Abstract: This paper reviews the current research status of networked control systems, and elaborates on the research progress made by domestic and foreign scholars in stability analysis, controller design, state estimator design, model-based fault diagnosis and fault-tolerant control of networked control systems from the perspective of control and information scheduling. On this basis, it analyzes the problems that urgently need to be solved in networked control systems and looks forward to future research directions. Keywords: Networked Control Systems; Stability Analysis; Controller Design; Scheduling; Fault Diagnosis [b][align=center]Survey on Status of Networked Control Systems ZHANG Wen-xia YUAN Jian[/align][/b] Abstract: The state-of-arts of NCS (Networked Control Systems) are surveyed first, and then some advances on stability, controller design, state estimator, model-based fault diagnosis and fault-tolerant control, and so on from control and scheduling are introduced in this paper. Finally, the demanding problems on NCS and future research fields are provided. Keywords: Networked Control Systems; stability analysis; controller design; scheduling; fault diagnosis 1 Introduction Networked Control Systems (NCS), also known as Integrated Communication and Control Systems (ICCS), first appeared in the paper published by Ray A. et al. ICCS is generally considered to be a fully distributed, networked real-time feedback control system, which connects the sensors, controllers, actuators, and other units of the control system through a communication network to form a closed-loop distributed control system. It encompasses two aspects: the distribution of system nodes and the networking of control loops. This networked control mode has advantages such as information resource sharing, a significant reduction in the number of connection lines, ease of expansion, and ease of maintenance. However, due to the large number of information sources in the network, information transmission consumes network communication resources in a time-sharing manner. Given the limited network capacity and communication bandwidth, collisions and retransmissions inevitably occur, resulting in unavoidable delays during data transmission. These delays are influenced by factors such as the communication protocol used by the network, load conditions, network speed, and data packet size, exhibiting characteristics that are either fixed or random, bounded or unbounded. This leads to a decline in control system performance and even instability, posing challenges to the analysis and design of the control system. The main problems that networks bring to NCS include: a non-negligible lag between the time delay sampling time and the actuator response time; time-related jitter within a certain time interval; and increased delays or even system instability due to data packet loss or collisions during network transmission. The performance of NCS depends not only on the design of the control strategy and controllers but also on the limitations of network communication and network resources. Information scheduling should avoid information conflicts and congestion in the network as much as possible, thereby greatly improving the service performance of the networked control system. A large number of domestic and foreign literatures have studied the analysis and design of networked control systems and information scheduling from different perspectives. 2 Problem Description The NCS structure diagram can be represented by Figure 1. Compared with the traditional point-to-point control system, the problems brought to the NCS system by the communication network are as follows: [align=center] Figure 1 Networked Control System Structure Fig. 1 A schematic diagram for an NCS[/align] 1) Control delay is the difference between a certain sampling time and the corresponding execution response time. From the perspective of control, delay will lead to lag and deteriorate system performance. From the perspective of information scheduling, delay will prevent information from arriving on time, lose the deadline, and even bring unpredictable communication domino effects. 2) Jitter is a sudden, distorted change related to time at any specific time interval, which can be regarded as a sudden fault; it manifests as control cycle jitter, delay jitter, sampling jitter; from the perspective of scheduling, jitter manifests as output jitter, queue jitter, deadline jitter, etc. 3) Transient errors are caused by the loss or collision of control signals during transmission in the network. This exacerbates data and communication delays, prevents timely arrival of timing sample values, and leads to empty sampling and sample data rejection problems. [align=center] Fig. 2 Structure chart of single-loop control system Fig. 3 Sample timing[/align] 3 Assumptions and Models of NCS Regarding the variable factors in the network, current assumptions mainly focus on the following aspects: 1) Assumption of driving mode: Sensors are all time-driven, with a sampling period of t. Actuators and controllers can use a combination of time-driven and event-driven methods. 2) Assumption of transmission delay τ: τ is usually assumed to be constant, randomly distributed, bounded, or unbounded. τ and T satisfy 0 < τ > T or 0 < τ > T. 3) Assumption of NCS data transmission: Each transmitted data packet is a complete data packet, or the data is divided into multiple data packets, i.e., single-packet and multi-packet transmission problems. 