Nonlinear Cyber-physical Systems Research Articles

Monitoring and Reconstruction of Actuator and Sensor Attacks for Lipschitz Nonlinear Dynamic Systems Using Two Types of Augmented Descriptor Observers

Fault data injection attacks may lead to a decrease in system performance and even a malfunction in system operation for an automatic feedback control system, which has motive to develop an effective method for rapidly detecting such attacks so that appropriate measures can be taken correspondingly. In this study, a secure descriptor estimation technique is proposed for continuous-time Lipschitz nonlinear cyber physical systems affected by actuator attacks, sensor attacks, and unknown process uncertainties. Specifically, by forming a new state vector composed of original system states and sensor faults, an equivalent descriptor dynamic system is built. A proportional and derivate sliding-mode observer is presented so that the system states, sensor attack, and actuator attack can be reconstructed successfully. The observer gains are obtained by using linear matrix inequality to secure robustly stable estimation error dynamics. Moreover, a robust descriptor fast adaptive observer estimator is presented as a complement. Finally, the efficacy levels of the proposed design approaches are validated using a vertical take-off and landing aircraft system. Comparison studies are also carried out to assess the tracking performances of the proposed algorithms.

An Artificial Neural Network-Based Data-Driven Embedded Controller Design for a Pneumatic Artificial Muscle-Actuated Pressing Unit

Obtaining mathematical models of nonlinear cyber–physical systems for use in controller design is both difficult and time consuming. In this paper, an ANN-based method is proposed to design a controller for a nonlinear system that does not require a mathematical model. The developed ANN-based control algorithm is implemented directly on a real-time field controller, and its performance is evaluated without the use of auxiliary devices, such as PCs or workstations. By executing machine learning algorithms on local devices or embedded systems, edge artificial intelligence (Edge AI) with transfer learning gives priority to processing data at the source, minimizing the necessity for continuous connectivity to remote servers. The control algorithm was developed using the Matlab Simulink environment. The first and second ANNs were cascaded, wherein the first ANN computes the appropriate pressure signal for the given displacement, while the second predicts the force based on the pressure value from the first ANN. Subsequently, the ANN-based control algorithm was converted to SCL code using the Simulink PLC Coder and deployed on the PLC for operation. The algorithm was tested using two different scenarios. The conducted tests demonstrated the successful prediction of pressure signals corresponding to the targeted displacement values and accurate estimation of force values. Experimental work was carried out on PAM manipulators as a nonlinear model application, and the obtained results were discussed.

Fixed-Time Adaptive Fuzzy Tracking Control for High-Order Uncertain Nonlinear Cyber–Physical Systems Under Malicious Attacks

Fixed-Time Adaptive Fuzzy Tracking Control for High-Order Uncertain Nonlinear Cyber–Physical Systems Under Malicious Attacks

H ∞-based truncated predictive control for switched nonlinear cyber physical systems subjected to actuator faults and deception attacks

ABSTRACT This paper emphasises the study of switched nonlinear cyber-physical systems (CPSs) subjected to input delay, actuator faults and deception attacks by a H ∞ -based truncated predictive control design. Particularly, the predictive controller uses delayed state information in addition to the traditional feedback control to estimate the present state for the feedback. Furthermore, the proposed control design is modelled with a truncated predictive approach which is also used to compensate the effects of actuator faults and attacks that also satisfy a predefined H ∞ index simultaneously. With the assistance of the Lyapunov stability theory, a novel set of adequate criteria are acquired in terms of LMIs which assure the asymptotical stability of the switched nonlinear CPS under prescribed predefined H ∞ performance levels. Eventually, the proposed theoretical results are validated through two numerical examples.

Command filtering event-triggered secure control for nonlinear cyber-physical systems under denial-of-service attacks and input saturation

For nonlinear cyber-physical systems (CPSs) with input saturation and denial-of-service (DoS) attacks, an adaptive secure control strategy is investigated in this paper. To estimate the unmeasurable states, a novel switched neural network (NN) observer is designed, where two sub-observers can be freely switched from each other. Considering unnecessary packet transmissions, an improved event-triggered mechanism (ETM) is introduced to reduce the communication burden in the controller-to-actuator channel. In addition, in order to simultaneously solve the input saturation and unknown control direction problems, a Nussbaum-type function is introduced to the control design process. Finally, it is proven that all closed-loop signals are the semiglobal uniformly ultimately bounded, and simulation results demonstrate the effectiveness of the proposed secure control scheme.

