Construction of Trajectories for System Stable Functioning by Their Hierarchical Models

The paper proposes the language for system model description in the form of a hierarchy of so-called control units (CUs). Each CU is characterized by a set of state parameters Q combining a set of X inputs and a set of internal parameters P; a set of secondary control units B1, ..., Bn; the control function F(i, X(t), Q(t-1)), which, by the number of the secondary unit i, the input parameters of the unit at time t and the state parameters at time t-1, determines the values of the input parameters of the secondary block Bi in moment of time t; the recalculation function of H(X(t), Q(t-1), Q1(t),..., Qn(t)), which determines P(t) values of the unit internal parameters according to the state parameter values of the secondary units at the moment of time t. An important advantage of this method of the model description for a particular system S is the possibility to construct the Boolean function FRI(QI(t-1), QI(t)) in the form of a BDD within a limited time, true t., etc. when QI(t) are the values of the unit I state parameters for the model of the system S at time t, and QI(t-1) are the values of the state parameters of the unit I at time t-1. The control functions in various CU from the model of the system S are, as a rule, nondeterministic. The task consists in finding the variants of their calculation at each moment of time t so that the state parameters of certain model CU satisfy certain requirements. If these requirements are written in the form of Boolean formulas or CTL logic formulas, the problem of finding the stable operation paths of the system S is reduced to the search for all executing sets of some Boolean function given in the form of BDD. This provides an effective solution to the problem of finding the trajectories of system S stable functioning. The obtained results were used in the development of complex socio-economic system models and "correct" programs for their development.