This article investigates the rendezvous optimization problem for second-order multiagent systems. This task is typically framed as a convex optimization with equality constraints, which must also adhere to the system dynamics. Traditional neurodynamic approaches may lead to strong oscillations or instability due to uncoordinated intrinsic system dynamics. Inspired by proportional-derivative control and accelerated optimization techniques, a neurodynamic approach with a generalized compensation term (NGCT) is proposed to achieve oscillation suppression. The advantages of the approach include: 1) using state derivatives to provide predictions for oscillation suppression and 2) employing a compensation term based on the equality constraint coefficient matrix$A$to enhance constraint matching sensitivity. The transformation properties of$A$enable convergence to specified geometries. It is proven that the proposed approach exponentially converges to the optimal solution. Numerical experiments have demonstrated the effectiveness of the proposed approach in different rendezvous optimization problems.

This article studies a neural network (NN)-based adaptive fault-tolerant control (FTC) scheme to solve the actuator failure problem of nonlinear systems with input saturation and time-varying state constraints. The introduction of asymmetric Barrier-Lyapunov function (BLF) makes controller design more difficult due to the occurrence of actuator saturation and failure. Therefore, the method proposed in this article proposes a saturation fault-tolerant controller with constraint compensation information under the backstepping control design framework to solve the state constraint asymmetry problem. By design-improved asymmetric time to change the BLF, the design of the state constraint controller will become more realistic and constraints will be weakened. Actuator failure in this article considers deviation failure and loss of effectiveness. Based on the nature of the index function, the improved BLF can make the boundaries of state constraints smaller and smaller, and the boundaries of constraints can change with the expected trajectory when satisfying the input saturation. Therefore, this article solves the FTC problem of non -linear strict feedback systems, overcoming the impact of non -symmetrical state constraints and input saturation on system performance. Simulation verified the feasibility of this control method.Note to Practitioners—This work implements asymmetrically constrained fault-tolerant control under actuator sensor failure for a nonlinear system with input saturation. Input saturation and state-constrained control asymmetries caused by actuator failures are still rarely studied. This article proposes an improved BLF to solve the asymmetry problem under actuator failure. A fault-tolerant control method is designed considering multivariable conditions and control input constraints, which covers information on actuator faults and amplitude saturation. Based on the properties of the exponential function, the improved BLF can make the bounds of the state constraints smaller and smaller, and the bounds of the constraints can change with the desired trajectory while satisfying input saturation. The proposed method has a general structure and has the potential to be implemented in real systems.

In the existing research on finite-time synchronization (FTS) control for fractional-order coupled neural networks (FOCNNs), signum function plays a crucial role in controller design. The discontinuity of the signum function causes the chattering phenomenon to worsen the performance of controlled system. In this paper, a saturation function is utilized instead of signum function in controller design, overcoming the shortcomings of previous control schemes. Due to the introduction of the saturation function, the system exhibits different dynamic behaviors within and outside the boundary of the saturation function. To further analyze this effect, the two-stage fractional-order nonlinear differential inequalities (TFNDIs) are established, which provides an effective tool for handling saturation function-based FTS control for FOCNNs. At last, the validity of proposed theoretical results is demonstrated through numerical simulations, which show that the chattering has been significantly suppressed.

This article considers the hierarchical containment control (HCC) for flexible mirrored collaboration, which accommodates the bipartite cluster consensus behavior in two symmetric convex hulls formed by multiple leaders. First, to achieve the mirrored collaboration in symmetric convex hulls, the layer-signed digraph is generated by involving the antagonistic interaction. Benefiting from the hierarchical structure, the antagonistic interaction in the assistant-layer replaces the assumption of in-degree balance for the existing cluster consensus issues. Second, the existing types of control protocols and the framework of cooperative output regulation limit the achievement of the studied hierarchical mirrored collaboration. To solve this problem, the hierarchical cooperative output regulation is extended based on the formulated hierarchical mirrored collaborative errors. Third, the layer-signal compensator is designed estimating the states of leaders as well as guaranteeing the convergence of collaborative behaviors. Combining with the designed layer-signal compensator, a novel HCC protocol is proposed so that the bipartite cluster consensus behavior can be achieved simultaneously in two symmetric convex hulls. Finally, theoretical results are verified by performing the numerical simulation.

Nonconvexity is a usually overlooked factor in economic dispatch (ED). Enhancing the nonconvexity of the objective function leads traditional convex optimization algorithms easily to fall into the local optimum. To address the above problem, a penalty removal search algorithm (PRSA) is proposed for ED nonconvex optimization. It is composed of two distributed optimization algorithms embedded in a reinforcement learning framework. In Phase I of PRSA, a distributed optimization algorithm with projection operators is designed. It uses fewer variables to locate the region where the optimal solution belongs by the cooperative Q-learning. In Phase II of PRSA, the sigmoid function serves as a penalty function to form the second distributed optimization algorithm. This is used to skip the searched solutions and allow the algorithm to continue searching for more feasible solutions. The PRSA solves the problem that the algorithm misses feasible solutions when the nonconvex coefficients increase. Finally, the effectiveness of the PRSA is verified by numerical examples.

This brief investigates the stability problem of recurrent neural networks (RNNs) with time-varying delay. First, by introducing some flexibility factors, a flexible negative-determination quadratic function method is proposed, which contains some existing methods and has less conservatism. Second, some integral inequalities and the flexible negative-determination quadratic function method are used to give an accurate upper bound of the Lyapunov-Krasovskii functional (LKF) derivative. As a result, a less conservative stability criterion of delayed RNNs is derived, whose effectiveness and superiority are finally illustrated through two numerical examples.

This article investigates the practical fixed-time synchronization of uncertain coupled neural networks via dual-channel event-triggered control. Contrary to some previous studies, the bipartite synchronization of signed graphs representing cooperative and antagonistic interactions is studied. The communication channel is introduced into deception attacks, which are described by Bernoulli's stochastic variables. Based on the concept of two channels, event-triggered mechanisms are designed for sensor-to-controller and controller-to-actuator channels to reduce communication consumption and controller update consumption as much as possible. Lyapunov and comparison theories are used to derive synchronization criteria and explicit expression of settling time. An example of Chua's circuit system is presented to demonstrate the feasibility of the obtained theoretical results.

In this article, the output synchronization of heterogeneous multiagent systems with sensor faults is considered. To detect and tolerate the faults, a number of detection mechanisms and fault-tolerant controllers (FTCs) have been proposed. Whereas, the existing methods require the precise model and they cannot be used when model information is unknown. Moreover, some designed parameters are required for the fault information in existing FTCs. To solve the above problems, the data-based detection mechanism and data-based FTC are proposed in this article. The disadvantage of inapplicability to unknown system model is overcome by the proposed methods. Furthermore, the fault information in the proposed controller is directly acquired from system data, where the additional parameters to be designed are avoided. Finally, the validity of the presented methods is shown via simulation example.

In this article, the data-based output consensus of discrete-time multiagent systems under switching topology (ST) is studied via reinforcement learning. Due to the existence of ST, the kernel matrix of value function is switching-varying, which cannot be applied to existing algorithms. To overcome the inapplicability of varying kernel matrix, a two-layer reinforcement learning algorithm is proposed in this article. To further implement the proposed algorithm, a data-based distributed control policy is presented, which is applicable to both fixed topology and ST. Besides, the proposed method does not need assumptions on the eigenvalues of leader's dynamic matrix, it avoids the assumptions in the previous method. Subsequently, the convergence of algorithm is analyzed. Finally, three simulation examples are provided to verify the proposed algorithm.

