Increasing investment activity is a key problem for Russia. Despite many state’s efforts, investment activity is low. The aim of the article is to propose an innovation management method based on a systems approach. The main objective of the research is to find an effective approach to optimizing state efforts to enhance financial management of innovative activity. The research methodology is based on the analysis of the enterprise closed innovation system. Economic and mathematical methods are used to represent the management function as an operator equation of the first kind. This allows to create a control algorithm to maximize the effectiveness. The methods of computational diagnostics and tomographic economics are used for the element-by-element analysis of the subsystems of the innovation system. The information base for the study was publications concerning the theory of management and business management. The possibility of applying computational diagnostic methods to optimize the financial management of innovation activity was proved by separating the controlling and controlled subsystems of the enterprise innovation system and observing all laws of production. A form of control functional was obtained on the sets of observable characteristics of the controlling and controlled subsystems while optimizing the results of innovative activity due to the feedback channel. The results of the study may be of practical interest for innovative projects in order to transfer the enterprise to innovative development, in particular, in relation to the restructuring of organizational structures and institutional support in the digital economy format.