Abstract: For the problem of low-cost control system construction in fog environments, due to the significantly heterogeneous hardware resources and network communication conditions, along with the different prices of the infrastructure in fog environments, it is difficult to directly assess and compare the total construction cost until all the applications are deployed and the system is finally established. While, the number of facility combinations for deploying applications reaches a power exponential level, when searching system construction solutions. If an optimal low-cost construction solution is determined by comparing all feasible solutions, the time spend will become unbearable with the increasing scale of the system. To overcome these challenges, a fast and low-cost multi-dimensionally heterogeneous fog control system programming method is proposed by considering the system′s multi-aspect, i.e., multi-dimensional resource requirements on facilities. First, the system definition for a multi-dimensionally heterogeneous fog control system under fog computing environments is clarified, where the facilities are heterogeneous in multi-aspect (multi-dimensional) hardware resources and communication links. Second, based on the system definition, the system′s multidimensional demand constraints on facilities are specified, with the objective of satisfying the multidimensional service resource and communication quality requirements. Finally, a specific programming method is proposed to comprehensively and multi-dimensionally model the problem into an optimal programming expression, and derive a solution through multi-constraint programming. The solution derived by this method not only determines the facility configuration for the system construction, but also specifies the specific deployment for all the applications. The experimental results under a representative case study show that, the proposed method can fast derive a total-cost-optimized system construction solution that generally outperforms all other comparison methods, with the solution time (average within 973 ms) in the same order of magnitude as that of a traditional linear complexity method (local optimum). In addition, by constructing fog control systems with our method, the total construction cost can averagely be reduced to 72. 5% or less that of other traditional/typical methods, while, with an average 30% surplus resource capacity gained, an additional application expansion can be satisfied with an average 60. 65% quantitative overrun.