Control of Nonlinear Dynamical Systems

1. Front Matter

   Pages I-9

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2. Optimal control

   • Felix L. Chernousko, Igor M. Ananievski, Sergey A. Reshmin

   Pages 11-29

3. Method of decomposition (the first approach)

   • Felix L. Chernousko, Igor M. Ananievski, Sergey A. Reshmin

   Pages 31-101

4. Method of decomposition (the second approach)

   • Felix L. Chernousko, Igor M. Ananievski, Sergey A. Reshmin

   Pages 103-145

5. Stability based control for Lagrangian mechanical systems

   • Felix L. Chernousko, Igor M. Ananievski, Sergey A. Reshmin

   Pages 147-155

6. Piecewise linear control for mechanical systems under uncertainty

   • Felix L. Chernousko, Igor M. Ananievski, Sergey A. Reshmin

   Pages 157-212

7. Continuous feedback control for mechanical systems under uncertainty

   • Felix L. Chernousko, Igor M. Ananievski, Sergey A. Reshmin

   Pages 213-243

8. Control in distributed-parameter systems

   • Felix L. Chernousko, Igor M. Ananievski, Sergey A. Reshmin

   Pages 245-273

9. Control system under complex constraints

   • Felix L. Chernousko, Igor M. Ananievski, Sergey A. Reshmin

   Pages 275-326

10. Optimal control problems under complex constraints

    • Felix L. Chernousko, Igor M. Ananievski, Sergey A. Reshmin

    Pages 327-365

11. Time-optimal swing-up and damping feedback controls of a nonlinear pendulum

    • Felix L. Chernousko, Igor M. Ananievski, Sergey A. Reshmin

    Pages 367-387

12. Back Matter

    Pages 389-396

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This book is devoted to new methods of control for complex dynamical systems and deals with nonlinear control systems having several degrees of freedom, subjected to unknown disturbances, and containing uncertain parameters. Various constraints are imposed on control inputs and state variables or their combinations. The book contains an introduction to the theory of optimal control and the theory of stability of motion, and also a description of some known methods based on these theories. Major attention is given to new methods of control developed by the authors over the last 15 years. Mechanical and electromechanical systems described by nonlinear Lagrange’s equations are considered. General methods are proposed for an effective construction of the required control, often in an explicit form. The book contains various techniques including the decomposition of nonlinear control systems with many degrees of freedom, piecewise linear feedback control based on Lyapunov’s functions, methods which elaborate and extend the approaches of the conventional control theory, optimal control, differential games, and the theory of stability. The distinctive feature of the methods developed in the book is that the c- trols obtained satisfy the imposed constraints and steer the dynamical system to a prescribed terminal state in ?nite time. Explicit upper estimates for the time of the process are given. In all cases, the control algorithms and the estimates obtained are strictly proven.

• algorithms
• control algorithm
• control theory
• dynamical system
• nonlinear control
• nonlinear control system
• optimal control
• stability
• system

From the reviews:

"This book have been devoted to the control of Lagrangian mechanical systems. … The presentation of the book is mathematical. … the book discovers a number of new and specific control theoretic ideas dedicated to mechanical systems that may arouse interest of control engineering community and provide a research inspiration to robotics community." (Krzysztof Tchon, Zentralblatt MATH, Vol. 1155, 2009)

“This book is for researchers interested in control of nonlinear systems subject to unknown disturbances, containing uncertain parameters, and having several degrees of freedom.” (IEEE Control Systems and Magazine, Vol. 30, June, 2010)

• Russian Academy of Sciences, Institute for Problems in Mechanics, Moscow, Russia 119526

  Felix L. Chernousko, Igor M. Ananievski, Sergey A. Reshmin

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