The article considers an intelligent automation system for optimization of the control process of forecasting the phase states of a linear discrete-time dynamical systems. The objective function of the control process estimates the guaranteed (minimax) result of forecasting the admissible states of the phase vector of the system object. For the process under study, the formalization of a multi-step problem of minimax estimation of the forecasting phase states of the system object in a given period of time. The solution to this problem is described in the form of a technique that allows for the implementation of intelligent automation of optimization of forecasting control process. The proposed technique is implemented as a finite sequence of one-step operations that allow their algorithmization. The results obtained in the article can be used in the development and creation of intelligent computer systems for optimizing the control of complex technical and socio-economic dynamical objects.