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The asymptotic synchronization problem of chaotic Lur'e systems in the master-slave framework was explored in this paper. A time-varying delay feedback controller with quantization considerations and a delay-product-type Lyapunov-Krasovskii functional technique were employed to tackle this problem. Consider an error system based on master and slave systems, for which sufficient asymptotic stability requirements are developed to assure that the addressed system achieves proper synchronization. Following that, the desired control gain was determined by finding a feasible solution to these stability requirements. The results of this paper were validated using a numerical example with simulations, which revealed that they were superior to previously published ones.

This work aims to focus on analyzing the consensus control problem in cooperative–competitive networks in the occurrence of external disturbances. The primary motive of this work is to employ the equivalent input-disturbance estimation technique to compensate for the impact of external disturbances in the considered multi-agent system. In particular, a suitable low-pass filter is implemented to enhance the accuracy of disturbance estimation performance. In addition, a specific signed, connected, and structurally balanced undirected communication graph with positive and negative edge weights is considered to express the cooperation–competition communication among neighboring agents. The cooperative–competitive multi-agent system reaches its final state with same magnitude and in opposite direction under the considered structurally balanced graph. By utilizing the properties of Lyapunov stability theory and graph theory, the adequate conditions assuring the bipartite consensus of the examined multi-agent system are established as linear matrix inequalities. An illustrative example is delivered at the end to check the efficacy of the designed control scheme.

The problem of robust nonfragile synchronization is investigated in this paper for a class of complex dynamical networks subject to semi-Markov jumping outer coupling, time-varying coupling delay, randomly occurring gain variation, and stochastic noise over a desired finite-time interval. In particular, the network topology is assumed to follow a semi-Markov process such that it may switch from one to another at different instants. In this paper, the random gain variation is represented by a stochastic variable that is assumed to satisfy the Bernoulli distribution with white sequences. Based on these hypotheses and the Lyapunov-Krasovskii stability theory, a new finite-time stochastic synchronization criterion is established for the considered network in terms of linear matrix inequalities. Moreover, the control design parameters that guarantee the required criterion are computed by solving a set of linear matrix inequality constraints. An illustrative example is finally given to show the effectiveness and advantages of the developed analytical results.

In this article, based on sampled-data approach, a new robust state feedback reliable controller design for a class of Takagi-Sugeno fuzzy systems is presented. Different from the existing fault models for reliable controller, a novel generalized actuator fault model is proposed. In particular, the implemented fault model consists of both linear and nonlinear components. Consequently, by employing input-delay approach, the sampled-data system is equivalently transformed into a continuous-time system with a variable time delay. The main objective is to design a suitable reliable sampled-data state feedback controller guaranteeing the asymptotic stability of the resulting closed-loop fuzzy system. For this purpose, using Lyapunov stability theory together with Wirtinger-based double integral inequality, some new delay-dependent stabilization conditions in terms of linear matrix inequalities are established to determine the underlying system's stability and to achieve the desired control performance. Finally, to show the advantages and effectiveness of the developed control method, numerical simulations are carried out on two practical models. © 2016 Wiley Periodicals, Inc. Complexity 21: 518-529, 2016 [ABSTRACT FROM AUTHOR]

This work aims to focus on analyzing the consensus control problem in cooperative–competitive networks in the occurrence of external disturbances. The primary motive of this work is to employ the equivalent input-disturbance estimation technique to compensate for the impact of external disturbances in the considered multi-agent system. In particular, a suitable low-pass filter is implemented to enhance the accuracy of disturbance estimation performance. In addition, a specific signed, connected, and structurally balanced undirected communication graph with positive and negative edge weights is considered to express the cooperation–competition communication among neighboring agents. The cooperative–competitive multi-agent system reaches its final state with same magnitude and in opposite direction under the considered structurally balanced graph. By utilizing the properties of Lyapunov stability theory and graph theory, the adequate conditions assuring the bipartite consensus of the examined multi-agent system are established as linear matrix inequalities. An illustrative example is delivered at the end to check the efficacy of the designed control scheme. [ABSTRACT FROM AUTHOR]

