This book analyzes control systems using results from singularity theory and the qualitative theory of ordinary differential equations. The main part of the book focuses on systems with two-dimensional phase space. The study of singularities of controllability boundaries for a typical system leads to the classification of normal forms of implicit first-order differential equations near a singular point. Davydov indicates several applications of these normal forms. The book is accessible to graduate students and researchers working in control theory, singularity theory, and various areas of differential equations, as well as in applications.

Readership

Graduate students and researchers working in control theory, singularity theory, and various areas of differential equations.

Reviews

"Addresses control theoretic problems from the viewpoint of a working mathematician ... presents a vast collection of theorems accompanied with rigorous proofs formulated in the language of differential topology, singularity theory and the theory of dynamical systems."

-- Zentralblatt MATH

Table of Contents

• Implicit first-order differential equations
• Local controllability of a system
• Structural stability of control systems
• Attainability boundary of a multidimensional system
• References