Dynamic Impulse Systems

1. Front Matter

   Pages i-xi

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2. Elements of the Theory of Schwartz Distributions

   • S. T. Zavalishchin, A. N. Sesekin

   Pages 1-14

3. Equations in Distributions: new approaches

   • S. T. Zavalishchin, A. N. Sesekin

   Pages 15-84

4. Applications to Problems of Dynamics and Control

   • S. T. Zavalishchin, A. N. Sesekin

   Pages 85-131

5. Applied Control Problems

   • S. T. Zavalishchin, A. N. Sesekin

   Pages 133-178

6. Discontinuous Solutions to Ordinary Nonlinear Differential Equations in the Space of Functions of Bounded Variation

   • S. T. Zavalishchin, A. N. Sesekin

   Pages 179-229

7. Properties of Attainability Sets for Dynamic Systems with Discontinuous Trajectories

   • S. T. Zavalishchin, A. N. Sesekin

   Pages 231-247

8. Back Matter

   Pages 248-260

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A number of optimization problems of the mechanics of space flight and the motion of walking robots and manipulators, and of quantum physics, eco­ momics and biology, have an irregular structure: classical variational proce­ dures do not formally make it possible to find optimal controls that, as we explain, have an impulse character. This and other well-known facts lead to the necessity for constructing dynamical models using the concept of a gener­ alized function (Schwartz distribution). The problem ofthe systematization of such models is very important. In particular, the problem of the construction of the general form of linear and nonlinear operator equations in distributions is timely. Another problem is related to the proper determination of solutions of equations that have nonlinear operations over generalized functions in their description. It is well-known that "the value of a distribution at a point" has no meaning. As a result the problem to construct the concept of stability for generalized processes arises. Finally, optimization problems for dynamic systems in distributions need finding optimality conditions. This book contains results that we have obtained in the above-mentioned directions. The aim of the book is to provide for electrical and mechanical engineers or mathematicians working in applications, a general and systematic treat­ ment of dynamic systems based on up-to-date mathematical methods and to demonstrate the power of these methods in solving dynamics of systems and applied control problems.

• construction
• differential equation
• mechanics
• optimization
• ordinary differential equation
• vibration
• ordinary differential equations

` ... is very well written and contains enough mathematical detail to permit the reader unfamiliar with the subject to quickly get up to speed in this important area of current research. Being unique in the field, the book is srongly recommended both for individual researchers in control systems and for the libraries.'
Applied Mechanics Reviews, 51:6 (1998)

• Section for Nonlinear Analysis, Institute of Mathematics and Mechanics, Ural Department of the Russia Academy of Sciences, Ekatarinburg, Russia

  S. T. Zavalishchin, A. N. Sesekin

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