This brief studies the stability problem of recurrent neural networks with time-varying delay. Based on one tunable parameter$\alpha $, a flexible terminal interpolation method is proposed to change the interval with fixed terminals as$2^{k+1}-3$ones with flexible terminals. Associated with the flexible subintervals, a novel Lyapunov–Krasovskii functional with more delay information is constructed. In order to estimate the Lyapunov–Krasovskii functional, a quadratic reciprocally convex inequality is proposed, which covers some existing ones as its special cases. Based on these ingredients, a new stability criterion is derived in the form of linear matrix inequalities. A comprehensive comparison of results is given to illustrate the newly proposed stability criterion.

This article focuses on the event-triggered consensus control (ETCC) issue of the time-varying delayed leader-following nonlinear multiagent systems (TVDLFNMASs). In order to minimize the influence on uncertain factors of the information transmission and the data information loss, the switching topologies are constructed as the generally uncertain Markovian jumping forms whose transition rates include completely unknown elements and estimate values of uncertain elements. In addition, the event-triggered (ET) transmission strategy is given based on the threshold parameter and the ET matrix to relieve the communication burden of TVDLFNMASs. The new leader-following (LF) consensus conditions and control gains are obtained based on ET strategy. Finally, the effectiveness of the ET consensus criteria is demonstrated in the simulation section.

This article reports the synchronization control of discrete-time complex networks using an event-triggered method. The main contributions are twofold: 1) a discrete-time scenario of the dynamic periodic event-triggered mechanism is developed to schedule the transmissions of measurements. The proposed mechanism monitors the synchronization error in a periodic manner, which is beneficial to reduce the calculation resources of sensors. Simultaneously, the proposed mechanism increases the triggering threshold so that it contributes to enlarging the average interevent interval and 2) a new Lyapunov functional is developed to deal with the periodic samplings. On the one hand, the proposed functional involves a delay-dependent term, which is convenient to formulate the synchronization criterion by the delay analysis technique. On the other hand, the functional takes the sawtooth constraint of periodic samplings into consideration by introducing a piecewise functional. Finally, a succinct criterion is derived such that the considered networks are synchronized with a predetermined error level. A simulation example is provided to show our advantages in comparison with the existing approaches.

The distributed resilient tracking problem for multiagent systems (MASs) is investigated in the presence of actuator/sensor faults over directed topology. Both actuator fault and sensor fault are taken into account. Meanwhile, using the local information, the fault compensators are introduced. Then, based on the fuzzy-logic systems (FLSs) and modification technique of adaptive law, a novel distributed adaptive resilient control protocol is developed, which can compensate the effect of faults on the actuator and sensor. It turns out that all signals of MASs are bounded, while the tracking errors enter an adjustable bounded region around the origin. Toward the end, two simulations are provided to validate the effectiveness of the theoretical results.

In this brief, the output synchronization of multi-agent systems (MAS) with actuator faults is studied. To detect the faults, a backward input-driven fault detection mechanism (BIFDM) is presented for MAS. Different from previous works, the system operation can be monitored without system model by the proposed BIFDM. Then to tolerate the faults, a novel fault-tolerant controller (FTC) based on reinforcement learning (RL) and backward information (BI) is proposed. Particularly, by the combination of BI, the design of additional parameters for faults is avoided. Furthermore, the proposed FTC overcomes the shortcoming that the previous FTCs cannot be applied to heterogeneous MAS. Finally, two simulation examples are given to verify the effectiveness of the proposed methods.

This brief investigates the problem of state estimation of quaternion-valued neural networks (QVNNs) with time-varying delays. First, by extending the Jensen inequality to quaternion domain, an extended Jensen inequality with quaternion term is derived. Second, a class of proportional-integral state estimator (PISE) with exponential decay term is proposed. Then, by constructing a suitable Lyapunov-Krasovskii functional (LKF), some sufficient conditions are obtained to ensure the existence of the designed PISE and the gain matrices of the designed PISE can be directly computed. Simulations are given to illustrate the advantage of the proposed method.

This article focuses on the synchronization problem of delayed inertial neural networks (INNs) with generally uncertain Markovian jumping and their applications in image encryption. The random connection weight strengths and generally uncertain Markovian are discussed in the INNs model. Compared with most existing INNs models that have constant connection weight strengths, our model is more practical because connection weight strengths of INNs may randomly vary due to the external and internal environment and human factor. The delay-range-dependent synchronization conditions (DRDSCs) could be obtained by adopting the delay-product-term Lyapunov-Krasovskii functional (DPTLKF) and higher order polynomial-based relaxed inequality (HOPRII). In addition, the desired controllers are obtained by solving a set of linear matrix inequalities. Finally, two examples are shown to demonstrate the effectiveness of the proposed results.

This brief addresses the stability analysis problem of a class of delayed recurrent neural networks (DRNNs). In previously published studies, the slope information of activation function (SIAF) is just reflected in three slope information matrices, i.e., the upper and lower boundary matrices and the maximum norm matrix. In practice, there are$2^{n}$possible combination cases on the slope information matrices. To exploit more information about SIAF, first, an activation function separation method is proposed to derive$n$slope-information-based uncertainties (SIBUs) containing SIAF; second, a quadratic matrix convex combination approach is proposed to dispose$n$SIBUs using$2^{n}$combination slope information matrices. Third, a stability criterion with less conservatism is established based on the proposed approach. Finally, two simulation examples are used to testify the validity of theoretical results.

This article investigates the finite-time extended dissipative filtering for singular T–S fuzzy Markov jump systems with time-varying transition probabilities (TPs). The time-varying TPs are considered to reside in a polytope. By resorting to a generalized performance index, the$H_{\infty }$,$L_{2}-L_{\infty }$, passive, and dissipative performance can be solved in a unified framework. Combining the free-weighting method and the proposed recursive method, a sufficient condition on singular stochastic extended dissipative finite-time boundedness (SSEDFTB) for a fuzzy filtering error system is obtained. By proposing a decoupling principle called double variables-based decoupling principle (DVDP) and a variable substitution principle (VSP), a novel condition on the existence of the fuzzy filter is presented in terms of linear matrix inequalities (LMIs). Compared with the existing works, the assumption on state variables and the constraints of slack matrices are overcome, which leads to more practical and less conservative results. A practical example is provided to demonstrate the effectiveness of the design methods.

This article investigates the integral sliding-mode control (SMC) problem for T-S fuzzy systems via the periodic event-triggered method. First, in order to remove the assumption that the inter-execution time has a uniform upper bound, a novel sliding variable error function is added into the event-triggering mechanism. Second, in order to avoid the extra information transmission, a new sliding-mode switching function consisting of the triggering state information is proposed to design the event-triggered integral SMC (ISMC) law. In addition, the ultimate boundedness of sliding motion can be ensured via using a designed event-triggered ISMC law. A sufficient condition of boundedness is given in the form of linear matrix inequality, which is employed to solve the controller gain matrix. Finally, the effectiveness of theoretical results can be illustrated via three illustrative examples.

