Input-to-State Stability of Switched Network Control Systems Under Unknown Deception Attacks.

In this paper, the problem of finite-time stability and finite-time boundedness for a class of linear switched singular positive time-delay systems with finite-time unstable subsystems is investigated. Necessary and sufficient positivity conditions for the systems are firstly presented by using the state-space singular value decomposition and monomial coordinate transformation methods. A class of quasi-alternative switching signals is then designed to analyze the switching behaviours of the systems. Mode-dependent average dwell time (MDADT) switching, consisting of a slow mode-dependent average dwell time (SMDADT) switching and a fast mode-dependent average dwell time (FMDADT) switching, is applied to the systems whose subsystems are stable and unstable. By establishing a suitable copositive Lyapunov-Krasovskii functional and adopting the MDADT switching strategy, all sufficient conditions guaranteeing the finite-time stability and finite-time boundedness of the considered systems are formulated in terms of linear vector inequalities as well as linear matrix inequalities. Several numerical examples are provided to illustrate the effectiveness of the proposed methods. Notably, a positive electrical circuit model is utilized to demonstrate the applicability of the theoretical results.

The problem of robust fault detection filters for switched systems systems with sensor fault. Different from the average dwell time (ADT) switching, the switched systems are switched with mode-dependent average dwell time switching law which means that each subsystem has its own ADT, its own decay rate of the Lyapunov-like function and its own increase coefficient of Lyapunov-like function at switching instants. An analysis condition to capture the weighted l <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> performance for switched systems with mode-dependent average dwell time (MDADT) is presented. With the aid of multiple Lyapunov-like functions and Projection Lemma, a procedure of robust fault detection filter synthesis is given in terms of linear matrix inequalities (LMIs). Finally, an example is given to illustrated the effectiveness of the proposed method.

The problem of asynchronous switching control is studied for a class of discrete-time switched delay systems with mode-dependent average dwell time switching, taking the time delay constraints of mode-dependent controllers into consideration. By constructing appropriate Lyapunov functionals, sufficient conditions that guarantee stability of the considered systems with mode-dependent average dwell time switching are obtained. Based on the stability result, existence conditions of the controllers are formulated in terms of a set of linear matrix inequalities. A numerical example is given to demonstrate the proposed theoretical result.

This article proposes a novel Lyapunov stability analysis for a class of switched nonlinear systems under the mode-dependent average dwell time (MDADT) switching signals. For the first time, a polynomial fuzzy model is used to describe the nonlinearity of the switched systems instead of a Takagi–Sugeno fuzzy model, which can represent a wider range of nonlinear plants. As existing advanced results are relatively conservative and lead to that tighter bounds on the dwell time are not easy to be obtained, therefore, the stability analysis for switched systems is still quite challenging. In this article, to tackle this problem, by developing a polynomial multiple Lyapunov function (MLF) approach and exploring the feature of the membership functions, relaxed stability conditions are derived for the switched polynomial fuzzy-model-based control systems. In particular, the polynomial MLF is guaranteed radially unbounded by a two-step procedure, making traditional quadratic MLF a specific case, thereby improved stability conditions can be established in the form of sum-of-squares. Moreover, the new algorithm for multivariate Chebyshev membership functions based on linear programming is proposed to introduce the information of membership functions and further relax the stability conditions to obtain tighter bounds on MDADT. Finally, a simulation example demonstrates the effectiveness of the developed techniques.

The aim of this article is to establish generic stability conditions for switched nonlinear systems with mode-dependent average dwell-time (MDADT) switching rules via Takagi–Sugeno (T–S) fuzzy modeling, which cover all unstable modes, all stable modes, and partially unstable modes as special cases. Different from traditional multiple and multiple discontinuous Lyapunov function (MDLF) methods, the proposed novel switching-signal-based multiple discontinuous Lyapunov function (SMDLF) approach divides each mode-running interval dynamically according to the actual switching of the system. The developed approach can not only yield less conservative bounds on the MDADT but can also handle all unstable subsystems, which cannot be done by means of the traditional MDLF. A class of SMDLF is constructed for continuous-time switched T–S fuzzy systems, and relaxed stability conditions are presented for the system with both stable and unstable subsystems, using a larger switching signal space. Then, novel stability conditions are deduced for all stable and unstable subsystems in terms of slow and fast MDADT switching signals, respectively. Finally, comparative simulation examples are provided to verify the advantages and effectiveness of the proposed approach.

In this paper, we present Lyapunov characterizations of the global asymptotic stability, the input-to-state stability (ISS), and the incremental input-to-state stability (δ-ISS) for discrete-time nonlinear systems with uncertain and time-varying time delays. We provide necessary and sufficient conditions for the global asymptotic stability and for the ISS and sufficient conditions for the δ-ISS, in terms of discrete-time Lyapunov-Krasovskii functionals. In particular, the Lyapunov characterization of the notion of δ-ISS is motivated by problems concerning the construction of discrete abstractions approximating discrete-time nonlinear systems. Uncertain and time-varying time delays occur very frequently, for instance, in networked control systems. Examples are included that illustrate the proposed methodologies.

Observer-based sliding mode control for fuzzy stochastic switching systems with deception attacks

This paper considers the input-to-state stability (ISS) problem for a class of hybrid time-delay systems with delay-dependent impulses by employing admissible impulsive edge-dependent average dwell time (AIED-ADT) switching. Under this method some sufficient conditions for ISS are presented. The results show that when all switching subsystems are ISS, even the impulses are destabilizing, a kind of switching signals with some corresponding positive lower bounds can still guarantee the ISS of the whole systems. Different from the existing results of related problems, the method can get smaller positive lower bounds. Finally, a numerical example to illustrate the effectiveness of the present method.

