Algorithm to Determine the Target State of a System and the Best Path to It

Abstract

In the planning and management they usually decide how to move some object from the state in which it is in a fixed time interval (given, start, or initial state) to another state in a future time interval (desired, target, or planned state). The initial state of the object is known, definite unequivocally and exists. Future states can be many, and they exist only in the form of images, visions and ideas of the plan developers or persons who order the plan. It is assumed that the transition from the initial state to the desired one is possible. There are many possible ways of transition. The task is to choose the best, according to some criterion, a sequence of transition. The algorithm for determining the sequence of transfers of some object from a given state to the desired one I presented in this paper. The algorithm takes into account the presence of different possible transitions from one state to another one and shows a point-multiple mapping of the initial state of an object in the set of its desired states. The sequence of transfers, in which the total expected gain from changing the state of the object in a given period reaches its extreme — maximum or minimum, is found in the process of comparing different variants of transferring this object from one state to another. An example of finding the trajectory of transferring the object from a given state to one of its possible desired states, on which the maximum total expected result is achieved, I gave in this article.