The work aims to present the results of elaborating an efficient method of synthesizing an equation of a dual discrete model and a regulator for a dynamic non-linear non-stationary blackbox-type object directly from the data of the real object state matrix measurements without conducting special experiments, calculating model coefficients or disrupting the normal technological process and with the training sequence of minimum length. The methods used are based on the matrix theory, difference equations, Cramer's rule for the solution of systems of linear algebraic equations. The work presents a novel demonstration that an expanded matrix of the controlled object state enables incorporating both the object model and the regulator and accomplishes principal concepts of dual control. Besides, Cramer's rule-based equations of a model enable assessing Lyapunov exponent signatures and therefore determining the current state of the controlled object pertaining to the attraction area or the repeller. During standard operation, parameters of technological objects often vary within a wide range as the objects are non-linear and/or non-stationary. Common present-day regulator methods are based on the assumption that controlled objects are linear and stationary. The assumption often leads to disturbances in the technological process control. The work develops and substantiates the approach based on the dual control concept enabling synthesis of regulators for linear, non-linear, non-stationary objects of control. There is no necessity of studying their physical nature, conducting special experiments to receive transient characteristics or transfer functions. The object is treated as a blackbox providing small sensitivity to external impacts and adaptation during normal performance. Results: the work suggests the methods of synthesizing a regulator which can be presented both numerically and analytically. The regulator enables implementing the set output value applying modern controllers.

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