Optimal Control of a Double Integrator

This book provides an introductory yet rigorous treatment of Pontryagin's Maximum Principle and its application to optimal control problems when simple and complex constraints act on state and control variables, the two classes of variable in such problems. The achievements resulting from first-order variational methods are illustrated with reference to a large number of problems that, almost universally, relate to a particular second-order, linear and time-invariant dynamical system, referred to as the double integrator. The book is ideal for students who have some knowledge of the basics of system and control theory and possess the calculus background typically taught in undergraduate curricula in engineering.

Optimal control theory, of which the Maximum Principle must be considered a cornerstone, has been very popular ever since the late 1950s. However, the possibly excessive initial enthusiasm engendered by its perceived capability to solve any kind of problem gave wayto its equally unjustified rejection when it came to be considered as a purely abstract concept with no real utility. In recent years it has been recognized that the truth lies somewhere between these two extremes, and optimal control has found its (appropriate yet limited) place within any curriculum in which system and control theory plays a significant role.

Presents the basic issues of Pontryagin's maximum principle in a reader-friendly yet rigorous way Discusses in detail a broad range of problems, allowing readers to readily grasp all aspects of the topic considered Explores the maximum principle in the presence of both simple and complex constraints Includes supplementary material: sn.pub/extras

Autorentext
Arturo Locatelli is Emeritus Professor of Control Theory at Politecnico di Milano, Italy.

Inhalt

Introduction.- The Maximum Principle.- Integral constraints.- Punctual and isolated constrains.- Punctual and global constraints.- Singular arcs.- Simple constraints: J = , x(t0) = given.- Simple constraints: J = , x(t0) = not given.- Simple constraints: J = + m, .- Non standard constraints on ... .- Minimum time problems.- References.