Event-based adaptive secure asymptotic tracking control for nonlinear cyber–physical systems against unknown deception attacks

This article addresses the event-triggered adaptive neural network asymptotic tracking control problem for a class of nonlinear cyber–physical systems under unknown deception attacks. In the process of recursive design, a novel adaptive asymptotic tracking control strategy is proposed based on bound estimation method, backstepping technique and some smooth functions. The designed asymptotic tracking controller can ensure that the output of the system asymptotically tracks the desired signal, while ensuring that all signals in the closed-loop system are bounded. Particularly, the underlying system can be guaranteed to possess faster convergence response and higher control precision. Additionally, the Zeno behavior is ruled out. Finally, a two-stage chemical reactor is employed as an example to demonstrate the feasibility and viability of the designed control algorithm.

Periodic and Dynamic Periodic Event-Triggered Control for Nonlinear Cyber-Physical Systems Under DoS Attacks via a Hybrid System Approach

This paper is focused on the problem of periodic and dynamic periodic event-triggered control for nonlinear cyber-physical systems (CPSs) under denial-of-service (DoS) attacks and exogenous disturbances. The analysis relies on a new model to design periodic event-triggered control and dynamic periodic event-triggered control schemes such that the nonlinear CPSs are resilient to a class of malicious attacks which can be characterized by attacking frequency and attacking duration. By developing an average dwell-time automaton and a time-ratio monitor to describe frequency and duration of the DoS attacks, general hybrid dynamical frameworks are firstly proposed for event-triggered nonlinear CPSs. Based on the established models, novel Lyapunov functions are constructed. Furthermore, thanks to the Lyapunov-based approach, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{2}$</tex-math></inline-formula> -gain performance of the considered nonlinear CPSs under DoS attacks is analyzed. Finally, the feasibility of the theoretical findings is demonstrated by a numerical example.

Predictor-Based Decentralized Event-Triggered Secure Control for Nonlinear Cyber-Physical Systems Under Replay Attacks and Time Delay

This paper investigates the problem of predictor-based decentralized event-triggered secure control for nonlinear cyber-physical systems (CPSs) subject to replay attacks and time delay. To overcome the limitation of the network bandwidth, a periodic decentralized event-triggered scheme (PDETS) is designed for non-strict feedback nonlinear CPSs in the presence of replay attacks. Then, decentralized output feedback controllers are constructed by designing predictor-based observers to attenuate the influences of replay attacks and time delay. Based on the proposed new framework, the global exponential stability (GES) of the resulting nonlinear CPSs can be guaranteed. Finally, two application examples verify the effectiveness of the proposed method.

Event-triggered adaptive secure tracking control for nonlinear cyber–physical systems against unknown deception attacks

This article presents an event-triggered adaptive neural networks secure tracking control method for a class of nonlinear cyber–physical systems under unknown sensor and actuator deception attacks. To obtain the desired system performance, dynamic surface technique is applied to design controller and radial basis function neural networks are introduced to deal with unknown nonlinear and actuator attacks. By skillfully combining compensation signals with the attack compensators, the unknown deception attacks are effectively mitigated. To reduce the transmission communication load, a novel event-driven control scheme is developed by applying relative threshold triggered mechanism. On this basis, all the signals of closed-loop system are bounded under deception attacks by using Lyapunov stability analysis. Additionally, the presented secure tracking control strategy can ensure the tracking error converges to a small neighborhood of origin and the Zeno behavior is ruled out. Finally, a practical example is employed to verify the feasibility and effectiveness of the designed control algorithm.

Design of nonsingular second-order terminal sliding mode controller for cyber-physical systems with time-delays and cyber-attack on actuators

This paper introduces an innovative adaptive nonsingular Second-Order Terminal Sliding Mode (SOTSM) control strategy specifically designed to stabilise disturbed nonlinear Cyber-Physical Systems (CPSs) within a finite timeframe. Unlike the conventional methods, our approach incorporates a novel nonlinear sliding surface that eliminates the need for a reaching step, significantly enhancing the system's robustness. Novel real-time adaptive control laws are developed to cope with external perturbations, time-varying delays, and cyber-attack on actuators without requiring the identification of their upper bounds. The proposed method ensures robust performance for time-varying delayed and disturbed nonlinear CPSs, even in the face of strong cyber-attacks targeting the actuators. Moreover, the proposed method has distinct advantages: it delivers rapid response times, enhanced flexibility, exceptional accuracy, smooth and robust control devoid of transient fluctuations or chattering, and ensures finite-time convergence. Simulation results comprehensively demonstrate the superior efficiency and success of our proposed technique compared to traditional methods such as integral Sliding Mode Control (SMC) and State-Feedback Control (SFC) schemes.