In this article, a new design method based on the echo state network with time-varying reservoir parameter (TVRP-ESN) is proposed to optimize the proportional-integral-derivative (PID) controller parameters for a class of discrete-time systems with time delay. The TVRP-ESN can quickly obtain the PID controller parameters to meet the control performance of the system. According to the network learning and approximation ability of TVRP-ESN, the output weights and the reservoir parameters of TVRP-ESN can be synchronously updated, and then the TVRP-ESN can improve the convergence speed of determining the PID controller parameters. In order to update the output weights and the reservoir parameters of TVRP-ESN, the partial derivative of the system output error is used. Three simulation examples are used to show the effectiveness of the proposed method.

This article investigates the stability analysis and stabilization problems for fractional-order T–S fuzzy systems via fuzzy Lyapunov function method. A membership-function-dependent fuzzy Lyapunov function instead of the general quadratic Lyapunov function is employed to obtain the stability and stabilization criteria. Different from the general quadratic Lyapunov function, the fuzzy Lyapunov functions contain the product of three term functions. Since the general Leibniz formula cannot be satisfied for fractional derivative, the current results on the fractional derivative for the quadratic Lyapunov functions cannot be extended to the fuzzy Lyapunov functions. Therefore, to estimate the fractional derivative of fuzzy Lyapunov functions, the fractional derivative rule for the product of three term functions is proposed. Based on the proposed fractional derivative rule, the corresponding stability and stabilization criteria are established, which extend the existing results. Finally, two simulation examples are presented to illustrate the effectiveness of the proposed theoretical analysis.

In this article, stability analysis and controller synthesis problems for Takagi–Sugeno (T–S) fuzzy systems with time-varying delay are studied. A generalized parameter-dependent reciprocally convex inequality (GPDRCI) is presented to handle the derivative of triple integral terms, which is more general than some existing ones. By choosing suitable flexible polynomials with tunable parameters, novel flexible polynomial-based functions (FPFs) are proposed in delay-product types, which overcome the incompletely slack matrices, higher-order time delay and insufficient parameters in the existing functions. Benefitting from completely slack matrices and lower-order time delay, coupling relationship among system states and time delay is fully linked. Based on the GPDRCI and FPFs, a stability condition is derived for T–S fuzzy systems. Based on the stability criterion, considering both the time-varying delay and its bounds, a generalized memory controller is designed for T–S fuzzy systems, which covers the memoryless and traditional memory ones as its special cases. In addition, the constraints on introduced slack matrices in some existing works are avoided with the help of a matrix inequality decoupling technique. These provide extra free dimensions in the solution space. Some examples are employed to illustrate the effectiveness of the proposed methods.

In this article, we investigate the periodic event-triggered synchronization of discrete-time complex dynamical networks (CDNs). First, a discrete-time version of periodic event-triggered mechanism (ETM) is proposed, under which the sensors sample the signals in a periodic manner. But whether the sampling signals are transmitted to controllers or not is determined by a predefined periodic ETM. Compared with the common ETMs in the field of discrete-time systems, the proposed method avoids monitoring the measurements point-to-point and enlarges the lower bound of the inter-event intervals. As a result, it is beneficial to save both the energy and communication resources. Second, the "discontinuous" Lyapunov functionals are constructed to deal with the sawtooth constraint of sampling signals. The functionals can be viewed as the discrete-time extension for those discontinuous ones in continuous-time fields. Third, sufficient conditions for the ultimately bounded synchronization are derived for the discrete-time CDNs with or without considering communication delays, respectively. A calculation method for simultaneously designing the triggering parameter and control gains is developed such that the estimation of error level is accurate as much as possible. Finally, the simulation examples are presented to show the effectiveness and improvements of the proposed method.

This brief investigates the reachable set estimation problem of the delayed Markovian jump neural networks (NNs) with bounded disturbances. First, an improved reciprocally convex inequality is proposed, which contains some existing ones as its special cases. Second, an augmented Lyapunov-Krasovskii functional (LKF) tailored for delayed Markovian jump NNs is proposed. Thirdly, based on the proposed reciprocally convex inequality and the augmented LKF, an accurate ellipsoidal description of the reachable set for delayed Markovian jump NNs is obtained. Finally, simulation results are given to illustrate the effectiveness of the proposed method.

This article studies the problem of the stability for Markovian neural networks (MNNs) with time delay. The transition rate is considered to be generally hybrid, which treats those existing ones as its special cases. The introduced generally hybrid transition rates (GHTRs) make these systems more general and practical. Apropos of the GHTRs, a double-boundary approach rather than the traditional estimation method is introduced to make full use of the error information in GHTRs. In order to fully capture system information, a parameter-type-delay-dependent-matrix (PTDDM) approach is proposed, in which the PTDDM approach removes some zero components on slack matrices in previous works. Thus, the PTDDM approach can fully link the relationship among time delay and state-related vectors. Based on these ingredients, a novel stochastic stability condition is proposed for MNNs with GHTRs. A numerical example is illustrated to demonstrate the effectiveness of the proposed approaches.

This article reports the synchronization of coupled neural networks (CNNs) by devising an event-dependent intermittent pinning controller. In this article, the Lyapunov–Krasovskii functional (LKF) is taken as an important element of the controller. Different from the preset technique in common intermittent control, the work/rest time is governed by an event-dependent intermittent mechanism which is described by the LKF and three partitions of non-negative real region. More specifically, the pinning controller is imposed on the CNNs only when the trajectory of LKF runs into the presupposed working regions. Under the proposed framework of intermittent control, a simple sufficient condition is formulated to guarantee the synchronization of CNNs. A numerical example is finally provided to demonstrate the validity of the theoretical results.

The fixed-time control problem for a class of interconnected systems is studied in this article via an asynchronous event-triggered control strategy, in which all subsystems are interconnected by discontinuous interactions. Especially, due to the discontinuity of interactions, the existence of solutions for the concerned systems is solved via the framework of differential inclusion. Unlike the common ones, the asynchronous event-triggered mechanism in this article generates samplings, triggering events, and control updates asynchronously among multiple subsystems. More significantly, due to the discontinuity of the interactions, a fixed-time discontinuous control law and a specific event-triggered scheme are designed to stabilize this class of interconnected systems in a fixed time. In addition, the interexecution time is lower bounded by a positive constant, and it is assured that the Zeno behavior will not happen. Finally, the effectiveness of the obtained results is illustrated by an example.

This article is concerned with the asynchronous reliable extended dissipative filtering problem for a class of continuous-time T–S fuzzy Markov jump systems. The modes of the encountered sensor failures and the designed filter are considered to be asynchronous with the original systems, which can be described by two mutually independent hidden Markov processes. By proposing double variables-based decoupling principle and variable substitution principle, a new condition is presented to guarantee the filtering error system to be stochastically stable and extended dissipative. Compared with the existing works, the proposed method does not impose constraints on Lyapunov variables and slack variables, and some unnecessary constraints on the system structure are removed. These directly lead to less conservative and more general results. An example is provided to illustrate the effectiveness of the proposed design method.

This paper presents a sliding mode dynamic surface control strategy for multi-machine power systems with static var compensator (SVC) to design the controller of the generator excitation system. Firstly, compared with the existing control methods, the combination of sliding mode control and dynamic surface control improves the robustness of the system and avoids the “explosion of complexity” problems. Subsequently, the fuzzy logic system is introduced to estimate the unknown continuous function in power system, and the norm of the weight vector is used to replace the estimation of the entire weight vector. In this way, computational burden will be reduced. In addition, the influences of unknown time delays and dead-zones are considered. Finite cover lemma is introduced to deal with unknown time delays, which enables arbitrarily small L∞ tracking performance. The unknown dead-zone is converted into the sum of linear dead zone and bounded nonlinear dead zone. Finally, the simulation results are provided to validate the feasibility and effectiveness of the proposed control strategy.

