Optimal control problem with partial derivative equation(PDE) constraint is a numericalwise difficult problem because the optimality conditions lead to PDEs with mixed types of boundary values. The authors provide a n...Optimal control problem with partial derivative equation(PDE) constraint is a numericalwise difficult problem because the optimality conditions lead to PDEs with mixed types of boundary values. The authors provide a new approach to solve this type of problem by space discretization and transform it into a standard optimal control for a multi-agent system. This resulting problem is formulated from a microscopic perspective while the solution only needs limited the macroscopic measurement due to the approach of Hamilton-Jacobi-Bellman(HJB) equation approximation. For solving the problem, only an HJB equation(a PDE with only terminal boundary condition) needs to be solved, although the dimension of that PDE is increased as a drawback. A pollutant elimination problem is considered as an example and solved by this approach. A numerical method for solving the HJB equation is proposed and a simulation is carried out.展开更多
As only about 15% of the total time of people in Hong Kong was spent outdoors, it would be more valuable if the associated effectiveness and impact of the recently proposed abatement measures could be expressed in ter...As only about 15% of the total time of people in Hong Kong was spent outdoors, it would be more valuable if the associated effectiveness and impact of the recently proposed abatement measures could be expressed in terms of the improvement in the total exposure levels. This paper uses an exposure assessment model developed from the local microenvironment concentration data together with our surveyed time activity patterns to evaluate the effectiveness of the proposed air pollution abatement policy. Prior to the enforcement of abatement measures, about 2.5% of the young group and 1.2% of the adult group having their exposure levels exceeded that defined by the current 8-hour PM10 standard (180 μg/m3). With the enforcement of abatement measures, only 0.3% of the adult group would be restored to a safe level.展开更多
文摘Optimal control problem with partial derivative equation(PDE) constraint is a numericalwise difficult problem because the optimality conditions lead to PDEs with mixed types of boundary values. The authors provide a new approach to solve this type of problem by space discretization and transform it into a standard optimal control for a multi-agent system. This resulting problem is formulated from a microscopic perspective while the solution only needs limited the macroscopic measurement due to the approach of Hamilton-Jacobi-Bellman(HJB) equation approximation. For solving the problem, only an HJB equation(a PDE with only terminal boundary condition) needs to be solved, although the dimension of that PDE is increased as a drawback. A pollutant elimination problem is considered as an example and solved by this approach. A numerical method for solving the HJB equation is proposed and a simulation is carried out.
文摘As only about 15% of the total time of people in Hong Kong was spent outdoors, it would be more valuable if the associated effectiveness and impact of the recently proposed abatement measures could be expressed in terms of the improvement in the total exposure levels. This paper uses an exposure assessment model developed from the local microenvironment concentration data together with our surveyed time activity patterns to evaluate the effectiveness of the proposed air pollution abatement policy. Prior to the enforcement of abatement measures, about 2.5% of the young group and 1.2% of the adult group having their exposure levels exceeded that defined by the current 8-hour PM10 standard (180 μg/m3). With the enforcement of abatement measures, only 0.3% of the adult group would be restored to a safe level.