Optimal Injection Attack Strategy for Nonlinear Cyber-Physical Systems Based on Iterative Learning

This paper aims to investigate the security problem of nonlinear cyber-physical systems (CPSs), which poses a challenge to handle compared with linear CPSs. A series of optimization problems for nonlinear CPSs under injection attack are constructed, which are based on a general model of the nonlinear systems with repetitive operation characteristics and a novel introduction of the key technical lemma. These optimization results are more general than the existing injection attack results and the requirements for attackers to obtain system information are relaxed. Also, the form of switching applied to the attack strategy possesses several advantages, including high stealthiness, lower cost, and more flexibility. Therefore, the new optimal injection attack strategies are expected to be more widespread and provide a basis for the design of defense strategies. The key to acquiring the designed optimal attack strategies is to adopt the linear input/output (I/O) data model for these systems via introducing an estimation term of the improved projection estimation method into the linear model. Finally, a networked GLUON-6L3 manipulator example validates the effectiveness of the proposed methods. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The main purpose of this paper is to study the cyber security of nonlinear cyber-physical systems from the perspective of attackers, which can help defenders fully understand the behavior of attackers. Most of the existing attack strategies aimed at linear systems or have a priori knowledge of the attacked systems. However, there are great limitations and difficulties in practical application. In this paper, the new attack strategies are proposed by combining system identification, iterative learning and control theory, which relaxes the requirement of the attacker’s ability. In detail, the attacker only needs to obtain the control input and output data of the attacked system and design the attack strategy according to it. Among them, the first-in, first-out queue storage method is applied to remove the requirements for the storage capability of the attacker. In practical applications, the attacker does not need to store the I/O data continuously, but only store the initial value and the data of two successive iterations. The mathematical analytic forms of two optimal attack strategies are given, and then their effectiveness are verified on a welding work of a networked six-axis manipulator. In the future, we will investigate the design of attack strategies for nonlinear systems with heterogeneous dynamics and multiple delays.

Resilient Self-Triggered Model Predictive Control of Discrete-Time Nonlinear Cyberphysical Systems Against False Data Injection Attacks

Resilient Self-Triggered Model Predictive Control of Discrete-Time Nonlinear Cyberphysical Systems Against False Data Injection Attacks

Event-triggered prescribed performance adaptive secure control for nonlinear cyber physical systems under denial-of-service attacks

For a class of nonlinear cyber physical systems (CPSs) under intermittent denial-of-service attacks (DoS), this paper investigates a novel adaptive security control scheme. A switched fuzzy observer is designed to estimate unmeasurable states. In addition, the relative threshold-based event-triggered approach is introduced to reduce the released data, and the dynamic surface control technique is used to remove the ‘explosion of terms’ problem. Meanwhile, an observer-based adaptive event-triggered prescribed performance controller is constructed, which ensures that all closed-loop signals remain bounded and system output approaches a designed performance bound within a predefined finite time. Simultaneously, the Zeno behavior can be thoroughly eliminated. Finally, a numerical simulation is used to demonstrate the validity of the results.

Adaptive Fixed-Time Control for State-Constrained High-Order Uncertain Nonlinear Cyber-Physical Systems Under Malicious Attacks

A novel fixed-time adaptive fuzzy tracking control strategy is developed to resolve the fixed-time tracking control issue for a category of state-constrained high-order uncertain nonlinear cyber-physical systems (CPSs), which suffer from malicious attacks launched in controller-actuator (C-A) channel. The proposed control strategy is independent of the exact system model and can accommodate external disturbances and malicious attacks. Meanwhile, distinguished from the existing control methods for state-constrained uncertain CPSs under malicious attacks which can only ensure the system performance when time leans towards infinity or in finite time, the presented control strategy can guarantee the system performance in fixed time. It has been substantiated that the developed control strategy can make sure that the output tracking error converges to a predefined small neighborhood of the origin, and all signals of the resulting closed-loop system satisfy the corresponding time-varying state constraints during the total operation. In particular, the settling time and tracking precision are known and can be preconfigured by selecting the design parameters appropriately. More significantly, all the initial states of the system are independent of the developed fixed-time adaptive fuzzy tracking control law and can be arbitrarily chosen in the constrained region specified by the corresponding time-varying state constraints conditions. Ultimately, a representative simulation is supplied to illustrate the effectiveness and superiority of the proposed control scheme.

