Relative predictability of failure event occurrences and its opacity-based test algorithm

ABSTRACT

In this paper, the problem of relative predictability of failure event occurrences is investigated. The notion of relative predictability is proposed for logical automata and the concept of predictable rate is introduced to characterise the predictability property of a discrete-event system, which takes values in the interval [0, 1]. Intuitively, a discrete-event system being relatively predictable means that there exist some failure events which can be predicted from the observations of the system. The relationship between relative predictability and predictability introduced by Sahika Genc et al. analysed and the analysis shows that relative predictability is weaker than predictability for discrete-event systems. Furthermore, a necessary and sufficient condition for relative predictability is presented. In particular, an opacity-based algorithm is developed to test the relative predictability, which is polynomial in the number of states of the system. Also, some examples are provided to illustrate the presented results.

KEYWORDS:

• Predictability
• relative predictability
• discrete-event systems
• opacity

Acknowledgments

The authors would like to thank the Associate Editor and the two reviewers for their invaluable suggestions and comments that greatly helped to improve the quality of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

National Natural Science Foundation of China [grant number 61273118], [grant number 61673122], [grant number 500150056]; Provincial Major Program of Guangdong Province [grant number 2014KZDXM033]; Public Welfare Research and Capacity Building Project of Guangdong Province [grant number 2015A020402006].