Nonlinear Control and Analytical Mechanics

Harry G.Kwatny and Gilmer L. Blankenship

Birkhäuser, 2000, Springer

The geometric theory of nonlinear control system analysis and design progressed substantially during the 1980s and 90s, providing crucial conceptual tools that addressed many of emerging applications - of specific interest to us, involving multibody electro-mechanical systems. However, as any control systems engineer can attest, issues of modeling, computation, and implementation quickly become the dominant concerns in practice. The problems of interest present unique challenges because of the need to build and manipulate complex mathematical models for both the plant and controller. As a result, along with colleagues and students, we set out to develop computer algebra tools to facilitate model building, nonlinear control system design, and code generation, the latter for both numerical simulation and real time control. This book is a result. The unique features of the book include an integrated treatment of nonlinear control and analytical mechanics and a set of symbolic computing software tools for modeling and control system design. By simultaneously considering both mechanics and control we achieve a fuller appreciation of the underlying geometric ideas and constructions that are common to both. Control theory has had a fruitful association with analytical mechanics from its birth in the late 19th century.