The issues of applying the knowledge system for managing innovative projects and programs to stimulate and improve innovation in Ukraine by analyzing the causes of weak innovation development and finding ways to improve this state are considered. The main directions of innovation activities of domestic enterprises, the reasons for failures to bring new products to the market are identified and analyzed. The types of innovations that are used for innovation activities in IT enterprises are highlighted. It is pointed out that the project approach to innovation is almost completely absent. At the same time, it is noted that traditional project management methodologies based on value systems do not fully allow us to effective management of innovative projects due to their significant complexity and risk. This leads to the need to find new approaches that would take into account the specifics of complex innovative projects and development programs, their elements, characteristics and parameters of connections. The issues of development and application of new models of innovative project management based on the value approach are considered. To do this, it is proposed to use a model of scientific cooperation based on franchising in terms of maximizing the values of all stakeholders of the project and the program, based on a comprehensive system approach to determining the state of activity in an innovative project. A structural scheme of interaction with the external environment in the implementation of innovative projects is proposed, which is a conceptual model of research. Based on this model and the scheme of innovative association, a mathematical model is proposed for determining the values of participants and stakeholders of an innovative project or program at all stages of functional interaction within the framework of the initiated project activity.