Quantized state estimation for neural networks with cyber attacks and hybrid triggered communication scheme
Introduction
In recent years, the dynamic behaviors of neural networks have been paid increasing attention due to their potential applications in automation, image recognition, data compression and large volume of high speed data processing. It is well known that understanding the neuron states is an indispensable step to apply the neural networks and realize the desired performance in practical application. A large number of researchers have made great achievements in the neuron state estimation problem [1], [2], [3], [4]. In [1], the authors investigate the variance-constrained state estimation problem for a class of networked multi-rate systems with network-induced probabilistic sensor failures and measurement quantization. The authors in [2] concentrate on the problem of stochastic finite-time state estimation for discrete time-delay neural networks with Markovian jumps. In literature [3], the authors consider the problem of state estimation with guaranteed performance for a class of switching fuzzy neural networks.
Over the past few decades, time triggered scheme (periodic sampling) is intensively applied for systems modeling in conventional control systems [5], [6], [7]. In [5], the authors consider the robust H∞ filtering problem for a class of uncertain nonlinear time-delay stochastic systems. In view of the limited network resources, the drawback of time triggered scheme which contains the transmitting of large repetitive signals is prominent day by day. To avoid the shortcoming of time triggered scheme, another triggered scheme named event triggered scheme is proposed, which is used to deal with many issues of data transmission for networked control systems. For example, a novel event triggered scheme, which is used to reduce the communication load of the network, is proposed in [8] to investigate the problem of H∞ controllers design for networked control systems with network-induced delay. Different from the time triggered scheme, the main idea of event triggered scheme mentioned above is that whether the settled threshold is violated or not can be the key rule of newly sampling data transmission. Based on the proposed event triggered scheme in [8], a large number of scholars concentrate on the investigations of event triggered scheme and have obtained abundant research results [9], [10], [11], [12]. For example, an adaptive event-triggered communication scheme is proposed in [9] which is applied for a class of networked Takagi–Sugeno (T–S) fuzzy control systems. In [10], the problem of event-triggered reliable H∞ filtering for networked systems with multiple sensor distortions is investigated. The authors in [11] are devoted to the design of event-triggered non-fragile state estimator for delayed neural networks subject to randomly occurring sensor nonlinearity. On the basis of the proposed event triggered scheme in [8], another triggered scheme named hybrid triggered scheme is proposed in [13], which is used to investigate the design of hybrid driven controller for networked control systems with network-induced delays. Inspired by the work mentioned above, some researchers make a further study about hybrid triggered scheme [14], [15], [16], [17]. The authors in [14] are devoted to the reliable controller design for hybrid-driven nonlinear systems via T–S fuzzy model with probabilistic actuator faults and probabilistic nonlinear perturbations. The problem of H∞ filter design for neural networks is investigated in [15] with hybrid triggered scheme and deception attacks. The hybrid-triggered H∞ filtering problem is considered for networked systems under stochastic cyber attacks in [16]. In this paper, the hybrid triggered scheme is introduced to investigate the state estimation for neural networks with cyber attacks.
Recently, the quantitative processing has drawn much attention which is an effective way to save the network resources besides the event triggered scheme mentioned above. In networked control systems, the quantitative processing which contains the compression and decompression of sampling data aims at reducing the pressure of transmission and save network resources. Motivated by the merit of quantization mentioned above, many researchers have taken the effect of quantization into consideration for networked systems [18], [19], [20]. The problem of H∞ output feedback control for event-triggered Markovian jump system is investigated in [18] with measured output quantizations. In [19], an event-driven networked control systems has been studied subject to quantization and packet losses. The authors in [20] investigate the dynamic output-feedback control problem for a class of discrete-time nonlinear stochastic systems with uniform quantization effects. In this paper, due to the quantitative processing which can reduce the pressure of network transmission in networked systems, the quantization is introduced in the investigation of state estimation for neural networks. To the best of authors’ knowledge, the state estimation for neural networks with hybrid triggered scheme and quantization has not been investigated yet, which is the motivation of this paper.
The insertion of network has posed many conveniences in data transmission, but it also brings a lot of challenges such as packet losses, nonlinear disturbance and network-induced delay. In addition, another offensive behavior named cyber attacks aims at destroying data transmission system, real-time sampling data, communication infrastructures and networked devices. According to descriptions in [21], [22], cyber attacks, which include an inaccurate sampling data and misidentification of the receiving devices, have generated greater threats to the safety of network. Given the importance of network security, enough attention should be paid to the risks of the cyber attacks. In recent years, large numbers of researchers are devoted to the investigations of cyber attacks and have obtained abundant research results [23], [24], [25]. For example, a novel approach of state filtering scheme and the sensor scheduling co-design for cyber–physical systems subject to random deception attacks is investigated in [23]. The authors in [24] investigate online deception attack strategy against remote state estimation with sensor-to-estimator communication rate constraint. A novel distributed state estimator with an event-triggered scheme is proposed in [25] to defend against false data injection attack. Drawing lessons from the existing achievements about cyber attacks, this paper is concerned with the design of state estimator for neural networks under hybrid triggered scheme subject to cyber attacks.
Motivated by the observations above, this paper is concerned with state estimation for neural networks with hybrid triggered scheme and quantization subject to cyber attacks. The hybrid triggered scheme and quantization are introduced to reduce the pressure of network transmission. Cyber attacks are also considered to make the state estimation for neural networks closer to the working condition of the actual system. Finally, a numerical example is given to show the usefulness of the proposed method.
