In this article, the problem of model-based dynamic event-triggered control (ETC) of cyber-physical systems (CPSs) with dynamic quantization effects and denial-of-service (DoS) attacks is studied. With the aid of a technique combining model-based CPSs and dynamic ETC scheme, the number of transmissions is significantly reduced to save the scarce network resources. An average dwell-time (ADT) automaton and a time-ratio monitor are firstly introduced to ETC systems to describe the frequency and duration of the DoS attacks, then a unified hybrid framework of CPSs with dynamic quantizer is established. In the presence of external disturbances, quantization effects and DoS attacks, by following the emulation approach some event-triggering conditions are designed to allow the robustness, the $L_{2}$ stability and the existence of a minimum inter-event time (MIET). Relying on a novel Lyapunov function, we derive new sufficient conditions on $L_{2}$ -gain performance of CPSs. Moreover, the Zeno phenomenon in the quantized ETC system is excluded due to the existence of a positive MIET. Finally, a numerical example is provided to demonstrate the feasibility of the approach proposed in this paper.

This article presents a co-design method of dynamic periodic event-triggering mechanism (DPETM) and output-based control law for networked control systems (NCSs) subject to inevitable imperfections such as limited network resources, exogenous disturbances and successive packet dropouts. The developed DPETM has the potential to make full use of scarce network resources compared to the periodic sampled-data control on the one hand, and is natural for practical digital platforms instead of a discretized version of continuous event-triggered control (CETC) one the other hand. In this paper, the whole closed-loop system is modeled a unified hybrid system by incorporating bilateral DPETM, successive packet dropouts effects and external disturbances, and an improved hybrid Lyapunov function is constructed for stability analysis. Based on the hybrid framework, some sufficient conditions are presented to guarantee $\mathcal{L}_2$ -stability of the system while tolerating a maximum allowable number of successive packet dropouts (MANSD). Furthermore, new linear matrix inequality (LMI) conditions for co-design of control law and triggering strategy are derived by introducing some constraints with the free variables and a modified Young’s inequality. In addition, this paper considers two scenarios relating to whether an acknowledgment scheme is employed or not. Finally, the effectiveness of the proposed method is verified by two illustrated examples and comparative studies. Note to Practitioners —With the increasing requirement for reducing unnecessary waste of communication resources in modern industries, it is necessary to consider an alternative paradigm of the time-triggered control. In many digital control applications such as smart power grid, vehicle and remote surgery, the control tasks are often executed periodically, which makes it difficult for the theoretical results of CETC to be directly applied to practical digital platforms. The DPETM proposed in this paper, which only verifies the triggering conditions periodically at each sampling instant, is more suitable for practical digital platforms such as time-sliced embedded architectures compared to CETC. This paper investigates the stability problem for NCSs with DPETM subject to packet dropouts. Different from most of the existing literature on randomness of packet loss, this paper focuses on impact of the continuity of packet dropouts on system performance. Based on the hybrid framework and the Lyapunov approach, a co-design methodology of triggering condition and control law is proposed to ensure that the system satisfies the desired performance and can admit a MANSD.

This article considers remote state estimation in cyber-physical systems (CPSs) with multiple sensors. Each plant is modeled by a discrete-time stochastic linear system with measurements of each sensor transmitted to the corresponding remote estimator over a shared communication network when their securities are interdependent due to network-induced risks. A dynamic nonzero-sum game with asymmetric information is formulated in which each sensor subject to a resource budget constraint needs to decide whether to invest in security for sending data packets, taking the behaviors of other sensors into account. To overcome the difficulty in characterizing or computing the Nash equilibria (NE), the game with asymmetric information is transformed into another game with symmetric information such that the equilibrium of the original game can be obtained by solving the equilibrium of the new game. Under certain conditions, we devise a backward induction algorithm to obtain a subclass of NE of the original game, known as common information-based Markov perfect equilibria (CIBMPE). Finally, a numerical example is provided to illustrate the results obtained.

This paper concentrates on the linear quadratic control of cyber-physical systems subject to denial-of-service attacks. A Stackelberg game framework is proposed to analyze the strategic interaction between a sensor and an attacker considering a standard block fading wireless communication channel. The reward function composing of the linear quadratic control consumption and the power consumption is provided on account of energy constraints of the sensor and the attacker. To proactively overcome the difficulty in characterizing or computing the Stackelberg equilibrium (SE), the formulated game is actively transformed into a Markov decision process (MDP) under a restricted information structure, enabling the extraction of essential SE properties. In addition, the reward function is approximated to derive an analytical expression of a suboptimal SE of the game based on an approximate dynamic programming. As a special case, the investigation also delves into the capacity achieving coding scheme. Finally, numerical examples are provided to illustrate the effectiveness of the obtained results.

This paper concentrates on the optimal denial-of-service (DoS) attack power allocation strategy for remote state estimation in cyber-physical systems with two-hop networks. An intelligent relay with the assumption that it can conduct some simple recursive algorithms aims at transmitting the system process state across a vulnerable communication channel to the remote estimator, referred to as a cooperative system with the sensor. In the meantime, a malicious attacker disrupts the transmission on the channel strategically to deteriorate the performance of the system, but can do this under an energy budget constraint over an infinite time horizon. The symbol error rate is introduced to characterize the probability of the error-free packet reception, while the channel noise and the interference from another communication channel are incorporated into the communication model. We present the optimal attack power control problem as a Markov decision process (MDP) framework by the fact that there exists at least one deterministic stationary strategy. The optimal power control strategy is derived with a stochastic predictive control formulation, and then we propose the corresponding strategy for implementation by borrowing extensively a Q-learning algorithm. In addition, two quick time-saving and less computational sub-optimal attack power strategies are provided to disguise the attacker from detection. Finally, the theoretical results are illustrated by some numerical examples.

remote state estimation for an arbitrary tree topology in cyber-physical systems (CPSs) subject to Denial-of-Service (DoS) attacks. A sensor transmits its local estimation to the root node of the tree, and the root node transmits the optimal estimation to its child nodes until the leaf nodes are reached. In the meanwhile, a malicious attacker can jam all communication channels strategically connected to the attacked node. With the energy constraints in mind, both the defender and attacker adopt strategies that involve allocating energy to determine which nodes to protect or attack at each time step. A Bayesian Stackelberg game (BSG) framework with incomplete information is implemented, where the defender has no access to the available energy of the attacker exactly except for its probability distribution. In addition, a Markov decision process (MDP) and a Stackelberg Q-learning algorithm are presented to obtain the Stackelberg equilibrium (SE) policy over a finite time horizon. Finally, a numerical example is provided to demonstrate our main results.