This paper discusses a synchronization issue of uncertain time-delay systems via flexible delayed impulsive control. A new Razumikhin-type inequality is presented, considering adjustable parameters the ϖ (t) , which relies on flexible impulsive gain. For the uncertain time-delay systems where delay magnitude is not constrained to impulsive intervals, sufficient conditions for global exponential synchronization (GES) are established. Furthermore, based on Lyapunov theory, a new differential inequality and linear matrix inequality design, and a flexible impulsive control method is introduced through using the variable impulsive gain and time-varying delays. It is interesting to find that uncertain time-delay systems can maintain GES by adjusting the impulsive gain and impulsive delay. Finally, two simulations are given to illustrate the effectiveness of the derived results. [ABSTRACT FROM AUTHOR]

This paper investigates a combined H∞$$ {H}_{\infty } $$ and anti‐disturbance control problem for a class of semi‐Markovian jump nonlinear systems with constant time delay, and both modeled and unmodeled disturbances. In particular, the modeled disturbance is thought to be produced by a nonlinear exogenous system and is estimated by introducing a mode‐dependent nonlinear disturbance observer. The desired controller for the addressed system is then proposed, which consists of two components: (i) state feedback, which ensures the system's stochastic stability by attenuating the unmodeled disturbance; and (ii) disturbance estimate, which compensates for the modeled disturbance effect. Following that, a novel mode‐dependent asymmetric Lyapunov‐Krasovskii functional is used to derive the sufficient conditions for the existence of the proposed controller and disturbance observer. The developed theoretical results are supported by three numerical examples that demonstrate the utility of the proposed design method. [ABSTRACT FROM AUTHOR]

A table of content for November-December 2016 issue of the journal "Complexity" is presented on topics including cardiac dynamics in heart failure, adaptive cluster synchronization, and Zipf's law for word.

This paper investigates the resilient H ∞ event-triggered control problem for Takagi-Sugeno fuzzy system with time-varying delay and external disturbance. Contrary to some existing results, the considered event-triggered conditions are verified only at each sampling instant because it is difficult to prove Zeno-freeness for a continuous event-triggered mechanism in the presence of external disturbance. Furthermore, by constructing an appropriate Lyapunov-Krasovskii functional, sufficient conditions are derived in the form of linear matrix inequalities to ensure the asymptotic stability and the H ∞ performances of closed-loop systems. More precisely, the proposed control design not only improve robust performance but also save the communication resources. Finally, the obtained theoretical results are verified through numerical simulation, which demonstrate the efficiency and advantages of the proposed method. [ABSTRACT FROM AUTHOR]

This technical note presents analytical investigations on detectability of Boolean network with pinning control and injection mode (BNPCIM). Detectability represents the property to uniquely determine the current state of the system according to known input-output sequences. Using Cheng product of matrices, BNPCIM can be converted into a special algebraic form of BCNs with mix-valued logical control. Based on different research requirements, three types of detectability for BNPCIM are proposed: weak detectability, detectability and strong detectability. Under free and networked input conditions, a sequence of matrices are constructed to reflect output and state information by explicit forms. Then by using the established matrices, several necessary and sufficient conditions for three types of detectability are derived. Moreover, to avoid unnecessary calculations, the maximum steps to achieve different detectability are gained. Finally, two illustrative examples are given to demonstrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of disturbance-observer-based sliding mode control for stabilization of stochastic systems driven by fractional Brownian motion (fBm). By proposing a novel disturbance observer, an integral-type sliding surface is put forward with the estimated disturbance error confined within a certain value. Meanwhile, by virtue of fractional infinitesimal operator and linear matrix inequality, a sufficient criterion is derived to guarantee the asymptotic stability of obtained sliding mode dynamics. Further, an observer-based sliding mode controller is designed to ensure finite-time reachability of state trajectories onto the predefined sliding surface. Lastly, an illustrative example is utilized to verify the reliability and applicability of the proposed control strategy. [ABSTRACT FROM AUTHOR]