Fuzzy-based adaptive event-triggered control for nonlinear cyber-physical systems against deception attacks via a single parameter learning method

This paper investigates the adaptive fuzzy control issue of cyber-physical systems (CPSs) against unknown deception attacks and external disturbance. Based on the backstepping design framework, the uncertainty term composed of the approximation error term generated by the fuzzy logic system, the external disturbance and the deception attack signals are regarded as a whole in the recursive design process. Then, by combining the single parameter learning method with the adaptive fuzzy technique, the uncertain terms containing approximation error, disturbance and injection attacks can be transformed into the form of linear parameterization with only one unknown scalar parameter, which greatly reduce the calculation process. In addition, the dynamic event-triggered adaptive control technology can be integrated into the control design to reduce the amount of data transmission. Theoretical analysis shows that all the signals in the closed-loop system are bounded under the proposed control scheme, and the Zeno behavior is excluded. Finally, the two-stage chemical reactor and mass-spring-damper systems are employed to demonstrate the validity of the proposed adaptive fuzzy control solution.

Reinforcement learning-based fixed-time resilient control of nonlinear cyber physical systems under false data injection attacks and mismatch disturbances

This paper presents a fixed-time adaptive resilient control framework based on reinforcement learning (RL), mismatch disturbance observer and nonsingular fast terminal sliding mode scheme for nonlinear cyber-physical systems (CPS) to enhance cyber-security under False Data Injection (FDI) attacks, as well as match and mismatch disturbances. The RL algorithm contains an actor-critic neural network (NN) in which the actor NN is employed to estimate the uncertainty while the critic NN is applied to evaluate the performance cost function. Next, to compensate the detrimental effects of attacks and mismatch disturbances, a new sliding mode-based adaptive disturbance observer is designed. To achieve high precision trajectory tracking within a fixed-time interval, a nonsingular fast terminal sliding mode scheme is designed. This scheme ensures fixed-time convergence of the tracking error and facilitates disturbance attenuation and attack mitigation which are the key features of the proposed fixed-time secure control strategy. Finally, the fixed-time stability analysis of is performed through Lyapunov theory. Results reveal the effectiveness of the proposed resilient control for wind turbine system as the nonlinear CPS.

State estimation for a class of nonlinear non‐Gaussian cyber–physical systems under false data injection attacks

AbstractIn this article, we consider the state estimation problem for nonlinear cyber–physical systems with non‐Gaussian process noises under actuator false data injection attacks from the perspective of defenders. The process noises and actuator false data injection attacks herein are regarded as non‐Gaussian noises. Then, the prior density of the state is considered as a sum of Gaussians with unknown covariance matrixes. The partial variational Bayesian method is applied to approximate the unknown covariance matrixes, and the unscented Gaussian sum filter is used for state estimation as well as decreasing the computing complexity. Finally, some simulation results are presented to show the effectiveness of the proposed state estimation method.

Attack Detection Based on Encoding–Decoding Approach for Cyber–Physical Systems

This article is concerned with the attack detection issue for a class of nonlinear cyber–physical systems (CPSs) with unknown-but-bounded (UBB) noises. The nonlinear system is linearized by utilizing first-order Taylor expansion with Lagrangian remainder, and an observer based on zonotopic sets is proposed to estimate the system states. Then, a novel encoding–decoding strategy (EDS) is provided to improve the attack detection rate by selecting appropriate parameters. In order to alleviate the impact introduced by malicious attacks, a countermeasure is taken into account when an attack is detected by the abnormal detector. Finally, the hardware-in-the-loop (HIL) simulation is provided to illustrate the effectiveness of the proposed results.

A Time-Varying Observer-Based Approach to Equilibrium Estimation and Compensation for Synchronization of Heterogeneous Nonlinear Cyber-Physical Systems

A Time-Varying Observer-Based Approach to Equilibrium Estimation and Compensation for Synchronization of Heterogeneous Nonlinear Cyber-Physical Systems

Event-Based Fixed-Time Secure Cooperative Control for Nonlinear Cyber-Physical Systems Under Denial-of-Service Attacks

This paper investigates the problem of the fixed-time secure cooperative control for a class of nonlinear cyber-physical systems (CPSs) under denial-of-service (DoS) attacks. First of all, an event-based data transmission scheme is proposed to solve the fixed-time secure leader-following consensus in the occurrence of connective-preserved DoS attacks. Besides, a novel measurement error is developed to avoid Zeno behavior. However, the initial communication topology may inevitably be disconnected by malicious adversaries. To solve this difficulty, a new fixed-time secure observer is designed to estimate the leader information. Moreover, a self-triggered control strategy is proposed, which not only avoids the continuous communication but also restores the secure leader-following consensus subject to connective-preserved/broken DoS attacks. Then the characteristic of the allowable connective-preserved/broken DoS attacks can be obtained. Finally, simulation results show the effectiveness of the proposed method.