This article visits the intermittent quasisynchronization control of delayed discrete-time neural networks (DNNs). First, an event-dependent intermittent mechanism is originally designed, which is described by the Lyapunov function and three non-negative real regions. The distinctive feature is that the controller starts to work only when the trajectory of the Lyapunov function goes into the presupposed work region. The proposed method fundamentally changes the principle of the existing intermittent control schemes. Under the proposed framework of the intermittent mechanism, the work/rest time of the controller is aperiodic, unpredictable, and initial value dependent. Second, several succinct sufficient conditions in terms of linear matrix inequalities are developed to achieve the quasisynchronization of the considered DNNs. A simple optimization algorithm is established to compute the control gains and the Lyapunov matrices such that synchronization error is stabilized to the smallest convergence region. Finally, two simulation examples are provided to demonstrate the feasibility of the designed intermittent mechanism.

This article concentrates upon the problem of practical fixed-time consensus for second-order nonlinear multiagent systems (MASs) under directed communication topology. The convergence time is independent of the initial condition. Both loss of effectiveness and bias fault are taken into account. Meanwhile, fuzzy-logic systems are introduced to approximate the unknown nonlinear functions. By the adding-a-power-integrator method, a distributed fuzzy adaptive practical fixed-time fault-tolerant control scheme is proposed. Then, the leader can be tracked in a settling time, and the consensus tracking errors converge to an adjustable neighborhood of the origin. Finally, two simulations are given to further illustrate the effectiveness of the theoretical result.

In this article, impulsive control issue of the interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy interconnected system is investigated via dynamic event-triggered mechanism (DETM), wherein deception attacks are considered. First of all, a more constrictive DETM is proposed, in which an exponential attenuation function is introduced to approximate the system states such that the error part is reconstructed. Then, under this exponential-type DETM, a new event-based impulsive control strategy is designed, which not only include the impulsive control on event instants, but also a state feedback control part with time-varying gains during the interval time of two consecutive events. The core idea is that the added feedback part can be regarded as a “bridge,” which connects the two consecutive impulse injections. Besides, input-to-state stability of the concerned system is investigated by transforming the attack signals into a residual term, so that some stability criteria are derived in spite of the unpredictable deception attacks. The nonexistence of Zeno behaviors is also guaranteed indirectly by utilizing the comparison relationship between DETM and its static counterpart. Finally, the validity of the proposed control strategy is verified by two illustrative examples.

The data loss and corresponding false fault features of single-phase or multiphase detection signals caused by sensors is a relatively troublesome problem, which can increase the difficulty to the fault diagnosis of switch fault and open-phase fault of inverter, and even can lead to false alarm. For these problems, a complementary virtual mirror fault diagnosis method for microgrid inverter is proposed to improve them. First, the virtual mirrors are constructed, which contain fault information in different angle. Second, a cross comparison processing method is used to gain the cross variables and corresponding mirror cross variables by the obtained virtual mirrors and detected signals, which can extract and normalize fault components from different angle in the same way, respectively. Thus, it can reduce the impact of data loss. Third, the self-correction fault degree (scf) and averages fault degree (af) are calculated. Specially, scf can further reduce the influence of data loss and false fault features through the complementarity of cross variables and mirror cross variables. For af, it is a steady-state expression of fault degree, which can reduce the fluctuation of fault degree variable and the possibility of false alarm. Then, fault detection is implemented through the joint decision of scf and af. Finally, the fault is located by the fault detection results and the extracted mirror complementary location information. Compared with the existing fault diagnosis methods, it not only can diagnose switch fault of inverter, but also can have certain robustness for single-phase or multiphase data loss. Meanwhile, it also has relatively fewer parameters and the lower difficulty of debugging, which are conducive to practical application. The effectiveness of the proposed method is validated by the experiment results.

This brief studies the problem of extended dissipativity analysis for the Markovian jump neural networks (MJNNs) with time-varying delay. A double-integral-based delay-product-type (DIDPT) Lyapunov functional is first constructed in this brief, which makes full use of the information of time delay. Moreover, some unnecessary constraints on the system structure are removed, which leads to more general results. A numerical example is employed to illustrate the advantages of the proposed method.

In this article, the adaptive fault-tolerant control (FTC) problem is solved for a switched resistance-inductance-capacitance (RLC) circuit system. Due to the existence of faults which may lead to instability of subsystems, the innovation of this article is that the unstable subsystems are taken into account in the frame of output constraint and unmeasurable states. Obviously, there are not any unstable subsystems in unswitched systems. The unstable subsystems will involve many serious consequences and difficulties. Since the system states are unavailable, a switched state observer is designed. In addition, the fuzzy-logic systems (FLSs) are employed to approximate unknown internal dynamics in the controller design procedure. Then, the barrier Lyapunov function (BLF) is exploited to guarantee that the system output satisfy its constrained interval. Moreover, by using the average dwell-time method, all signals in the resulting systems are proofed to be bounded even when faults occur. Finally, the proposed strategy is carried out on the switched RLC circuit system to show the effectiveness and practicability.

This paper investigates the problem of adaptive fault-tolerant tracking control for the multiagent systems (MASs) under the time-varying actuator faults and bounded unknown control input of the leader. On the basis of the local state information of neighboring agents, an adaptive fault-tolerant control protocol, which consists of the adaptive estimation of faults, is constructed to compensate for the loss of actuator effectiveness in the leader-follower consensus of MASs. Moreover, the modification term in the adaptive estimation can avoid high-frequency oscillations. It is shown that the tracking errors converge to a neighborhood around the origin in the presence of actuator faults, and the performance of the tracking problem is improved. Furthermore, the protocol is distributed in the sense that the coupling gains are independent. Finally, two examples are given to show the effectiveness of the proposed control protocol.

An event-triggered sliding-mode control problem is investigated for a class of multiple-input Takagi-Sugeno (T-S) fuzzy systems via designing a linear switching function. An assumption that all local linear systems share a common input matrix is removed. Then, a novel event-triggered sliding-mode controller with asynchronous premise variables is designed, which can ensure that the trajectory of multiple-input T-S fuzzy systems can be driven onto the region near the sliding surface after finite time. A sufficient condition is established to guarantee the stability of sliding motion, and the sliding-mode controller gain is obtained by solving a set of linear matrix inequalities. The positive lower bound of the interexecution time can be ensured, which means that there is no Zeno phenomenon. In the end, the advantages and effectiveness of the theoretical results are illustrated by two examples.

This paper investigates the fixed-time stabilization for IT2 T-S fuzzy interconnected systems via event-triggered mechanism. In order to reduce the amount of triggering events, an exponential gain method is proposed. The main novelty of this new method lies in the introduction of an exponential term, which makes control gains alterable in the interval of two consecutive event times. Then, by designing controllers with exponential gains, some sufficient conditions are derived which guarantee the fixed-time stabilization of the concerned system. Since sign functions are no longer contained in the newly designed controller, the chattering phenomena are also avoided. Additionally, the existence of a positive lower bound for the inter-execution is verified, which implies that the concerned system does not exhibit Zeno behaviors. Finally, several illustrative examples are provided to show the effectiveness of the main results.

