Optimal control of sources on some classes of functions

Abstract

In this work, we investigate the problems of the control of sources’ motion and power, which influence the state of the objects described by partial differential equations. The functions defining the sources’ operation are taken from different classes of functions that are easy to implement from the technical point of view. For numerical solution to the problems considered, we obtain and validate formulae for the gradient of a target functional, which allow using first-order optimization methods, e.g. gradient projection method.

Keywords:

• impulsive control
• piece-wise constant control
• Heaviside function
• gradient of functional
• lumped sources
• movable sources