Ebook: Dynamic Impulse Systems: Theory and Applications

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.

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This book provides a general and systematic treatment of dynamic systems. Based on up-to-date mathematical methods, including distribution theory, it demonstrates the power of these methods in solving dynamics of systems and applied control problems. First, new approaches to the construction problem of the general theory of linear dynamic systems are suggested. Then a new theory of differential equations with nonlinear operations over impulse input actions is developed. Finally, some singular optimization problems are treated on the subject of the mechanics of space flight, the motion transport manipulators in a viscous medium, quantum physics and economics.
Audience: This volume will be of interest to electrical and mechanical engineers, as well as to applied mathematicians, whose work involves ordinary differential equations, control and optimization, circuit synthesis, or dynamics and vibration.

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This book provides a general and systematic treatment of dynamic systems. Based on up-to-date mathematical methods, including distribution theory, it demonstrates the power of these methods in solving dynamics of systems and applied control problems. First, new approaches to the construction problem of the general theory of linear dynamic systems are suggested. Then a new theory of differential equations with nonlinear operations over impulse input actions is developed. Finally, some singular optimization problems are treated on the subject of the mechanics of space flight, the motion transport manipulators in a viscous medium, quantum physics and economics.
Audience: This volume will be of interest to electrical and mechanical engineers, as well as to applied mathematicians, whose work involves ordinary differential equations, control and optimization, circuit synthesis, or dynamics and vibration.
Content:
Front Matter....Pages i-xi
Elements of the Theory of Schwartz Distributions....Pages 1-14
Equations in Distributions: new approaches....Pages 15-84
Applications to Problems of Dynamics and Control....Pages 85-131
Applied Control Problems....Pages 133-178
Discontinuous Solutions to Ordinary Nonlinear Differential Equations in the Space of Functions of Bounded Variation....Pages 179-229
Properties of Attainability Sets for Dynamic Systems with Discontinuous Trajectories....Pages 231-247
Back Matter....Pages 248-260

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This book provides a general and systematic treatment of dynamic systems. Based on up-to-date mathematical methods, including distribution theory, it demonstrates the power of these methods in solving dynamics of systems and applied control problems. First, new approaches to the construction problem of the general theory of linear dynamic systems are suggested. Then a new theory of differential equations with nonlinear operations over impulse input actions is developed. Finally, some singular optimization problems are treated on the subject of the mechanics of space flight, the motion transport manipulators in a viscous medium, quantum physics and economics.
Audience: This volume will be of interest to electrical and mechanical engineers, as well as to applied mathematicians, whose work involves ordinary differential equations, control and optimization, circuit synthesis, or dynamics and vibration.
Content:
Front Matter....Pages i-xi
Elements of the Theory of Schwartz Distributions....Pages 1-14
Equations in Distributions: new approaches....Pages 15-84
Applications to Problems of Dynamics and Control....Pages 85-131
Applied Control Problems....Pages 133-178
Discontinuous Solutions to Ordinary Nonlinear Differential Equations in the Space of Functions of Bounded Variation....Pages 179-229
Properties of Attainability Sets for Dynamic Systems with Discontinuous Trajectories....Pages 231-247
Back Matter....Pages 248-260
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