7R16. Nonlinear Control and Analytical Mechanics: A Computational Approach. - HG Kwatny (Dept of Mech Eng and Mech, Drexel Univ, Philadelphia PA 19104) and GL Blankenship (Dept of Elec and Comput Eng, Univ of Maryland, College Park MD 20742). Birkhauser Boston, Cambridge MA. 2000. 317 pp. CD-ROM included. ISBN 0-8176-4147-5. $59.95.

Reviewed by SC Sinha (Dept of Mech Eng, Auburn Univ, 202 Ross Hall, Auburn AL 36849-5341).

This book is intended for graduate students, faculty, and researchers in engineering and applied mathematics who are interested in the computational aspect of nonlinear dynamics and control algorithms developed via geometric theory in the past two decades. Readers with a background in second level ordinary differential equations, nonlinear dynamics, and a second course in control engineering should have no trouble following the material. Familiarity with Mathematica would be helpful but not necessary because the book comes with a CD-Rom containing the software called ProPac that uses Mathematica.

After a brief discussion of the scope of the book and the contents of the ProPac software in Chapter 1, the authors present an introduction to the geometrical dynamical systems; stable, unstable, and center manifolds; and Lyapunov stability in Chapter 2. Chapter 3 deals with an introductory material on differential geometry. Basic computations using ProPac are introduced. Kinematics of multibody mechanical systems represented by tree and/or chain structure is discussed in Chapter 4. The systems considered here consist of rigid bodies connected by joints. The computations are implemented through the software. The authors developed the dynamics of such systems in Chapter 5 using the Poincare´’s form of Lagrange’s equations. Algebraic, holonomic, or nonholonomic differential constraints can be included in the model. Equation derivation and applications to some typical systems such as undersea/ground vehicles and robots are demonstrated via the ProPac software.

In Chapter 6, the basic concepts of controllability and observability for a smooth affine nonlinear control system are discussed. Computations are presented for several examples. The emphasis is on feedback linearization and dynamic inversion. State (exact) as well as input-output linearizations are discussed in detail. Once again computations are carried out using ProPac. The last two chapters (7 and 8) deal with the design of robust controllers. In Chapter 7, perturbations of both SISO and MIMO feedback linearizable systems are presented. The problems of Lyapunov redesign and robust stabilization via backstepping are discussed. Methods of adaptive control and adaptive tracking are described, and suitable algorithms are included. The example problems help one to understand the applicability of the software package. Variable structure control is the subject of discussion in Chapter 8. The idea is presented as a nonsmooth, robust class of controllers designed via input-output linearization technique. After a discussion of basic properties of discontinuous systems, methods of sliding mode and reaching control designs are described. Chattering reduction using regularization and a backstepping procedure for SISO variable structure control design in the presence of uncertain, nonsmooth nonlinearities are discussed in detail. The application of the software package is demonstrated through examples.

In this reviewer’s opinion, the authors have succeeded in presenting an integrated approach to nonlinear dynamics and control mostly based on geometrical methods. This book should be appealing to engineers due to the fact that the computational aspects are included in every section and solutions of examples are demonstrated through the use of fine software package called ProPac. Additional problems and references are included at the end of each chapter. The writing style is clear and concise, the figures are clearly drawn, and the book has a nice appearance. Nonlinear Control and Analytical Mechanics is recommended for individuals including graduate students and libraries.