Fault diagnosis of a microgrid inverter is susceptible to asymmetric interference such as overcurrent component and bias component. It may lead to uncertain fluctuation of diagnosis features, even false alarm and erroneous triggering of protection units. Therefore, for a microgrid inverter, a robust fault diagnosis algorithm is necessary to cope with such asymmetric interference. Motivated by this observation, first, a new fault feature extraction method is proposed in this paper by the trend relationship of adjacent fold lines for data curve. It can be used to extract the fault feature and it is not affected by asymmetric interference. Second, a trend encoding method is proposed to encode the trend feature of a fold line, which is well visualized, easily identified, stored, and calculated. Third, two main indexes are calculated by the encoded features to represent the degree of abnormal and location information. Fourth, the diagnosis results are realized through the logical relation operations. Compared with the existing fault diagnosis algorithms, multiswitches fault can be accurately diagnosed in the case of asymmetric interference. Finally, the detailed experiment results and comparisons are shown to validate the proposed algorithm.

In this paper, a decentralized neural network (NN) output feedback fault tolerant control (FTC) problem is addressed for a class of multi-input multi-output systems with actuator fault. In order to avoid the noncausal problem, the original system is transformed into an input-output expression in accordance with the diffeomorphism theory. Then, in order to establish a quick response to the fault, the fault tolerant controller with minimum learning parameters has been designed such that the semiglobal uniform ultimate boundedness of all the variables in the resulting closed-loop systems can be guaranteed. Finally, the output feedback FTC approach is applied to the interconnected CSTRs, and the comparisons with existing methods are provided to show the effectiveness of the proposed strategy.

In this paper, the stability problem of sampled data Takagi-Sugeno fuzzy control systems with packet dropouts is investigated. A sampling-dependent time-varying Lyapunov function (SDTVLF) is constructed to analyze the stability problem of the system and a switched system approach is proposed to model the packet dropouts phenomenon. On this basis, by dividing the sampling input available interval and unavailable interval into several segments, the matrix functions of the SDTVLF are chosen to be continuous piecewise linear. Then, by using the proposed SDTVLF approach, computable convex conditions are obtained for the sampling input unavailable interval and the sampling input available interval in framework of dwell time. By confining the sampling input unavailable interval with an upper bound and confining the sampling input available interval with a lower bound, the SDTVLF is always decreasing in all sampling input available and unavailable interval, which can make the sampled control system tolerate a larger packet dropout rate. A numerical example is provided to show the efficiency of the proposed results.

This paper aims at investigating the master-slave quasi-synchronization of delayed memristive neural networks (MNNs) by proposing a region-partitioning-dependent intermittent control. The proposed method is described by three partitions of non-negative real region and an auxiliary positive definite function. Whether the control input is imposed on the slave system or not is decided by the dynamical relationships among the three subregions and the auxiliary function. From these ingredients, several succinct criteria with the associated co-design procedure are presented such that the synchronization error converges to a predetermined level. The proposed intermittent control scheme is also applied to the event-triggered control, and an intermittent event-triggered mechanism is devised to investigate the quasi-synchronization of MNNs correspondingly. Such mechanism eliminates the events in rest time, and then it reduces the amount of samplings. Finally, two illustrative examples are presented to verify the effectiveness of our theoretical results.

This paper investigates the finite-time decentralized control problem for interconnected systems with discontinuous interconnections. By using the interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy model, a unified IT2 T-S fuzzy interconnected system is provided, in which the global system is described as a fuzzy blending of local subsystems under IF-THEN rules. In addition, based on the differential inclusion theory, the solutions of such discontinuous system are defined in the sense of Filippov. In order to stabilize the considered system in finite time, several decentralized discontinuous state feedback controllers are proposed. Furthermore, by the finite-time stabilization theory and generalized Lyapunov functional method, decentralized control is carried out and several sufficient criteria are derived to ensure the finite-time stabilization of the concerned system. Correspondingly, the settling times for stabilization are given. Finally, the proposed methodology is illustrated by an example.

This paper studies an optimal consensus tracking problem of heterogeneous linear multiagent systems. By introducing tracking error dynamics, the optimal tracking problem is reformulated as finding a Nash-equilibrium solution to multiplayer games, which can be done by solving associated coupled Hamilton-Jacobi equations. A data-based error estimator is designed to obtain the data-based control for the multiagent systems. Using the quadratic functional to approximate every agent's value function, we can obtain the optimal cooperative control by the input-output (I/O) Q -learning algorithm with a value iteration technique in the least-square sense. The control law solves the optimal consensus problem for multiagent systems with measured I/O information, and does not rely on the model of multiagent systems. A numerical example is provided to illustrate the effectiveness of the proposed algorithm.

This paper investigates the finite-time stabilization for a class of interconnected systems with nonlinear discontinuous interconnections in which the time-varying delay are considered. By utilizing the universal approximation ability of the fuzzy model, a unified interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy-model-based interconnected delayed system is provided. Then, in order to solve the existence of solution for the concerned system with discontinuous right-hand side, the Filippov solutions are defined based on differential inclusion theory and set-valued analysis. Furthermore, by the IT2 T-S fuzzy model approach, a delayed state feedback controller equipped with discontinuous term and time-varying delays term is proposed. According to the classical finite time stability theory and generalized Lyapunov approach, finite-time stabilization for the discontinuous interconnected delayed system is achieved, and the estimate of settling time is given. Moreover, when the detailed information of time-varying delays is unknown, the finite-time stabilization is also realized via another improved controller, which only depends upon the upper bound of time-varying delays. Finally, the proposed methodologies are illustrated by a numerical example.

For most existing aperiodic fault diagnosis algorithms of microgrid inverter, because of the common aperiodic processing features, they have relatively higher amount of algorithm startup, calculation, and complexity. These features increase the hardware requirements and realization difficulty, greatly affect the practicability. In order to improve above-mentioned problems, a practical fault diagnosis algorithm is investigated. In this paper, first, aperiodic corrected-second low-frequency processing method is proposed to get aperiodic small low-frequency data (ASLFD) by a simple way in the real time, which greatly reduces the amount of algorithm startup and corresponding calculation. Second, these ASLFD are processed by the real-time normalization method. Next, the degree of asymmetry and distortion degree of root mean square are extracted, respectively. Furthermore, the feature variables and results are realized through the logical operations. Compared with the existing fault diagnosis algorithms, the proposed algorithm has lower amount of startup and calculation, smaller complexity, and easy realization, which are conducive to practical applications. The detailed experimental results and comparisons are shown to validate the proposed algorithm.

This paper is focused on the data-driven model-free adaptive fault detection and estimation (FDE) and fault-tolerant control (FTC) problems for multi-input multi-output (MIMO) discrete-time systems with unknown sensor faults. First, in the light of the compact form dynamic linearization method, the initial systems are transformed into a novel data-based model with only one unknown parameter. Second, a fault estimator is established to detect the sensor faults. Noting that a time-varying residual threshold is developed to determine whether the sensor faults occur or not. Then, the unknown faults are approximated based on the powerful approximation capability of a generalized fuzzy hyperbolic model and the FTC approaches are reconstructed by applying the optimality criterion. In contrast to the previous schemes, the main contributions are twofold: first, it is the first time to solve the FDE and FTC problems for model-free MIMO discrete-time systems; second, the proposed FTC policy is simple to be implemented with reducing computational burden. Finally, two examples are used to demonstrate the effectiveness of the proposed FDE and FTC methods.