Improving the stability and safety is of great significance for the in-wheel electric vehicle. There are many studies only concentrating on active front steering (AFS) control or direct yaw-moment control (DYC). However, When the in-wheel electric vehicle is under extreme conditions, AFS or DYC alone is not effective. In this paper, an integrated controller of AFS and DYC is proposed. Firstly, the ideal values of yaw rate and sideslip angle can be calculated based on the two-degree-of-freedom vehicle model. Secondly, the AFS controller is obtained according to the backstepping-based fast terminal sliding mode (FTSM). Then, the DYC controller which consists of the upper controller and the lower controller is constructed. The upper controller is developed via the integral-based second-order sliding mode (SOSM). The appropriate torque is outputted to each wheel by the lower controller. Finally, the simulation results show that the actual yaw rate and sideslip angle can approach the ideal ones as closely as possible under the proposed integrated controller. [ABSTRACT FROM AUTHOR]

The issues of input–output finite-time stability and stabilization of Takagi–Sugeno (T–S) fuzzy systems with time-varying state delay and exogenous input signal are studied in this article. For the stabilization process, a controller that does not share the same membership functions as the system is considered and the state feedback is quantized by using a logarithmic quantizer. The desired stability criterion for the addressed fuzzy system is first derived without the control term. It is then extended to the case in which the proposed controller is present. The stability criteria are given in the form of matrix inequalities, which are supported by the augmented Lyapunov–Krasovskii functional, generalized free-weighting-matrix approach and Finsler’s lemma. Moreover, as a special case, an asymptotic stability criterion is obtained and used in a comparative study. As a result, the time-delay interval is much larger than some of the works published very recently, which is due to the augmented Lyapunov–Krasovskii functional construction. In addition, the effectiveness and practicability of the theoretical findings are validated with simulation examples. [ABSTRACT FROM AUTHOR]

In this work, the problem of fault and state estimation is studied for Takagi–Sugeno fuzzy systems with time-varying delay and external disturbance over a finite horizon. A fuzzy rule-based fault estimator with two tuning parameters, including the current system output information, is designed. Based on which, the Luenberger state observer is then considered to estimate the immeasurable states of the system addressed. The aim of taking into account the tuning parameters in the estimator design is to improve the accuracy of the fault estimation. More precisely, by defining error variables in accordance with actual and estimated system states and faults, an augmented system is formulated to achieve the desired results. By using the existing stability theory and integral inequality, a delay-dependent criterion for ensuring that the states of the augmented system are bounded over a finite horizon is derived. Subsequently, conditions for determining the observer gain matrices are presented. Two simulation examples, including an application example of the truck-trailer model, are provided to demonstrate the advantages of the theoretical results that have been established. In particular, the importance of the use of tuning parameters is discussed. [ABSTRACT FROM AUTHOR]

This paper discusses the problem of stabilization of interval type-2 fuzzy systems with uncertainties, time delay and external disturbance using a dynamic sliding mode controller. The sliding surface function, which is based on both the system's state and control input vectors, is used during the control design process. The sliding mode dynamics are presented by defining a new vector that augments the system state and control vectors. First, the reachability of the addressed sliding mode surface is demonstrated. Second, the required sufficient conditions for the system's stability and the proposed control design are derived by using extended dissipative theory and an asymmetric Lyapunov-Krasovskii functional approach. Unlike some existing sliding mode control designs, the one proposed in this paper does not require the control coefficient matrices of all linear subsystems to be the same, reducing the method's conservatism. Finally, numerical examples are provided to demonstrate the viability and superiority of the proposed design method. [ABSTRACT FROM AUTHOR]

This paper considers the attitude tracking control problem for a rigid body. In order to avoid the complexity and ambiguity associated with other attitude representations (such as Euler angles or quaternions), the attitude dynamics and the proposed control system are represented globally on special orthogonal groups. An adaptive controller based on a Lie subgroup of SO(3) is developed such that the rigid body can track any given attitude command asymptotically without requiring the exact knowledge of the inertia moment. In the presence of external disturbances, the adaptive controller is enhanced with an additional robust sliding mode term by following the same idea within the framework of SO(3). Finally, simulation results are presented to demonstrate efficiency of the proposed controllers. [ABSTRACT FROM AUTHOR]

