Interacting dynamic Systems Model Complex Specification

The article is devoted to working out of theoretic base for development of computer tools for collection of interacting processes realization. The goal of the work is development of formalism enabling an unambiguous non-contradictory description of complex dynamic systems, which have holonic structure. Such systems can contain subsystems of the same structure. The formalism must enable specification of the same structure model complex. It must have rather high expressive ability that is it must be suitable for convenient depiction of very different dynamic systems. It must also be suitable for an effective program realization.
The goal is achieved at the expense of the known situation-event formalism for a freestanding system processes specification. The formalism is based on a use of a mathematical model of a hybrid automaton, and on the automaton transition function representation by means of transformation rules. Conditional parts of these rules are conjunctions of processes logic states. The conjunctions are naturally interpreted as dynamic situations. The formalism modification consists in the following. The set of model variables is expanded. Logic variables of the model submodels states are introduced. These states may be used for composing the model and its submodel situations. New sets of logic and real output variables are introduced. The sets are subsets of the model proper states variables. The output variables may be used in composing transformation rules of the same and upper level models. In that way connections between all complex models are provided. Introduction into the model description elements of the same type as the model itself turns the description into recursive one. Such a description enables to describe the model complex. Program objects having such descriptions may be effectively realized with help of a recursive mechanism, compilers of most program languages having such mechanisms. A recursive algorithm structure is demonstrated by the examples of a model complex construction algorithm and an algorithm of models states updating. An experimental test was done by means of development on base of the formalism proposed a threelevel seven-model complex for processes coordination system simulation. The system coordinates processes in two automatic systems of a roll on a plane positioning. A small labor intensiveness of complex development and a convenience of model experiment conducting have proved the expected high effectiveness of the formalism. The effectiveness is produced with capability of repeated use of the same subsystem models and with convenience of simulating results interpreting. Then it is provided with a high effectiveness of the model program realization.