Method of spherical harmonic series in the problem of minimization of atmosphere pollution by fractions of harmful admixtures

The problem of minimization of atmosphere pollution by fractions of harmful admixtures is studied. It is supposed that a controlled object is described by non-stationary integral–differential transfer equation with special boundary conditions and control parameters, which are included in the right part of equation as delta-functions. Minimized integral quadratic functional characterizes energy expenditure for control and depends on the average squared deflection of fraction concentration from the desired final state. Optimal conditions are obtained with the help of Pontryagin’s maximum principle. The method of spherical harmonic series is applied. -

Keywords: The problem of minimization; Controlled object; Non-stationary integral–differential transfer equation; Minimized integral quadratic functional; Maximum principle