In large-scale networked control systems (NCSs), an important issue is how to guarantee the systems performance under the limited network bandwidth and stochastic cyber attacks. Centralized event-triggering mechanisms (ETMs) are now regarded as a desirable solution to ease the bandwidth pressure, but the application in large-scale NCSs is constrained by overall management complexity. In this paper, we will firstly propose a software defined centralized ETM to cost-efficiently conduct event-triggering decision based on global system states so as to assure the system transmission performance. Then, by taking deception attacks, which can hardly be detected and pose serious threats to NCSs, into account, we study secure control problem over a large-scale NCS with the presented centralized ETM. The considered deception attacks compromise controller-to-actuator channels, and the specific behaviors of the attacks on different channels are depicted by different Bernoulli processes. To solve the problem, a formal model of the envisioned large-scale system is established, the sufficient conditions that achieving the uniformly ultimately bounded (UUB) stability of the formulated system are analyzed, and then the controller gains are designed accordingly. The effectiveness of the proposed approach is finally validated by an illustrative example.

SummaryIn this article, we are concerned with the problem on input‐to‐state stability (ISS) for discrete‐time time‐varying switched delayed systems. Some Krasovskii and Razumikhin ISS criteria are provided by using the notions of uniformly asymptotically stable (UAS) function and mode‐dependent average dwell time (MDADT). With the help of the concept of UAS function, the advantage of our results in this article is that the coefficients of the first‐order difference inequalities for the mode‐dependent Krasovskii functionals and mode‐dependent Razumikhin functions are allowed to be time‐varying, mode‐dependent, and can even take both positive and negative values, and the whole switched system can be allowed to have both ISS subsystems and non‐ISS subsystems. With the aid of the notion of MDADT, each subsystem can have its own average dwell time. As an application, we also provide an ISS criterion for discrete‐time time‐varying switched delayed Hopfield neural networks with disturbance inputs. Numerical simulations verify the effectiveness of the established criteria.

New stability results for discrete-time switched systems under admissible edge-dependent average persistent dwell-time or admissible edge-dependent persistent dwell-time switching

The main objective of this paper to design a robust reliable \(H_{\infty }\) control and a switching law for a class of uncertain switched systems under an average dwell time switching signal that guarantees ISS not only when all the actuators are operational, but also when some of them experience failure. The faulty actuator output is assumed to be nonzero, which is treated as a disturbance signal that is augmented with the system disturbance input. The input-to-state stability (ISS) property is analyzed by the multiple Lyapunov functions and comparison principle approach. A numerical example is introduced to illustrate the validity of the theoretical results.

This paper focuses on the membership-functions-dependent reachable set (RS) synthesis of a class of Takagi-Sugeno (T-S) fuzzy singular multi-agent systems subject to deception attacks. To do this, with the help of the T-S fuzzy model, the nonlinear system model is transformed into a quasi-linear system. Then, the control method in the linear system is used to solve this kind of nonlinear problem. Firstly, two suitable non-singular value matrices M and N are obtained by singular value decomposition, and then the singular system is decomposed into algebraic subsystem and differential subsystem by matrices M and N. Secondly, a consensus topology with communication delay under deception attack is designed. In this cases, the sufficient conditions of RS for the simultaneous existence of external disturbances and deception attacks are given, and the specific value of the RS is obtained by solving the linear matrix inequality using the matrix decoupling method. Finally, the effectiveness of the proposed method is verified by taking the actual DC motor built on the physical platform and a class of nonlinear single-species bio-economic system as examples.Note to Practitioners—In the context of contemporary huge industry and engineering, while rapid development, security is also one of the issues that must be considered. However, the modern engineering system has the characteristics of complexity and variability, and a single module cannot operate it completely, so multiple separate modules need to work together through a unique connection. For this reason, security issues will become much more difficult. In addition, in modern network engineering, there are often some criminals who destroy the system, resulting in its normal operation, economic losses, serious situations, or endanger personal safety. Such behavior is usually called network attacks. Deception attacks are part of network attacks, which can harm the system by spreading false information. Therefore, in researching security issues, deception attacks need to be paid attention. Based on the above analysis, the membership-functions-dependent reachable set synthesis of a class of Takagi-Sugeno fuzzy singular multi-agent systems subject to deception attacks is studied in this paper.

Given a sample from an unknown probability distribution over strings, there exist algorithms for inferring the structure and parameters of stochastic grammatical representations of the unknown distribution, i.e. string grammars. Despite the fact that research on grammatical representations of sets of graphs has been conducted since the late 1960’s, almost no work has considered the possibility of stochastic graph grammars and no algorithms exist for inferring stochastic graph grammars from data. This paper presents PEGG, an algorithm for estimating the parameters of stochastic context-free graph grammars given a sample from an unknown probability distribution over graphs. It is established formally that for a certain class of graph grammars PEGG finds parameter estimates in polynomial time that maximize the likelihood of the data, and preliminary empirical results demonstrate that the algorithm performs well in practice.KeywordsGraph TransformationGraph GrammarMaximum Likelihood ParameterStart SymbolEstimate Maximum Likelihood ParameterThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Input-to-state stability for networked control system with predictive scheme