In this paper, a one-dimensional dynamical system is investigated. The system is determined by an inclusion. The values of the multi-function in the inclusion are closed bounded intervals. The new element of the orbit is an element of...
moreIn this paper, a one-dimensional dynamical system is investigated. The system is determined by an inclusion. The values of the multi-function in the inclusion are closed bounded intervals. The new element of the orbit is an element of value of the multi-function (called realization) modified by an additive control. If the value of the control variable must be chosen before the realization becomes known, then the control is called a priori, otherwise a posteori. The problem to be solved is that if the orbit starts from a given initial condition x0 and it must reach a target interval [A,B] in exactly k iterations, then what is the minimal cost control sequence. In special cases, exact formulas are provided. In the general case, a generalization of the Bellman principle is adapted.
