Analytical Methods Of Optimization

by D. F. Lawden

• ISBN13: 9780486450346
• ISBN10: 0486450341
• Format: Paperback
• Copyright: 2006-05-05
• Publisher: Dover Publications

Summary

Suitable for advanced undergraduates and graduate students, this text surveys the classical theory of the calculus of variations. Topics include static systems, control systems, additional constraints, the Hamilton-Jacobi equation, and the accessory optimization problem. Emphasis throughout the text is placed upon methods and principles, which are illustrated by worked problems and sets of exercises. 1975 edition.

Table of Contents

Preface	v
Static Systems	1	(23)
Statement of the Problem	1	(1)
Unconstrained Control	2	(5)
Equality Constraints	7	(6)
The Lagrange Multipliers	13	(1)
Inequality Constraints	14	(3)
Linear Programming	17	(7)
Control Systems	24	(38)
Definitions	24	(2)
Linear Control Systems	26	(4)
Infinite Series of Matrices	30	(3)
Autonomous Linear Systems	33	(3)
Optimal Control	36	(1)
Necessary Conditions for Optimal Control	37	(10)
Optimization of Linear Systems	47	(6)
Escape from a Circular Orbit	53	(9)
Additional Constraints	62	(41)
Constraints on the Final State	62	(10)
An Integral of Hamilton's Equations	72	(6)
Calculus of Variations Problem	78	(3)
Non-differential Constraints	81	(5)
Integral Constraints	86	(2)
Discontinuous Controls	88	(6)
Linear Systems	94	(9)
Hamilton-Jacobi Equation	103	(20)
Optimal Cost Function	103	(1)
Hamilton-Jacobi Equation	104	(4)
Derivatives of the Optimal Cost Function	108	(3)
Pontryagin's Principle	111	(5)
Optimal Rocket Trajectories	116	(4)
Weierstrass and Clebsch Conditions	120	(3)
The Accessory Optimization Problem	123	(30)
Second Variation of the Cost	123	(3)
Accessory Problem. Conjugate Points	126	(3)
Solution of the Accessory Equations	129	(4)
The Accessory Riccati Equation	133	(5)
Sufficiency Conditions	138	(15)
Bibliography	153	(2)
Index	155