Robustness improvement for cyber physical system based on an optimization model of interdependent constraints.

With the rapid development of information technology, traditional infrastructure networks have evolved into cyber physical systems (CPSs). However, this evolution has brought along with it cyber failures, in addition to physical failures, which can affect the safe and stable operation of the whole system. In light of this, in this paper, we propose an interdependence-constrained optimization model to improve the robustness of the cyber physical system. The proposed model includes not only the realistic physical law but also the interdependence between the physical network and the cyber network. However, this model is highly nonlinear and cannot be solved directly. Therefore, we transform the model into a bi-level mixed integer linear programming problem, which can be easily and effectively solved in polynomial time. We conduct the simulation based on standard Institute of Electrical and Electronics Engineers test cases and study the impact of the disaster level and coupling strength on the robustness of the whole system. The simulation results show that our proposed model can effectively improve the robustness of the cyber physical system. Moreover, we compare the performance of the power supply in different CPSs, which have different network structures of the cyber network. Our work can provide useful instructions for system operators to improve the robustness of CPSs after extreme events happen in them.