A Quantitative Method for Measuring Hybrid Uncertainty Information in Cyber Physical Systems

In most technical systems, various uncertainties are unavoidable and no matter how well a system is designed they are threats to a system always, including the Cyber physical systems (CPS). CPS is the integration of computation and physical processes and generally used in large-scale and critical tasks. As a complex hybrid system, the consistency and reliability of CPS are much more important. Therefore, during the real operation of CPS, it is critical to deal with the uncertainties by a suitable method. The focus of this paper is to address the fuzziness and the randomness information at the physical layer which are most affected by complex environmental factors and the subjective information, coming from the decision-making in the cyber layer, which is actually the fuzziness that comes from experts' judgments. Since the fuzziness and the randomness are contained in the CPS simultaneously, a suitable quantitative method is needed to handle the hybrid uncertainties in both the physical and the cyber subsystem. Through introducing the chance theory which can be regarded as a mixture of the probability theory and credibility theory, this paper presents a quantitative method that utilizes the chance theory to describe the mixed uncertainties in the CPS to improve the robustness and stability of the design. In the proposed method, the chance measure is adopted to quantify the performance and reliability of the CPS under the influence of the fuzziness and randomness. The concept of hybrid variables is utilized to represent the random and fuzzy parameters, based on which an algorithm is designed. The results of the application demonstrate the validity of the proposed method.