Optimal approximation of a process by a single-variable model from the response

The approximation optimality is measured as verisimilitude of the model and the process in thes desired sense which is dictated by the assignment function. If the assignment function and the process response are linear in terms of their variable, then the approximation error can be made equal to zero; solution of such a problem is provided. A procedure for obtaining an optimal model in the nonlinear case is described. Examples are given.