In this article, an adaptive asymptotic tracking control scheme is proposed for fractional order nonlinear systems (FONSs) with time-varying disturbance. By introducing some well defined smooth functions and the bounded estimation approach, the effects caused by the unknown virtual control coefficients (UVCC) and unknown nonlinear functions are counteracted. For the UVCC, we only need to assume that their lower bounds are positive constants. Fuzzy logic systems (FLSs) are applied to approximate unknown nonlinear functions. Moreover, the fractional directed Lyapunov method is used to prove that the tracking error asymptotically converges to zero. Finally, an illustrative simulation example is applied to verify the superior performance of the presented control algorithms. [ABSTRACT FROM AUTHOR]

In order to solve the control problem of Underwater Vehicle with Manipulator System (UVMS), this paper proposes a finite-time sliding mode control strategy via T-S fuzzy approach. From the general dynamic model of UVMS and considering the influence between the manipulator and the underwater vehicle, hydrodynamic damping, buoyancy and gravity as the fuzzy items, we establish global fuzzy dynamic model and design a closed-loop fuzzy sliding mode controller. We prove the model in theory from two aspects: the reachability of sliding domain and the finite-time boundedness. We also give the solution of the controller gain. A simulation on the actual four joint dynamic model of UVMS with two fuzzy subsystems is carried out to verify the effectiveness of this method. [ABSTRACT FROM AUTHOR]

In this paper, the problem of sliding mode observer (SMO) based sliding mode control (SMC) for nonlinear descriptor delay systems is studied. First, based on the T-S fuzzy dynamic modeling technique, the nonlinear descriptor system is transformed into a combination of local linear models. Then, a integral-type sliding surface (ITSS) based SMO is constructed for the error system. In the sequel, sufficient linear matrix inequality (LMI) conditions are established to ensure the admissibility of the sliding motions and obtain the observer gain matrix. Furthermore, two novel SMC laws are developed to ensure the reachability conditions and stabilize the descriptor systems. Finally, simulations are provided to show the effectiveness of the method. [ABSTRACT FROM AUTHOR]

This article intends to provide an integrated robust synchronization and anti-disturbance control design for a nonlinear multiweighted complex network with the use of fuzzy modeling approach. The network takes the effect of both matched and mismatched disturbances into account, wherein the matched one is unknown and caused by some exogenous systems. In order to estimate the unknown disturbance, a disturbance observer is precisely considered. By exploiting the parallel distributed compensation strategy and the output of disturbance observer, the desired fuzzy rule-based control law is formulated. Based on these settings, the required control gain matrices that affirm asymptotic synchronization of the addressed network are determined with the support of the Lyapunov functional method and extended Wirtinger’s integral inequality. The method of this article can render better system performance than the existing $H_{\infty }$ control method, which is demonstrated via simulations. In addition, a three-dimensional Lorenz chaotic model is employed to certify the applicability of the theoretical findings. [ABSTRACT FROM AUTHOR]

This article investigates the problem of mode‐dependent intermediate variable‐based fault estimation for Markovian jump systems subject to time‐varying delay, exogenous disturbance, process, and sensor faults. The advantages of the proposed design method are: (i) it estimates not only the unknown fault signals, but also the immeasurable states of the system; and (ii) it relaxes the observer matching condition that should be essential for most of the existing fault estimation strategies. In order to facilitate the analysis, the actual system is transformed into an augmented system by including the sensor fault as an auxiliary state. On the basis of which, the intermediate variable and the corresponding observers are established. Following this, two error dynamics are formulated in such a way that a new mode‐ and delay‐dependent boundedness criterion in the probability sense is developed in accordance with the traditional Lyapunov method. Then the theoretical results obtained are validated by using an example based on the F‐404 aircraft engine system. In addition, a comparative study is carried out in the deduced form of the actual system as a special case, where it is shown that the proposed method widens the delay interval compared with some of the recently existing works. [ABSTRACT FROM AUTHOR]

