1 Introduction
In this chapter, descriptions of traditional physical and cyber systems are provided to identify existing challenges. Current research trends of cyber‐physical systems (CPSs) are then illustrated to address these challenges. The major applications of the proposed methods in CPSs are reviewed.
1.1 Challenges of Traditional Physical and Cyber Systems
Over the past three decades, studies have addressed numerous concerns regarding the capability of traditional static modeling methodologies, such as the fault tree method and the event tree method, to adequately and quantitatively analyze the impact of hardware and software interaction on the stochastic behavior of CPSs [1,2]. During the past decade, the dynamical Markov reliability model was proposed to solve similar problems in CPSs [3]. Control block diagrams were presented for cooling loop systems. The reliability block diagram (RBD) was then established and used to describe the overall reliability status of individual components in a simplified form [4,5]. However, RBDs are incapable of describing the dynamic maintenance and repairable activities; thus, various dynamic modeling methods have been reviewed in [6,7]. The Markov methodology has the advantage of tracking the dynamic changes and time‐dependent features of CPSs, and simply integrates all failure states that occur after each working state into one failure state. The Markov methodology eliminates most of the failure states into a system failure state (absorbing node) by conducting a necessary fault injection test and achieving a sparse transfer matrix but may still result in a very large model due to many existing surviving states. Its modeling precision largely depends on the number of fault injection tests, and more cycles yield higher accuracy. To avoid the disadvantages of these two methodologies, some studies have proposed hybrid reliability models combining RBDs and Markov models for CPSs [8].
The control block diagram introduces blocks to represent each part of the control system, including the controllers, actuators, and control objectives. Control block diagrams are widely used in modern control systems because they can visually describe the relations among the important components, data flow, and control sign flow. In addition, compared with other mathematical models, they have the advantage of simply reflecting the actual correlations in a CPS. It is reasonable to build a reliability model based on the control block diagram of a CPS. In the model, the controller has many input signals, including commands and system state feedback. In general, commands are the system's expected outputs. Control signal flows are given in the control block diagram, and sensors play an important role in this feedback system. This control block diagram clearly indicates the internal dynamic relations of the system, covering most of the aspects that need to be studied.
For applications in CPSs, we are interested in real‐time performance. Therefore, from a control perspective, the ability to adjust the transient and steady‐state response of a feedback CPS is a beneficial outcome of the design of the CPS. One of the first steps in the design process is to specify the performance measures. In this chapter, we introduce common time‐domain specifications, such as percent overshoot, settling time, time to peak, time to rise, and steady‐state tracking error. We will use selected input signals, such as the step and ramp, to test the response of the CPS. The correlations between the system performance and the stability, reliability, and resilience strategies of CPSs are investigated. We will develop valuable relationships between the performance specifications and the component states for CPSs.
The ability of a feedback CPS to compensate for the consequences of the inherent faults redefines the concept of failures, i.e., the reliability of the CPS is dependent not only on the type of failure that may occur, but also on the evolving states of system output and control signals in each period [9,10]. Classical reliability evaluation methods, such as fault tree analysis, event tree analysis, and failure mode and effect analysis, are not appropriate for application to these evolving states due to the level of complexity and dynamics of CPSs. In [11,12], structured analyses and design techniques based on Monte Carlo simulation (MCS) for reliability evaluation are presented. This approach explicitly formalizes the functional interactions between subsystems, identifies the characteristic values affecting the reliability of complex CPSs, and quantifies the reliability, availability, maintainability, and safety (RAMS) parameters related to the operational architecture. As the remaining ability of the system to maintain the expected control goal after faults occur is crucial, ordered sequences of multi‐failure methods have been applied to assess the reliability of all possible CPS architectures [10]. A new methodology called a multi‐fault tree is proposed, and time‐ordered sequences of failures are addressed.
In contrast to the aforementioned studies, the reliability of a CPS as a function of the required performance from a control viewpoint is evaluated in [13]. The CPS is regarded as a failure if the dynamic performance does not satisfy all the requirements. Difference equations are introduced to describe the stochastic model of the CPS, explicitly illustrating the influence of the transmission delays and packet dropouts on changing the model parameters. A linear discrete‐time dynamic approach for modeling the signal flow in, out, and among all subsystems promotes straightforward calculation of fundamental dynamic aspects, such as times and fault characteristics [14].
MCS has been shown to be a straightforward yet accurate approach for the study of such complex systems [11–13,15]. The general approach in MCS for reliability assessment is to generate operational requirements that lead to the failure of the entire system. However, this approach requires knowledge of the system requirements‐to‐failure distribution in advance. In [16], an event‐based MCS method was proposed for multi‐component systems, in which the failure time for each component is generated and then used to verify the success or failure of the system subject to the required operational time. Because no attempt is made to generate the failure time for the entire system, which requires knowledge of the time‐to‐failure distribution of the entire system as well as the distribution approximation at the component level, it is quite different from previous methods and can reduce the possible error and computational effort in estimating the system reliability.
In [13], this method was extended to estimate the reliability of CPSs and replaces the constraint on the number of replications used in [16] with two other constraints, namely, a precision interval and a percentage of simulations belonging to this interval. The networked degradations for each channel are generated and are then used to determine the success or failure of the CPS for a given combination of operational requirements. Therefore, the reliability of the CPS is estimated as a tabulated function of the operational requirements. Compared with the results in [16], the results obtained in [13] guarantee the estimated reliability to satisfy a given precision.
1.2 Research Trends of CPSs
1.2.1 Stability of CPSs
In power systems, communication delays always occur in the transmission of frequency measurements from sensors to the control center (S‐C channel), and control signals from the control center to the plant side (C‐A channel) [17,18]. In local networks, time delays are usually ignored because the control is mainly applied locally, and communication delays are negligible compared with the subsystem time constants [19]. In recent years, with the rapid development of wide‐area measurement systems (WAMSs), a large number of phasor measurement units (PMUs) have been deployed to facilitate the real‐time control of wide‐area power systems (WAPSs) to improve the load frequency control (LFC) performance [20–22]. However, when data packets are transmitted across a WAMS, communication delays may become significant and cannot be ignored [23–25].
The conventional control of WAPSs is centralized and employs dedicated communication channels over a closed communication network. However, new regulatory guidelines require coordination across multiple hierarchical levels of power systems for more effective market operations and, as a result, open communication infrastructures have been deployed to promote the control of these increasingly complex systems [26,27]. While open networks have economic, maintenance, and reliability advantages, they are subject to time delays that are inherently stochastic (e.g., multiple delays [20] and probabilistic interval delays [24]), and thus cannot be calculated based on the procedures for dedicated networks. Numerical investigations show that time delays