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The world is at the threshold of the fourth industrial revolution, which has already begun. It requires enterprises and even sectors to move toward Industry 4.0. Innovative systems (IS) play an important role in this process. In the article, the innovative systems in Industry 4.0 are considered to be complex systems whose components have a lot of tasks; in particular, to produce innovative policy; to provide the subjects of innovative activity with the necessary resources; to participate directly in the process of creation, commercialization, and the practical use of new knowledge; to implement integration approaches between these processes, etc. The complexity of the innovation system leads to the development of modern approaches to their modeling, as a tool for further designing, creating, and modifying real innovative systems of different levels of organization under the conditions of Industry 4.0. In the simulation of IS under the conditions of Industry 4.0, the description of the subsystems by a number of sets is proposed. The model is described by the graph of relationships, including the abstract level of the hierarchical model of IS, its elements, indicators and their values, functions, actions and operations, their states and efficiency, and the tree of goals. In order to make optimal solutions, using the mathematical apparatus of the theory of Markov chains to study the dynamic and static characteristics of the states of the IS is proposed. This approach can be widely used in the simulation, designing, development, and rebuilding of IS at different levels of an organization.

Simulation of Innovative Systems under Industry 4.0 Conditions