4) NCS Data Packet Loss: During transmission, network congestion, interruptions, and other reasons can lead to problems such as disordered data packet timing or data packet loss. 4. Current Status of NCS Research: NCS research involves both control and communication networks. The same problem can be studied from the perspectives of control, information scheduling, or a combination of both. 4.1 Current Status of Control Method Research: Control delays in NCS mainly include: communication delay between the sampler and the controller; communication delay between the controller and the actuator; and the controller's execution time. Generally, the controller's execution time can be attributed to the communication delay between the controller and the actuator, thus simplifying the above three delays to only and . In the simplest case, assuming and are constant, the problem can be transformed into a general constant-delay control problem for research. Commonly used control strategies are: time-driven sensors and controllers, and event-driven actuators. Ray A et al. were among the first to discuss and study the modeling, analysis, and design of ICCS (Inductively Coupled Control System). They investigated the observer-based compensator design for ICCS with distributed network-induced delays and designed an output feedback controller for stochastic network delays. Faik G et al. also studied the impact of network introduction on the system's stability. Liou LW and Ray A et al. studied the regulator design problem for stochastic ICCS. Lian Feng-li analyzed the performance of NCS (Non-Stochastic Control System) and performed modeling and controller design work, considering the impact of communication networks on control systems. Wittenmark B and Nilsson J studied the stochastic optimal control problem for stochastic real-time control systems. Zhu Qixin and Hu Shousong extended this to cases where the delay is greater than the sampling period and studied the design problems of stochastic state estimators and stochastic optimal controllers for networked control systems. Fang Huajing et al. reviewed model-based fault diagnosis and fault-tolerant control problems for networked control systems. Zhang Wei et al. analyzed the system stability and designed a controller for this case. Salt J et al. studied the implementation problem of multi-rate control and discussed the variable delay problem in the multi-rate case. Rivera MG et al. studied the stability analysis problem of NCS with packet loss and network-induced delay. Xie Lihua et al. studied the optimal filtering problem of linear NCS with multiple data loss, and gave the design process of optimal state filter and predictor. 4.1.1 Multi-rate sampling theory For time-driven NCS, most literature assumes that the sampling rate of sensor, controller and actuator is consistent when analyzing NCS, that is, it studies the case of single-rate sampling system. However, for NCS, due to the dispersion of nodes, a single sampling rate does not conform to the actual situation. Multi-rate sampling conforms to the actual situation of the system. Salt et al. studied the control problem of multi-rate sampling. There is a small time deviation when the sensor and controller start up, and the probability of the new sensor value reaching the controller is assumed to be known. If so, it means that the control signal is calculated under the condition that the new measurement data is unknown. However, for multi-rate sampling system, the time-driven sampling method often has many problems. For example, too much redundant signal will make the system delay, empty sampling and packet loss more serious, thus leading to the deterioration of system performance. 4.1.2 Event-Driven Sampling Theory: Astrom KJ et al. studied the performance comparison between periodic sampling systems and event-based sampling systems for first-order stochastic systems. Hennningsson et al. extended this to event-driven distributed control of multi-loop systems, studying event-based scheduling and stochastic estimator and controller design problems; they also studied the optimal observer design problem with logarithmically convex noise. They also studied the recursive state estimator design problem for linear systems with mixed stochastic and bounded set perturbations. Sandee JH et al. studied the software design and control performance synthesis of event-based networked control systems. 4.1.3 Markov Jumping Systems: Time delays can be modeled as Markov chains. All nodes are time-driven. The necessary and sufficient condition for zero-order mean-square exponential stability is derived using Markov jumping system theory. Chan H et al. also applied Markov jumping systems to model systems, deriving a crossover-free optimal control strategy. Nilsson et al. studied the LQG optimal control problem under independent random time delay and time delay conditions with Markov characteristics, and gave the conditions for the LQG optimal controller and the mean square stability of the closed-loop system under different time delay characteristics. The paper assumes + 5. Outlook Currently, there is considerable research on the stability of NCSs under time delay and packet loss conditions, as well as on the optimal control problem of NCSs with random noise. However, research on the optimal disturbance suppression problem and fault diagnosis problem of NCSs with deterministic disturbances is less common. Applying optimal disturbance suppression theory to NCSs with time delay and packet loss to achieve optimal disturbance suppression of the system is an important research direction. When modeling NCSs using Markov chains, it is assumed that the states and their transition probabilities are known. However, in reality, there are cases where the states in the Markov chain are unknown. How to identify the number of Markov states and their transition probabilities using HMM (Hidden Markov Model) is a problem that must be faced in the analysis and design of NCSs. The estimation theory based on HMM is a powerful tool for handling identification problems in mixed situations. Applying HMM theory to NCSs is also an important direction for NCS research and design. Most research on NCS information scheduling is limited to single control loops. Further research is needed on the optimal scheduling of multiple control loops in shared networks. Considering multiple constraints such as network utilization, packet loss rate, and system stability, a mathematical model for multi-objective optimization of NCSs should be established. Furthermore, considering the real-time requirements of NCS, a solution method for the hierarchical multi-objective optimization problem of NCS is studied.