In this paper, the dissipativity problem of discrete-time memristive neural networks (DMNNs) with time-varying delays and stochastic perturbation is investigated. A class of logical switched functions are put forward to reflect the memristor-based switched property of connection weights, and the DMNNs are then recast into a tractable model. Based on the tractable model, the robust analysis method and Refined Jensen-based inequalities are applied to establish some sufficient conditions that ensure the of DMNNs. Two numerical examples are presented to illustrate the effectiveness of the obtained results.

This paper investigates the event-triggered stabilization of neural networks (NNs) subject to input saturation. The main core lies in the design of a novel controller with time-varying switching gains and the associated switching event-triggered condition (ETC). The ETC is essentially a switching between the aperiodic sampling and continuous event trigger. The control gains of the designed controller are composed of an exponentially decaying term and two gain matrices. The two gain matrices are required to be switched when the switching between the aperiodic sampling and continuous event trigger is met. By employing the generalized sector condition and switching Lyapunov function, several sufficient conditions that ensure the local exponential stability of the NNs are formulated in terms of linear matrix inequalities (LMIs). Both the exponentially decaying term and switching gains improve the feasible region of LMIs, and then they are helpful to enlarge the set of admissible initial conditions, the threshold in ETC, and the average waiting time. Together with several optimization problems, two numerical examples are employed to validate the effectiveness of our results.

This paper is concerned with the robust optimal tracking control strategy for a class of nonlinear multi-input multi-output discrete-time systems with unknown uncertainty via adaptive critic design (ACD) scheme. The main purpose is to establish an adaptive actor-critic control method, so that the cost function in the procedure of dealing with uncertainty is minimum and the closed-loop system is stable. Based on the neural network approximator, an action network is applied to generate the optimal control signal and a critic network is used to approximate the cost function, respectively. In contrast to the previous methods, the main features of this paper are: 1) the ACD scheme is integrated into the controllers to cope with the uncertainty and 2) a novel cost function, which is not in quadric form, is proposed so that the total cost in the design procedure is reduced. It is proved that the optimal control signals and the tracking errors are uniformly ultimately bounded even when the uncertainty exists. Finally, a numerical simulation is developed to show the effectiveness of the present approach.

Neural networks (NNs) in the stochastic environment were widely modeled as stochastic differential equations, which were driven by white noise, such as Brown or Wiener process in the existing papers. However, they are not necessarily the best models to describe dynamic characters of NNs disturbed by nonwhite noise in some specific situations. In this paper, general noise disturbance, which may be nonwhite, is introduced to NNs. Since NNs with nonwhite noise cannot be described by Itô integral equation, a novel modeling method of stochastic NNs is utilized. By a framework in light of random field approach and Lyapunov theory, the global asymptotic stability and stabilization in probability or in the mean square of NNs with general noise are analyzed, respectively. Criteria for the concerned systems based on linear matrix inequality are proposed. Some examples are given to illustrate the effectiveness of the obtained results.

This paper investigates the problem of optimal fault-tolerant control (FTC) for a class of unknown nonlinear discrete-time systems with actuator fault in the framework of adaptive critic design (ACD). A pivotal highlight is the adaptive auxiliary signal of the actuator fault, which is designed to offset the effect of the fault. The considered systems are in strict-feedback forms and involve unknown nonlinear functions, which will result in the causal problem. To solve this problem, the original nonlinear systems are transformed into a novel system by employing the diffeomorphism theory. Besides, the action neural networks (ANNs) are utilized to approximate a predefined unknown function in the backstepping design procedure. Combined the strategic utility function and the ACD technique, a reinforcement learning algorithm is proposed to set up an optimal FTC, in which the critic neural networks (CNNs) provide an approximate structure of the cost function. In this case, it not only guarantees the stability of the systems, but also achieves the optimal control performance as well. In the end, two simulation examples are used to show the effectiveness of the proposed optimal FTC strategy.

This paper is concerned with a reinforcement learning-based adaptive tracking control technique to tolerate faults for a class of unknown multiple-input multiple-output nonlinear discrete-time systems with less learning parameters. Not only abrupt faults are considered, but also incipient faults are taken into account. Based on the approximation ability of neural networks, action network and critic network are proposed to approximate the optimal signal and to generate the novel cost function, respectively. The remarkable feature of the proposed method is that it can reduce the cost in the procedure of tolerating fault and can decrease the number of learning parameters and thus reduce the computational burden. Stability analysis is given to ensure the uniform boundedness of adaptive control signals and tracking errors. Finally, three simulations are used to show the effectiveness of the present strategy.

This paper is concerned with the exponential stabilization of memristive neural networks (MNNs) by taking into account the sampled-data control and actuator saturation. On the one hand, the MNNs are converted into a tractable model by defining a class of logical switched functions. Based on this model, the connection weights of MNNs are dealt with by a robust analysis method. On the other hand, a saturating sampled-data controller containing an exponentially decaying term is designed. With the help of generalized sector condition and the Lyapunov stability theory, a novel sufficient condition ensuring the local exponential stability of the closed-loop systems is formulated in terms of linear matrix inequalities. In addition, three optimization problems are given to design the control gain with the aims of enlarging the sampling interval, expanding the estimation of the domain of attraction, and minimizing the size of actuators, while preserving the stability of the closed-loop systems. Two numerical examples are provided to illustrate the effectiveness of the obtained theoretical results.

This paper is concerned with the finite-time synchronization problem of coupled hierarchical hybrid delayed neural networks. This coupled hierarchical hybrid neural networks consist of a higher level switching and a lower level Markovian jumping. The time-varying delays are dependent on not only switching signal but also jumping mode. By using a less conservative weighted integral inequality and stochastic multiple Lyapunov-Krasovskii functional, new finite-time synchronization criteria are obtained, which makes the state trajectories be kept within the prescribed bound in a time interval. Finally, an example is proposed to demonstrate the effectiveness of the obtained results.

An adaptive predefined performance control problem is investigated for a class of multiple-input multiple-output systems with unknown control direction and unknown backlash-like hysteresis nonlinearities by using generalized fuzzy hyperbolic model (GFHM). Compared with the existing methods, the main features are as follows: the prediction error is introduced to construct the adaptive laws, which means that the approximate accuracy of the GFHM is solved; the Nussbaum-type gain is utilized to deal with the unknown control direction, which avoids the requirement of directiona priori; and by transforming the tracking errors into new error variables, the prescribed steady-state and transient performance can be ensured. It is shown that the proposed control approach can guarantee that all the signals of the resulting closed-loop systems are bounded, and the output tracks a desired trajectory, while the tracking errors are confined all times within the prescribed bounds. Finally, two simulation results and some comparisons are provided to verify the effectiveness of the proposed approach. Since the proposed control strategy is only implemented in a healthy case, how to extend the strategy to a faulty case will be a further topic.

This brief is concerned with the stability criteria for recurrent neural networks with time-varying delay. First, based on convex combination technique, a delay interval with fixed terminals is changed into the one with flexible terminals, which is called flexible terminal method (FTM). Second, based on the FTM, a novel Lyapunov-Krasovskii functional is constructed, in which the integral interval associated with delayed variables is not fixed. Thus, the FTM can achieve the same effect as that of delay-partitioning method, while their implementary ways are different. Guided by FTM, Wirtinger-based integral inequality and free-weight matrix method are employed to develop several stability criteria, respectively. Finally, the feasibility and the effectiveness of the proposed results are tested by two numerical examples.

