Aperiodic Sampled-Data Control of Distributed Networked Control Systems Under Stochastic Cyber-Attacks Kritika Bansal and Pankaj Mukhija Abstract—This paper examines the stabilization problem of a distributed networked control system under the effect of cyber- attacks by employing a hybrid aperiodic triggering mechanism. The cyber-attack considered in the paper is a stochastic deception attack at the sensor-controller end. The probability of the occurrence of attack on a subsystem is represented using a random variable. A decentralized hybrid sampled-data strategy is introduced to save energy consumption and reduce the transmission load of the network. In the proposed decentralized strategy, each subsystem can decide independently whether its state should be transmitted to the controller or not. The scheme of the hybrid triggering mechanism for each subsystem composed of two stages: In the first stage, the next sampling instant is computed using a self-triggering strategy. Subsequently, in the second stage, an event-triggering condition is checked at these sampling instants and the control signal is computed only if the event-triggering condition is violated. The self-triggering condition used in the first stage is dependent on the selection of event- triggering condition of the second stage. Finally, a comparison of the proposed approach with other triggering mechanisms existing in the literature is presented in terms of the sampling instants, transmission frequency and performance measures through simulation examples. Index Terms—Cyber-attack, distributed networked control system, event-triggered control, hybrid aperiodic sampled-data control, selftriggered control.   I. Introduction D ISTRIBUTED networked control system (DNCS) consists of geographically distributed subsystems that are connected together via a common communication network. The controller of each subsystem shares its state information with the controller of its neighbouring subsystems in a DNCS. Such systems are found throughout the infrastructure of society, such as smart grids, transportation networks, and robotics [1]. These interconnections among the subsystems increase the system complexity as the dynamics of each subsystem are governed not only by its own state but also by the states of its neighbouring subsystems. Furthermore, the presence of a network in a DNCS gives rise to several issues such as network induced delay, data loss [2], and cyber security [3]. The consideration of these network-induced effects in an interconnected system makes the control of these systems more challenging. The problem of cyber-attacks such as denial-of-service (DoS) attacks, deception attacks, replay attacks on networked control systems (NCS) has recently attracted the attention of several researchers [4]–[12]. These cyber-attacks risk the security and safety of DNCS and at the least degrade the performance of the system. Thus, it becomes essential to analyze the effect of cyber-attacks on the stability and control of a system. The stability of networked systems in the presence of DoS attacks is ensured in [4] by determining the suitable scheduling of the transmission times for the sensor and controller. In [5], a solution to the problem of optimal location switching data injection attacks is presented for NCS with distributed actuators. The system under dynamic sensor attack is considered in [6] and an index is provided giving the minimum number of sensors to be attacked for the attack to remain undetected. The problem of stability and stabilization of the system under cyber-attacks in the sensor-controller channel is considered in [7], [8]. In [7], stochastic cyber-attack with delay in the channel is considered whereas [8] considers the false data injection attacks whereby the attacker can access and manipulate the controller gain causing gain fluctuations. A distributed attack detection method for sensor networks under deception attacks is presented in [9]. The systems considered in [4]–[9] for the analysis of cyber-attacks are isolated in nature in the sense that no interconnection with other systems is considered. The problem of cyber-attacks on interconnected subsystems is examined in [10]–[12]. Attack on the subsystem dynamics and communicated data between subsystems is considered in [10]. An unknown input observer scheme is proposed to detect, locate, and identify the nature of the attack. In [11], an optimization problem from the outlook of a DoS attacker that maximizes the attacking effect under energy constraint is investigated. The consensus control of multi-agent systems with connectivity maintained and connectivity broken attacks on the edges is investigated in [12]. However, to the best of authors’ knowledge, the effect of cyber-attacks on the DNCS in which different subsystems may suffer attacks of different intensities has not been explored. Due to the spatial nature of the system and the sharing of a Manuscript received December 26, 2019; revised February 26, 2020; accepted April 2, 2020. Recommended by Associate Editor Qinglong Han. (Corresponding author: Kritika Bansal.) Citation: K. Bansal and P. Mukhija, “Aperiodic sampled-data control of distributed networked control systems under stochastic cyber-attacks,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 4, pp. 1064–1073, Jul. 2020. The authors are with the Department of Electrical and Electronics Engineering, National Institute of Technology Delhi, Delhi 110040, India (e- mail: kritikabansal@nitdelhi.ac.in; pankajmukhija@nitdelhi.ac.in). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JAS.2020.1003249 1064 IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 7, NO. 4, JULY 2020