On differential-integral optimal control problems

In this paper, we will study the  optimal control problem of a system containing a differential integral (D-I) operator. We will deduce the necessary optimality conditions and apply it first to the problem of minimum energy to find the lowest energy for an electrical circuit containing a resistor, a coil and a capacitor (RLC circuit), and second to the problem of the minimum time to transfer electrical current in  RLC circuit from one state to another in the shortest possible time.

Keywords:

optimal control , differential-integral equations , minimum energy problem , minimum time problem