This paper investigates sampled-data synchronization problem of Markovian coupled neural networks with mode-dependent interval time-varying delays and aperiodic sampling intervals based on an enhanced input delay approach. A mode-dependent augmented Lyapunov-Krasovskii functional (LKF) is utilized, which makes the LKF matrices mode-dependent as much as possible. By applying an extended Jensen's integral inequality and Wirtinger's inequality, new delay-dependent synchronization criteria are obtained, which fully utilizes the upper bound on variable sampling interval and the sawtooth structure information of varying input delay. In addition, the desired stochastic sampled-data controllers can be obtained by solving a set of linear matrix inequalities. Finally, two examples are provided to demonstrate the feasibility of the proposed method.This paper investigates sampled-data synchronization problem of Markovian coupled neural networks with mode-dependent interval time-varying delays and aperiodic sampling intervals based on an enhanced input delay approach. A mode-dependent augmented Lyapunov-Krasovskii functional (LKF) is utilized, which makes the LKF matrices mode-dependent as much as possible. By applying an extended Jensen's integral inequality and Wirtinger's inequality, new delay-dependent synchronization criteria are obtained, which fully utilizes the upper bound on variable sampling interval and the sawtooth structure information of varying input delay. In addition, the desired stochastic sampled-data controllers can be obtained by solving a set of linear matrix inequalities. Finally, two examples are provided to demonstrate the feasibility of the proposed method.

In this paper, the optimal output regulation problem for partially model-free heterogeneous linear multiagent systems with disturbance generated by an exosystem is addressed by using adaptive dynamic programming and double compensator method. The topology graph for the information exchange of the agents has a spanning tree. The dynamic of individual agent is assumed to be nonidentical and of different dimensions. One distributed compensator is designed to deal with the nonidentical agents, and the other compensator is used to handle the optimal performance index. By constructing the double compensator, the distributed feedback control laws are designed to make the output of each agent synchronize with the reference output and minimize the energy of the output error simultaneously. To overcome the lack of the dynamics knowledge of each agent, a novel online policy iteration algorithm is developed to obtain the optimal feedback gain matrix. Finally, two examples are presented to illustrate the effectiveness of our results.

In this paper, a dynamic delay interval (DDI) method is proposed to deal with the stability problem of neural networks with two delay components. This method extends the fixed interval of a time-varying delay to a dynamic one, which relaxes the restriction on upper and lower bounds of the delay intervals. Combining the reciprocally convex combination technique and Wirtinger integral inequality, the DDI method leads to some much less conservative delay-dependent stability criteria based on a linear matrix inequality for neural networks with two delay components. Furthermore, the criteria for the system with a single time-varying delay are provided. Some examples are given to illustrate the effectiveness of the obtained results.

This paper investigates the problem of sampled-data synchronization for Markovian neural networks with generally incomplete transition rates. Different from traditional Markovian neural networks, each transition rate can be completely unknown or only its estimate value is known in this paper. Compared with most of existing Markovian neural networks, our model is more practical because the transition rates in Markovian processes are difficult to precisely acquire due to the limitations of equipment and the influence of uncertain factors. In addition, the time-dependent Lyapunov-Krasovskii functional is proposed to synchronize drive system and response system. By applying an extended Jensen's integral inequality and Wirtinger's inequality, new delay-dependent synchronization criteria are obtained, which fully utilize the upper bound of variable sampling interval and the sawtooth structure information of varying input delay. Moreover, the desired sampled-data controllers are obtained. Finally, two examples are provided to illustrate the effectiveness of the proposed method.

In this paper, the main focus is to cope with the fault detection and estimation (FDE) and fault-tolerant control (FTC) issues of nonlinear single input single output model-free system (MFS), while only the input/output data are utilized. First, in accordance with the pseudo-partial-derivative approach, the original system is transformed into a compact form dynamic linearization data model, in which only one parameter is employed. Second, an estimator is developed to detect the fault. A key highlight is the design of a time varying residual threshold. Moreover, an online neural network (NN) approximator is utilized to learn the unknown fault dynamics and an FTC strategy is reconstructed based on the optimality criterion. In contrast to the previous methods, the main features of the proposed method are as follows: 1) the fault related problem is solved for MFS; 2) the number of system parameters is largely reduced; and 3) NNs are utilized to establish a novel fault estimation scheme. Finally, a numerical simulation is provided to show the effectiveness of the proposed FDE and FTC strategy.

In this paper, the local synchronization problem of Markovian nonlinearly coupled neural networks with uncertain and partially unknown transition rates is investigated. Each transition rate in this Markovian nonlinearly coupled neural networks model is uncertain or completely unknown because the complete knowledge on the transition rates is difficult and the cost is probably high. By applying the Lyapunov-Krasovskii functional, a new integral inequality combining with free-matrix-based integral inequality and further improved integral inequality, the less conservative local synchronization criteria are obtained. The new delay-dependent local synchronization criteria containing the bounds of delay and delay derivative are given in terms of linear matrix inequalities. Finally, a simulation example is provided to illustrate the effectiveness of the proposed method.

This paper investigates the cluster output consensus of heterogeneous linear multi-agent systems, where the agents are coupled. The aim is to regulate the outputs of the agents tracking the reference signals, which belongs to the different cluster. Because some agents can not access the information of the exosystem, the distributed compensator is reconstructed via local interaction, where the coupling gain matrix can be obtained by solving related algebraic Riccati equation. This paper proposes multiple leaders control law for each agent, and provide sufficient algebraic condition of the parameters which relate to the interaction graph. Finally, simulation examples are provided to verify the effectiveness of the proposed approach.

This paper is concerned with the exponential stability and stabilization of memristive neural networks (MNNs) with delays. First, we present some generalized double-integral inequalities, which include some existing inequalities as their special cases. Second, combining with quadratic convex combination method, these double-integral inequalities are employed to formulate a delay-dependent stability condition for MNNs with delays. Third, a state-dependent switching control law is obtained for MNNs with delays based on the proposed stability conditions. The desired feedback gain matrices are accomplished by solving a set of linear matrix inequalities. Finally, the feasibility and effectiveness of the proposed results are tested by two numerical examples.

A novel synchronization analysis method is developed to solve the complete synchronization problem of many Boolean networks (BNs) coupled in the leader-follower configuration. First, an error system is constructed in terms of the algebraic representation using the semitensor product of matrices. Then, the synchronization problem of coupled BNs is converted into a problem whether all the trajectories of the error system are convergent to the zero vector. Second, according to the structure analysis of this error system, which is in the form of a switched system with leader BN states as the switching signal, a necessary and sufficient synchronization condition is derived. An algorithm is developed, which helps to determine as soon as possible whether complete synchronization among coupled BNs is achieved. Finally, a constructive design approach to follower BNs is provided. All of these follower BNs designed by our approach can completely synchronize with a given leader BN from the (Tt+ 1)th step at most, where Ttis the transient period of the leader BN.

This paper concentrates on the reinforcement learning (RL)-based fault-tolerant control (FTC) problem for a class of multiple-input-multiple-output (MIMO) nonlinear discrete-time systems. Both incipient faults and abrupt faults are taken into account. Based on the approximation ability of neural networks (NNs), an RL algorithm is incorporated into the FTC strategy, in which an action network is developed to generate the optimal control signal and a critic network is used to approximate the novel cost function, respectively. Compared with the existing results, a novel fault tolerant controller is proposed based on an RL method to reduce a long-term performance index after a fault occurs. The meaning of minimizing the performance index after a fault occurs in an MIMO system is that waste will be decreased and energy will be saved. Note that the weights of NNs are adjusted online rather than offline. Then, it is proven that the adaptive parameters, tracking errors, and optimal control signals are uniformly bounded even in the presence of the unknown fault dynamics. Finally, a numerical simulation is provided to show the effectiveness of the proposed FTC approach.

