Optimum Control of Environment Development System

Abstract

The paper deals with optimization of a class of systems called the environment development systems (EDS) such as e.g. ecological, social, demographic or economic systems, urban development or transport systems, which change their structure in time as a result of growth, evolution, development, investments, etc. These systems have been studied in the present paper from the point of view of the optimum control theory. The model of EDS which is introduced in the paper can be treated as an extension of multisector economic growth. It is described by a system of nonlinear differential equations which include n exogeneous and m endogeneous controlled factors or processes. Then several optimum control problems can be formulated for the EDS model. The first class, which is solved in the paper, is optimum allocation of resources of endogeneous factors under the assumption that the global amount of resources is fixed. The next class of optimization problems is the optimum investments or reproduction policy. That class of problems can be solved only for relatively simple systems. However, the decomposition of complex problems into a number of simple subproblems is possible. The model studied has an important property. The macro-model represent an aggregated system of the collection of micro-models. As a result the decentralization of control actions at the macro-level, e.g. the government-level and the micro-level, e.g. the production plant-level, follows. The overall optimum planning strategy can be achieved by exchange of information between macro- and micro-levels. The results obtained in the paper can be used in the decentralized development planning models. As a concrete example, the development planning of an integrated power system has been studied.