Control of Substance Concentrations in Natural and Artificial Aquatic Ecosystems in Problems of Management of Biosphere Compatible Technical Systems

摘要

Purpose Motivated by applications in ecological tasks, this research considers the mathematical problem of the control of the Reaction-Convection-Diffusion Equation System. Such a mathematical problem appears in many engineering applications where as there is a need to describe and control dynamics of the reactants. In this study, two important implementations have been investigated: 1) the control problem of biogen dynamics in a bio-aeration tank and 2) the optimization of pollutant discharge into reservoirs that can be used in the water utilization systems management meeting the requirements of the biosphere-compatibility. Method The distinguishing features of our mathematical problem are as follows: the first is non-linearity of direct initial boundary problem for parabolic equations, which makes it difficult to use for operational environmental management; the second is that a control problem includes constraints on the state variables. The numerical solution of such problems is usually difficult and the questions of algorithms for such tasks are still unsolved. To solve problems mentioned above two techniques are suggested. To reduce the task, linearization of an aquatic ecosystem model is used, namely, the substitution of a direct problem by a problem in variations. Further, to escape constraints on the state variables, the method of G. Marchuk1 based on the adjoint approach is used. Results & Discussion Tasks control of substance concentrations in natural and artificial aquatic ecosystems, namely, in a bioaeration tank Reservoir, are formulated as mathematical models. This paper shows an algorithm to solve control problems of the tasks by reducing those to a linear optimization problem. As a consequence, this study presents the results of computational experiments and shows the efficiency of the algorithm for large-scale problems.