The aim of this article is to analyze the problem of fault estimation for mode-dependent interval type-2 fuzzy systems with quantized output measurements. Different from the existing fault estimation methods requiring the observer matching condition, a new fault estimation technique is proposed, wherein a stochastically intermediate variable subject to the information on operating modes is considered, under which a robust observer is constructed to simultaneously estimate the state and faults. Based on the strategy of linear matrix inequality, sufficient conditions are established to ensure that the states of resulting systems are bounded in probability sense. By offering three illustrative examples, in which two of them are practical models, namely, tunnel diode circuit system and Rössler system, the availability and feasibility of the proposed design method are explained. [ABSTRACT FROM AUTHOR]

In this paper, based on the Takagi–Sugeno fuzzy model approach, a novel output feedback control strategy is developed for a class of continuous-time nonlinear time delay systems via modified repetitive control scheme. The main objective of this paper is to design a fuzzy rule-based modified repetitive controller such that the system output can track any given periodic reference signal even in the presence of periodic disturbances. For this purpose, by employing fuzzy-dependent Lyapunov–Krasovskii functional together with the free-weighting matrix technique, a new set of sufficient conditions is presented in terms of linear matrix inequalities to guarantee the robust stability of the resulting closed-loop system. Based on these conditions and using internal model principle, it is shown that the system output tracks the given reference input within the desired error. Finally, two application-oriented examples are presented to validate the obtained theoretical results in which the proposed control design scheme gives better performance over the existing control scheme. [ABSTRACT FROM AUTHOR]

Based on state feedback control approach and disturbance observer method, a new composite synchronization control strategy is presented in this study for a class of delayed coupling complex dynamical networks with two different types of disturbances. Herein, one of the disturbances is produced by an exogenous system which acts through the input channel, while the other is usual norm-bounded. The main objective of this study is to exactly estimate the disturbance at the input channel, whose output is integrated with the state feedback control law. In this study, the composite control strategy is designed in two forms according to the present and past states' information about the system. By applying the Lyapunov–Krasovskii stability theory, a new set of sufficient conditions is obtained for the existence of both control strategies separately through the feasible solution of a series of matrix inequalities. The superiority and validity of the developed theoretical results are demonstrated by two numerical examples, wherein it is shown that the proposed control strategy is capable of handling multiple disturbances in the synchronization analysis. [ABSTRACT FROM AUTHOR]

In this study, the authors precisely concentrate on the issue of state estimator‐based non‐fragile reliable control design of the vehicle dynamics in critical situations via the extended dissipative theory. In particular, the vehicle dynamics for rollover mitigation with input time delay and the state estimator are represented by the Takagi–Sugeno (T‐S) fuzzy model. Moreover, by constructing a suitable Lyapunov–Krasovskii functional, sufficient conditions for asymptotic stability and extended dissipativity of the proposed T‐S fuzzy control system are formulated in terms of linear matrix inequalities (LMIs) such that the estimated state values are exactly synchronised with the actual state values of the considered vehicle model. Also, a non‐fragile reliable control design method is then presented via the formulated LMI‐based conditions, which can satisfactorily prevent the vehicle rollover in critical situations. Finally, the proposed theoretical results are verified through simulations wherein the significance and importance of the designed non‐fragile controller are clearly illustrated. [ABSTRACT FROM AUTHOR]

A nondeterministic actuator fault model-based reliable control design method is presented for the leader-following consensus of a multiagent system (MAS) subject to input time-varying delay and the nonlinear phenomenon through the observer framework. Notably, a more generalized practical actuator fault model is proposed where the faults of each actuator are assumed to occur randomly and the fault rates are characterized by stochastic variables that satisfy certain probability conditions. To trace the leader dynamics, a reliable observer-based state feedback consensus algorithm is developed for the pursuing agents. After that, in light of graph theory and the Lyapunov–Krasovskii stability theorem, the required conditions are achieved to guarantee the leader-following consensus of the considered MAS, and then the corresponding reliable controller design method is proposed. Furthermore, simulations are eventually conducted to exhibit the efficiency of the newly developed control scheme, where it is shown that the obtained conditions guarantee the consensus of the considered MAS in the case of possible actuator faults. [ABSTRACT FROM AUTHOR]

