Practical Methods for Optimal Control Using Nonlinear Programming

by Betts, John T.

• ISBN13: 9780898714883
• ISBN10: 0898714885
• Format: Hardcover
• Copyright: 2001-05-01
• Publisher: Society for Industrial & Applied

Summary

This is quite possibly the first book on practical methods that combines nonlinear optimization, mathematical control theory, and numerical solution of ordinary differential or differential-algebraic equations to successfully solve optimal control problems. The focus of the book is on practical methods, i.e., methods that the author has found to actually work. Everything described in the book has been implemented in production software and used to solve real problems.The author's general discussion of the topic maintains a focused and concise presentation. Using modern computational methods based on nonlinear programming algorithms, he introduces the basic material necessary to solve an optimal control problem. There are two major parts of a successful optimal control solution technique. The first part is the optimization method. The second part is the differential equation method. Betts's goal is to suggest that methods used to solve differential equations and optimize the functions are intimately related.

Table of Contents

Preface	ix
Introduction to Nonlinear Programming	1	(36)
Preliminaries	1	(1)
Newton's Method in One Variable	2	(1)
Secant Method in One Variable	3	(2)
Newton's Method for Minimization in One Variable	5	(2)
Newton's Method in Several Variables	7	(1)
Unconstrained Optimization	8	(2)
Recursive Updates	10	(2)
Equality-Constrained Optimization	12	(3)
Inequality-Constrained Optimization	15	(2)
Quadratic Programming	17	(3)
Globalization Strategies	20	(7)
Nonlinear Programming	27	(1)
An SQP Algorithm	28	(2)
What Can Go Wrong	30	(7)
Large, Sparse Nonlinear Programming	37	(24)
Overview: Large, Sparse NLP Issues	37	(1)
Sparse Finite Differences	38	(2)
Sparse QP Subproblem	40	(2)
Merit Function	42	(2)
Hessian Approximation	44	(1)
Sparse SQP Algorithm	45	(3)
Defective Subproblems	48	(1)
Feasible Point Strategy	49	(3)
Computational Experience	52	(4)
Nonlinear Least Squares	56	(5)
Optimal Control Preliminaries	61	(20)
The Transcription Method	61	(1)
Dynamic Systems	61	(1)
Shooting Method	62	(1)
Multiple Shooting Method	63	(2)
Initial Value Problems	65	(7)
Boundary Value Example	72	(3)
Dynamic Modeling Hierarchy	75	(1)
Function Generator	76	(5)
The Optimal Control Problem	81	(52)
Introduction	81	(3)
Necessary Conditions for the Discrete Problem	84	(1)
Direct versus Indirect Methods	85	(2)
General Formulation	87	(2)
Direct Transcription Formulation	89	(3)
NLP Considerations---Sparsity	92	(15)
Mesh Refinement	107	(14)
Scaling	121	(2)
Quadrature Equations	123	(2)
What Can Go Wrong	125	(8)
Optimal Control Examples	133	(44)
Space Shuttle Reentry Trajectory	133	(5)
Minimum Time to Climb	138	(9)
Low-Thrust Orbit Transfer	147	(5)
Two-Burn Orbit Transfer	152	(13)
Industrial Robot	165	(5)
Multibody Mechanism	170	(7)
Appendix: Software	177	(4)
A.1 Simplified Usage Dense NLP	177	(1)
A.2 Sparse NLP with Sparse Finite Differences	177	(1)
A.3 Optimal Control Using Sparse NLP	178	(3)
Bibliography	181	(8)
Index	189