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Optimal control theory has been used in the solution of an enormous variety of problems in physics, engineering, economic and biology. Many of the problem of design in airframe, shipbuilding, electronic, and other engineering fields are in essence, problems of control. The most widely studied type of problem in the mathematical theory of control is the "time optimal" control problem. The aim of control in this problem is to transform any initial state of a dynamic system into a desired stationary state in minimal time.

Perhaps the most widely studied type of problem in the mathematical theory of control is the "time optimal" control problem. The aim of control in this problem is to transform(or steering) any initial state y0 of a dynamic system into a desired stationary state (or to hitting a target set K H ) in minimal time. i.e., the cost function in this problem is the time in which a system is driving to desired state. Such problems are physical meaningful only if constraints are imposed on the control variables u U H since otherwise, trivially, the desired state could be achieved in zero time by the...

In this book we highlighted: the basics of sleep physiology, milestone in development of knowledge about Sleep Disordered Breathing (SDB), detailed discussion of SDB: classification, epidemiology, pathophysiology, diagnosis and treatment. Also, this book reported different definitions and classifications of Diabetes Mellitus (DM). We have reviewed different literatures to find the links and pathophysiologic mechanisms in between SDB and DM and how each affects the other. Moreover, we have reviewed different methods of diagnosis of SDB used in many researches and studies in both topics....

Elasticity is a fundamental property of all substances occurring in nature. The theory of elasticity is concerned with the study of the response of elastic bodies to the action of forces. The importance of the application of the theory of elasticity in physics and technical mechanics involved in the stated problems from the viewpoint of mathematical analysis attracted the attention of the greatest investigators of the 20th centuries to this branch of science. This thesis is devoted to study some problems in the mechanics of elastic bodies, which might have some interesting applications in the...