Identification of the steady state operator for discrete self-optimizing systems

When one attempts to design self-optimizing or adaptive control systems for plants with unknown dynamic characteristics, a major problem is that, due to the unknown initial conditions on the plant, the plant dynamics may inadvertently be identified in terms of an operator which is not unique. Since erroneous results are obtained when optimization is performed in terms of a nonunique operator, a means of characterizing a plant in terms of a unique steady-state operator, is described. This paper considers the problem for discrete-time plants and shows that the entire operator need not be identified but only certain essential characteristics of the operator. A general procedure for performing the identification and some simplifications which are applicable in special cases are described.