Correlation Dimension Based Stability Analysis for Cyber-Physical Systems

Cyber-physical systems (CPSs) realize the automatic control of entities through computing systems and networks. Stability is an important factor in CPS for system upgrading and troubleshooting. Traditional analysis methods focus on simulation and formal analysis, which have two major limitations: first, the current state information of CPS is difficult to obtain; second, most CPS face the state space explosion problem. These problems can be avoided and a good analysis can be provided based on empirical data. The main work of this article is summarized as follows: first, a phase space reconstruction method is designed to divide the dataset into several subsequences with the same shape; second, we propose a stability analysis method based on correlation dimensions. Results indicate that the proposed approach can obtain a stable correlation dimension. CPS perform better if the correlation dimension is maintained within a certain range; otherwise, a destabilizing factor exists. The proposed stability analysis has less complexity and running time.

I. Introduction

Cyber-physical systems (CPSs) are hybrid systems that integrate communication, computing, and the physical world that have high reliability, real time, and stability requirements [1]. Fig. 1 shows a typical automotive CPS architecture that displays three important pieces of information. First, CPS can realize self-control by dynamically analyzing information received from sensors. Second, CPSs are indispensable for exchanging information with other objects at runtime, such as other automobiles, humans, and base stations. This process may bring latent dangers to the system in the aspects of stability and reliability [2]. Third, various systems inside automobiles also communicate with each other, which may also introduce some security risks. Therefore, studying the functional properties of CPS, such as stability, reliability, and predictability, has practical significance.