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.

In modern conditions of instability, systematic crises and global transformations the problem of developing methods and technologies for analysis, modeling, management, forecasting and decision making for stable development of viable socioeconomic systems has become the most important. These systems are characterized by complex structure and behavior, the synergison and non-linearness and have all sorts of "NOT" and "MANY" factors characteristics. The study of model's systems, which include in their structure the humanitarian component (socio-ecological, economic and humanitarian subsystems -SEEHS, i.e. it is aspect of integration of 4 spheres) as a system of the noosphere type, is very actually problem. The greens innovations economics in the conditions of "Industry -4.0", such as man-made integral industrial systems, are systems of type SEEHS. The peculiarity of the processes of stable development management, prediction and maned decision-making in the modern conditions of socio-economic, ecological, social and humanitarian crises, and the system crisis as a whole, as well as in the conditions of necessity and importance of stable and safe development of industrially of economic structures consists in accounting of the influence of uncertainties as on the object of control as well as and behavior of decision-makers. The there has been proposed models and control technologies of viable, stable and safe development of SEEHS systems based on the integrated "object and subject" oriented approach, a conceptual model, a generalized model of the synergistic dynamics with the regard of the uncertainties of on both stochastic and chaotic factors, of on base nonlinear dynamic and others.

The paper deals with the problem of sustainable development and innovative integral modeling and forecasting approach in the management of technogenic objects and processes (TOP) as a system of socio-eco-economic and humanitarian type (SEEH). Based on the use of information and innovation technologies in order to forecast the non-linear dynamics of eco-economic and socio-humanitarian systems, integrated stochastic models of objects and processes were developed and studied, suitable for the conditions of systemic crises. The paper handles the aspect of integration of 4 business and functioning areas of the modern complex systems. It proposes a general conceptual integrated model, generalized synergetic model of dynamics, considering different uncertainty (stochastic and chaotic components). The paper examines the aspects of integration of multiple business areas and sectors of the modern complex systems functioning and developing under the present conditions of non-linearity, instability and crises. An integrated stochastic non-linear phase-space growth dynamics model was developed and studied to forecast the development of the state of an innovative economy. The paper looks into the aspects of activity management of the modern complex systems functioning and developing under the present conditions of instability.

In modern conditions of crises and instability of the functioning and development of socio-economic systems, an important problem of providing management tools and making effective decisions is the development of models, methods and information technologies for optimization and decision-making in a situation of risk and in a mixed information environment. Moreover, the widespread introduction of optimization methods, decision making and optimal control was facilitated by the fact that applied optimization problems in most cases are reduced to standard problems solved, and the growth of the power of updated computer tools contributes to the expansion of the spheres of successful application of decision optimization methods in solving complex and diverse economic problems. The paper proposes models of risk functions related to the decision-making task for harmonizing and optimizing risks and security of a complex system in a mixed information environment, and also proposes a model of penalties for damage to ensure the safety of functioning of complex systems. The work is a continuation of some of the authors' research in the field of modeling, forecasting and managing complex socio-ecological and economic systems to ensure safe, sustainable, sustainable and harmonious development in the face of modern risks and crises.

The monograph examines the prerequisites and scientific foundations for creation of the Strategy for Artificial Intelligence Development in Ukraine as well as means and ways of its effective implementation. For specialists, postgraduate, and graduate students in the field of artificial intelligence, information technologies, philosophy, state formation, and economics