A distributed optimal control problem of gaseous pollutants by transient air pollution source

Abstract

Here we have investigated theoretically the distribution of horizontally homogeneous pollutant concentration, when the fixed emission sources are taken as controls with respect to time, such that the meansquare deviation of the pollutant concentration from the desired level (air quality standard) is minimised within the critical period over the entire boundary layer under impending adverse meteorological situation. KEY WORDS: Pollution, optimal control, air quality standard, point source. NOMENCLATURE X -horizontally integrated concentration distribution of the pollutant. C -desired level of the concentration (air quality standard) h -height of boundary layer / -height of the source u(t) -volume control (elevated source) co(t) -boundary control (area source) q { -horizontally integrated concentration of pollutant in the middle point of the interval s -length of interval into which the segment (0, h) is divided in n equal parts T -total time of the process t -time h -switching time Ti -switching time (dimensionless) = ktJS 2 -T_ __ -total time (dimensionless)_f= (kt/S 1 ) A 2r Ax -constraints of ¥I(T) where A t = Aj&lk (i = 1, 2)