Compromise solution in the problem of change state control for the material body exposed to the external medium

The problem of finding optimal temperature control of the material body state under the unknown in advance parameters of the external medium is formalized and studied in this paper. The problems of this type arise frequently in the real life. An optimal thermal regime is necessary to apply at the soil thawing or freezing, drying the building materials, heating the concrete to obtain the required strength, and so on. Problems of such type one can analyze making use the apparatus and methods of game theory. For describing the influence of external medium on the characteristics of different materials we make use the many-step two person zero-sum game in this paper. The compromise solution is taken as the optimality principle. The numerical example is given.