The problem of robust nonfragile synchronization is investigated in this paper for a class of complex dynamical networks subject to semi-Markov jumping outer coupling, time-varying coupling delay, randomly occurring gain variation, and stochastic noise over a desired finite-time interval. In particular, the network topology is assumed to follow a semi-Markov process such that it may switch from one to another at different instants. In this paper, the random gain variation is represented by a stochastic variable that is assumed to satisfy the Bernoulli distribution with white sequences. Based on these hypotheses and the Lyapunov-Krasovskii stability theory, a new finite-time stochastic synchronization criterion is established for the considered network in terms of linear matrix inequalities. Moreover, the control design parameters that guarantee the required criterion are computed by solving a set of linear matrix inequality constraints. An illustrative example is finally given to show the effectiveness and advantages of the developed analytical results. [ABSTRACT FROM AUTHOR]

This study examines the problem of fault‐tolerant sliding mode control (SMC) design subject to actuator saturation for a class of Takagi–Sugeno fuzzy systems with time‐varying delay and external disturbances. Our main attention is to propose the fault‐tolerant SMC such that for given any initial condition, the system trajectories are forced to reach the sliding surface within a finite time. On the basis of the SM surface and Lyapunov stability theorem, a new set of sufficient conditions in terms of linear matrix inequalities (LMIs) is established to not only guarantee the passivity and asymptotically stability of the resulting closed‐loop system in the designed sliding surface, but also cover the issues of actuator saturation and performance constraints. Then, the desired gain matrix of the fault‐tolerant SMC is obtained in respect of the previously established LMIs such that the reachability of the predefined sliding surface is ensured. It is worth pointing out that the obtained sufficient conditions can preserve the trade‐off between the maximisation of admissible upper bound of time‐varying delay and enlarging the estimation about the domain of attraction for the closed‐loop system. Eventually, the effectiveness and robustness of the proposed control approach are demonstrated via simulation results. [ABSTRACT FROM AUTHOR]

In this paper, the consensus problem of uncertain nonlinear multi-agent systems is investigated via reliable control in the presence of probabilistic time-varying delay. First, the communication topology among the agents is assumed to be directed and fixed. Second, by introducing a stochastic variable which satisfies Bernoulli distribution, the information of probabilistic time-varying delay is equivalently transformed into the deterministic time-varying delay with stochastic parameters. Third, by using Laplacian matrix properties, the consensus problem is converted into the conventional stability problem of the closed-loop system. The main objective of this paper is to design a state feedback reliable controller such that for all admissible uncertainties as well as actuator failure cases, the resulting closed-loop system is robustly stable in the sense of mean-square. For this purpose, through construction of a suitable Lyapunov-Krasovskii functional containing four integral terms and utilization of Kronecker product properties along with the matrix inequality techniques, a new set of delay-dependent consensus stabilizability conditions for the closed-loop system is obtained. Based on these conditions, the desired reliable controller is designed in terms of linear matrix inequalities which can be easily solved by using any of the effective optimization algorithms. Moreover, a numerical example and its simulations are included to demonstrate the feasibility and effectiveness of the proposed control design scheme. © 2016 Wiley Periodicals, Inc. Complexity 21: 138-150, 2016 [ABSTRACT FROM AUTHOR]

This article examines the reliable L2 - L∞ control design problem for a class of continuous-time linear systems subject to external disturbances and mixed actuator failures via input delay approach. Also, due to the occurrence of nonlinear circumstances in the control input, a more generalized and practical actuator fault model containing both linear and nonlinear terms is constructed to the addressed control system. Our attention is focused on the design of the robust state feedback reliable sampled-data controller that guarantees the robust asymptotic stability of the resulting closed-loop system with an L2 - L∞ prescribed performance level γ > 0, for all the possible actuator failure cases. For this purpose, by constructing an appropriate Lyapunov-Krasovskii functional (LKF) and utilizing few integral inequality techniques, some novel sufficient stabilization conditions in terms of linear matrix inequalities (LMIs) are established for the considered system. Moreover, the established stabilizability conditions pave the way for designing the robust reliable sampled-data controller as the solution to a set of LMIs. Finally, as an example, a wheeled mobile robot trailer model is considered to illustrate the effectiveness of the proposed control design scheme. © 2016 Wiley Periodicals, Inc. Complexity 21: 309-319, 2016 [ABSTRACT FROM AUTHOR]