Green's function approach to optimal control of unsteady heat conduction field

摘要

This paper presents a new methodology for optimal control of an unsteady heat conduction field with heat sources. The optimal control problem considered is that of determining the time changes of heat-source intensities to produce desired temperatures at several reference points. Using Green's functions, which are pre-calculated numerically under a point heat source approximation, it is shown that the distributed parameter system described fly a multi dimensional heat conduction equation can he reduced to a lumped parameter system maintaining the distributed property. Thus the optimal control problem becomes low-dimensional and a fast optimal control scheme can be developed for an arbitrarily shaped region. Some examples demonstrate the capability of the proposed method.