of the Euler-Lagrange Theorem
Alternate Form of the Transversality ConditionExercisesApplication of the Euler-Lagrange TheoremTwo-Point Boundary-Value Problem (TPBVP)
Two Approaches to Terminal Constraints
Transversality Condition
Case 1 Final Time Specified
Case 2 Final State Specified
Case 3 Final Endpoint Specified
General Case of Supplying Needed B.C.s
Adjoined Method
Un-adjoinedMethod
Examples
A Cookbook for Optimization Problems
Examples of Step
Constant HamiltonianExercisesThe Weierstrass ConditionStatement of the Weierstrass Necessary Condition
Proof Outline of the Weierstrass Necessary ConditionTrue or False Quiz for Chaps. 1–5The Minimum PrincipleStatement of the Minimum Principle
Problem Statement
Pontryagin’sMinimum Principle
Examples
Legendre-Clebsch Necessary Condition
Notes on Necessary and Sufficient Conditions
Weak and Strong Extremals
An Example of a Weak but Not Strong Minimum
Second-Order Necessary and Sufficient Conditions
Examples Illustrating the Concept of a Conjugate PointExercisesSome ApplicationsAircraft Performance Optimization
Maximization of the Range of a Rocket
Integration of Equations of Motion When f Is Constant
The Optimal Trajectory
Maximum Range Equation
Time Optimal Launching of a Satellite
Integration of the EOMs
TPBVP
Flat-Earth Launch Including Atmospheric DragExercisesWeierstrass-Erdmann Corner ConditionsStatement of the Weierstrass-Erdmann Corner Conditions
Proof Outline of Weierstrass-Erdmann Corner ConditionsBounded Control ProblemsOptimal Control Problems with Constraints
Examples of Bounded Control Problems
Singular ArcsExercisesGeneral Theory of Optimal Rocket TrajectoriesEquations of Motion
High and Low-Thrust Engines
Cost Functionals for Rocket Engines
First-Order Necessary Conditions
Optimal Constant Specific Impulse Trajectory
Optimal Impulsive Trajectory
Optimal Variable Specific Impulse Trajectory
Optimal Trajectories in a Uniform FieldExercises
True or False Quiz for Chaps. 6–10AppendicesA Time-Optimal Lunar AscentMatLAB’s Two-Point Boundary-Value Solver
SolutionMethod
MatLAB CodeB Time-Optimal Launch of a Titan II
Scaling the TPBVP
Solution Method
Results
MatLAB CodeC Optimal Low-Thrust LEO to GEO Circular Orbit Transfer
Optimization Problem
Scaling the Equations of Motion
Applying the Euler-Lagrange Theorem
Boundary Conditions and the TPBVP
Results
MatLAB CodeD Curious Quotations
Bibliography (Books)
Bibliography (Aerospace Applications Papers and Reports)