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...