On the basis of modern mathematical models, methods and information and technologies, for example, an integrated stochastic nonlinear model of manmade processes and objects, suitable for the conditions of systemic crises, were investigated and developed. Considered in this article are some aspects of integration of a lot of domains and sectors of operation of modern complex systems which are functioning and developing in the present-day conditions of instability, crises and nonlinearity. In order to predict the development of the state of an innovation economy, the nonlinear integrated stochastic model of growthing dynamic in the phase space has been investigated and developed. In the article, problem of the optimization of the management of the activity of modern complex systems that develop and function regarding current conditions of the instability are considered. The prospect of further research based on the developed models is to conduct computer experiments and their practical usisng. The development and study of criterias, methods and models for optimal management of man-made objects and the creation of making decision systems based on the proposed integral models in the state space are also promising.