Nowadays the problem of sustainable development became one of the topical issues. However, many authors point to conceptual complexity, which is that the concept "sustainable development" includes two terms "development" and "sustainability." At the same time, each of these terms is treated not unambiguously. It leads to the emergence of different interpretations of sustainable development in relation to specific systems. A new concept of sustainable development of systems is proposed. According to this concept, the sustainable development of a complex multidimensional system will be understood as the dynamics consisting in the presence of a trend of balanced change in the entropies of randomness and self-organization while maintaining an acceptable risk level in multidimensional systems. The proposed concept is approved on practical examples. Dynamics of vector entropy and multidimensional risk of Yekaterinburg and Sverdlovsk regions in 1992-2017 is given.Thirdly, formalization of sustainable development is a complicated complexity of the studied systems and the phenomena. Currently, there is no unambiguous, accurate interpretation of a concept of the complex system. However, there are characteristic signs, such as multidimensionality, multiconnectivity, a multiloop, multileveled (hierarchy), the composite and multipurpose nature of construction, and also indeterminacy and stochasticity of behavior. We will give below the definition which, in our opinion, most adequately characterizes the concept of the complex system. Definition 1. A complex system is called a system in the model of which there is not enough information to effectively manage this system [3].This fact leads to different understandings of "sustainable development" in relation to particular systems [4][5][6][7][8][9][10][11]. For example, in [12], there are more than 50 different interpretations of the "sustainable development" concept.The implementation of sustainable development implies that certain monitoring of the studied system or phenomenon should be carried out. Monitoring is understood as a system of constant overseeing by the current of any phenomenon for the establishment of its compliance to the initial assumptions or desirable result. This phenomenon can occur in any sphere-in social relations, in nature, in the financial and economic sphere, etc. Within monitoring, there is assessment, control of the system, and the formation of management recommendations (management of its state) depending on the impact of particular factors.Therefore, the formulation of the formalized concept of monitoring sustainable development, which could be concretized for particular cases, seems to be an urgent problem. One of the possible ways is to use a systems approach [13]. Let us make an attempt to formulate monitoring of the sustainable development concept of complex systems with the example of territories.