This paper is organized as follows. In Section 2, a mathematical model of the estimating error system is constructed by taking the effects of hybrid triggered scheme and cyber attacks into consideration. Sufficient conditions which can guarantee stability of the estimating error system are established and a state estimator design method is provided in Section 3. A numerical example is given in Section 4 to show the usefulness of the proposed method. The conclusion is given in the final part.
Notation: and denote the n-dimensional Euclidean space, and the set of n × m real matrices; Matrix X > 0, for means that the matrix X is real symmetric positive definite. represents the mathematical expectation of X. For a matrix B and two symmetric matrices A and C, denotes a symmetric matrix, where * denotes the entries implied by symmetry. I is the identity matrix of appropriate dimension. In addition, T stands for the transpose of matrix.
Section snippets
System description
This paper is concerned with state estimation for neural networks with hybrid triggered scheme and quantization subject to cyber attacks. As is shown in Fig. 1, the hybrid triggered scheme and quantization are introduced to reduce the pressure of network transmission. A random variable which satisfies Bernoulli distribution is employed to describe the stochastic switch between the time triggered scheme and event triggered scheme in the hybrid triggered scheme. Consider the following neural
Main results
In this section, by applying Lyapunov functional approach and linear matrix inequality technique, considering the hybrid triggered scheme and cyber attacks, the sufficient conditions will be derived which guarantee the stability of the estimation error system (14).
Theorem 1 For given parameters: the bounds of time-delay ϕm, ϕM, τM, ηM and dM, the event triggered parameter σ, the expectations of Bernoulli variables and the constant matrix G, the augmented system (14) is asymptotically stable, if
Numerical examples
In order to illustrate the usefulness of the proposed method in this paper, a numerical example is given as follows:
The parameters of system (1) are given as follows:
The neuron activation function g(x(t)) in (13) is defined as follows:
Suppose the function of cyber attacks .
Conclusions
This paper is concerned with state estimation for neural networks with hybrid triggered scheme and quantization subject to cyber attacks. The hybrid triggered scheme and quantization are introduced to reduce the burden of network transmission and improve the efficiency of data communication. Two random variables which satisfy Bernoulli distribution are employed to describe the hybrid triggered scheme and the stochastic cyber attacks, respectively. By applying Lyapunov stability theory and LMI
Acknowledgments
This work is partly supported by the National Key Technologies Research and Development Program of China under grant (no. 2015BAD-18B02), the National Natural Science Foundation of China (nos. 61403185, 61773218, 61473156), the Natural Science Foundation of Jiangsu Province of China (nos. BK20171481, BK20161561), Six Talent Peaks Project in Jiangsu Province (no. 2015- DZXX-21), major project supported by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (no.
Jinliang Liu was born in Shandong Province, China, in 1980. He received the Ph.D. degree in School of Information Science and Technology at Donghua University. He was a post doctoral research associate in School of Automation, Southeast University, Nanjing, China from December 2013 to June 2016. From October 2016 to October 2017, he was a visiting researcher/scholar with the Department of Mechanical Engineering, the University of Hong Kong. Since November 2017 to January 2018, he was a visiting
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2021, ISA TransactionsCitation Excerpt :Compared with the linear system with quantized observation, the quantized identification of the nonlinear system is more challenging problem and complex due to its nonlinear characteristic. For the nonlinear system, some significant models have been considered to identify nonlinear systems with quantized observation involving neural networks [24,25], nonlinear difference models [26,27] and block-oriented models [28,29]. Among these nonlinear models, the topic of the quantized identification for the block-oriented model has only emerged in recent years and has attracted increasing attention [29–31].
Jinliang Liu was born in Shandong Province, China, in 1980. He received the Ph.D. degree in School of Information Science and Technology at Donghua University. He was a post doctoral research associate in School of Automation, Southeast University, Nanjing, China from December 2013 to June 2016. From October 2016 to October 2017, he was a visiting researcher/scholar with the Department of Mechanical Engineering, the University of Hong Kong. Since November 2017 to January 2018, he was a visiting scholar in the Department of Electrical Engineering, Yeungnam University, South Korea. He is currently an associate professor at Nanjing University of Finance and Economics, Nanjing, China. His main research interest is networked control systems, complex dynamical networks, T–S fuzzy systems and time delay systems.
Jilei Xia was born in Jiangsu Province, China, in 1992. He received his B.S. degree from Changshu Institute of Technology in 2015. Currently, he is pursuing an M.S. degree in College of Information Engineering, Nanjing University of Finance and Economics. His research interests include networked control systems, T–S fuzzy systems, and time delay systems.
Jie Cao was born in Jiangsu Province, China, in 1969. He received his doctor’s degree from Southeast University, in 2003. He is currently a professor at the Nanjing University of Finance and Economics, Nanjing, China. His main research interest is complex dynamical networks, data mining, business intelligence and recommendation system.
Engang Tian was born in Shandong Province, China, in 1980. He received the B.S. degree, M.S. degree and Ph.D. degree from Shandong Normal University, Nanjing Normal University and Donghua University, in 2002, 2005 and 2008 respectively. Since 2008, he has been with the School of Electrical and Automation Engineering, Nanjing Normal University. From February 2010 to May 2010, he was a visiting scholar with Northumbria University, Newcastle, England. From August 2011 to August 2012, he was a postdoctoral in Hong Kong Polytechnic University. Since August 2015 to August 2016, he was a visiting scholar in Brunel University, UK. His current research interests include networked control systems, T–S fuzzy systems and time delay systems.