In this paper, we study the global exponential stability in Lagrange sense for memristor-based neural networks (MBNNs) with time-varying delays. Based on the nonsmooth analysis and differential inclusion theory, matrix measure technique is employed to establish some succinct criteria which ensure the Lagrange stability of the considered memristive model. In addition, the new proposed criteria are very easy to verify, and they also enrich and improve the earlier publications. Finally, two example are given to demonstrate the validity of the results.

A secondary delay partitioning method is proposed to study the stability problem for a class of recurrent neural networks (RNNs) with time-varying delay. The total interval of the time-varying delay is first divided into two parts, and then each part is further divided into several subintervals. To deal with the state variables associated with these subintervals, an extended reciprocal convex combination approach and a double integral term with variable upper and lower limits of integral as a Lyapunov functional are proposed, which help to obtain the stability criterion. The main feature of the proposed result is more effective for the RNNs with fast time-varying delay. A numerical example is used to show the effectiveness of the proposed stability result.

This paper investigates the stochastic synchronization problem for Markovian hybrid coupled neural networks with interval time-varying mode-delays and random coupling strengths. The coupling strengths are mutually independent random variables and the coupling configuration matrices are nonsymmetric. A mode-dependent augmented Lyapunov-Krasovskii functional (LKF) is proposed, where some terms involving triple or quadruple integrals are considered, which makes the LKF matrices mode-dependent as much as possible. This gives significant improvement in the synchronization criteria, i.e., less conservative results can be obtained. In addition, by applying an extended Jensen's integral inequality and the properties of random variables, new delay-dependent synchronization criteria are derived. The obtained criteria depend not only on upper and lower bounds of mode-delays but also on mathematical expectations and variances of the random coupling strengths. Finally, two numerical examples are provided to demonstrate the feasibility of the proposed results.

This paper focuses on the composite adaptive tracking control for a class of nonlinear multiple-input-multiple-output (MIMO) systems with unknown backlash-like hysteresis nonlinearities. A dynamic surface control method is incorporated into the proposed control strategy to eliminate the problem of explosion of complexity. Compared with some existing methods, the prediction error between system state and serial-parallel estimation model is combined with compensated tracking error to construct the adaptive laws for neural network (NN) weights. It is shown that the proposed control approach can guarantee that all the signals of the resulting closed-loop systems are semi-globally uniformly ultimately bounded and the tracking error converges to a small neighborhood. Finally, simulation results are provided to confirm the effectiveness of the proposed approaches.

In this paper, distributed control for second-order leader-following multi-agent systems has been solved. All the outputs of the agents reach a common trajectory. The dynamic of the leader agent is different with the follower agents. If the digraph contains a spanning tree, then the problem is solved using an appropriate control law. A compensator is designed to making the closed-loop system matrix stable. Simulation results are further presented to show the effectiveness and performance of our work.

This paper investigates the adaptive actuator failure compensation control for a class of uncertain multi input single out (MISO) discrete time systems with triangular forms. The systems contain the actuator faults of both loss of effectiveness and lock-in-place. With the help of radial basis function neural networks (RBFNN) to approximate the unknown nonlinear functions, an adaptive RBFNN fault-tolerant control (FTC) scheme is designed. Compared with some exist result in which solving linear matrix inequality (LMI) is required, we introduce the backstepping technique to achieve the FTC task. It is proved that the proposed control approach can guarantee that all the signals of the closed-loop system are bounded and that the output can successfully track a reference signal in the presence of the actuator failures. Finally, simulation results are provided to confirm the effectiveness of the control approach.

In the stability analysis of recurrent neural networks, one of the tasks is to reduce the conservativeness of the stability criterion. Along this routine, there are two ways to be considered. One is how to construct the Lyapunov-Krasovskii functional (LKF), and the other is how to use mathematical skills to estimate the derivatives of the LKF. The purpose of this paper is to present a brief review on the evolution on the construction of LKF for recurrent neural networks with single time-varying delay. By summarizing the observation, one can find the core elements in the construction of LKF. Moreover, one can find the evolution history on the delay-partitioning and its applications in the construction of LKF.

Stability problems of continuous-time recurrent neural networks have been extensively studied, and many papers have been published in the literature. The purpose of this paper is to provide a comprehensive review of the research on stability of continuous-time recurrent neural networks, including Hopfield neural networks, Cohen-Grossberg neural networks, and related models. Since time delay is inevitable in practice, stability results of recurrent neural networks with different classes of time delays are reviewed in detail. For the case of delay-dependent stability, the results on how to deal with the constant/variable delay in recurrent neural networks are summarized. The relationship among stability results in different forms, such as algebraic inequality forms, M-matrix forms, linear matrix inequality forms, and Lyapunov diagonal stability forms, is discussed and compared. Some necessary and sufficient stability conditions for recurrent neural networks without time delays are also discussed. Concluding remarks and future directions of stability analysis of recurrent neural networks are given.

In this paper, we develop and analyze an optimal control method for a class of discrete-time nonlinear Markov jump systems (MJSs) with unknown system dynamics. Specifically, an identifier is established for the unknown systems to approximate system states, and an optimal control approach for nonlinear MJSs is developed to solve the Hamilton-Jacobi-Bellman equation based on the adaptive dynamic programming technique. We also develop detailed stability analysis of the control approach, including the convergence of the performance index function for nonlinear MJSs and the existence of the corresponding admissible control. Neural network techniques are used to approximate the proposed performance index function and the control law. To demonstrate the effectiveness of our approach, three simulation studies, one linear case, one nonlinear case, and one single link robot arm case, are used to validate the performance of the proposed optimal control method.

This paper is concerned with the adaptive fault tolerant synchronization problem for a class of complex interconnected neural networks against sensor failure and coupling failure. As sensor and coupling failure may lead to performance degradation or even instability of the whole network, adaptive approach is proposed to adjust unknown coupling factors for the deteriorated network compensations, as well as to estimate controller parameters to compensate the effects of failed coupling. Through Lyapunov functions and adaptive schemes, three kind of fault tolerant controllers are constructed to ensure the synchronization of the networks in the presence of the network deterioration. Simulation results are given to verify the effectiveness of the proposed method.

The globally exponential stabilization problem is investigated for a general class of stochastic Cohen-Grossberg neural networks with both Markovian jumping parameters and mixed mode-dependent time-delays. The mixed time-delays consist of both discrete and distributed delays. This paper aims to design a memoryless state feedback controller such that the closed-loop system is stochastically exponentially stable in the mean square sense. By introducing a new Lyapunov-Krasovskii functional that accounts for the mode-dependent mixed delays, stochastic analysis is conducted in order to derive delay-dependent criteria for the exponential stabilization problem. Three numerical examples are carried out to demonstrate the feasibility of our delay-dependent stabilization criteria.

Global asymptotic stability problem is studied for a class of recurrent neural networks with distributed delays satisfying Lebesgue-Stieljies measures on the basis of linear matrix inequality. The concerned network model includes many neural network models with various delays and structures as its special cases, such as the delays covering the discrete delays and distributed delays, and the network structures containing the neutral-type networks and high-order networks. Therefore, many new stability criteria for the above neural network models have also been derived from the present stability analysis method. All the obtained stability results have similar matrix inequality structures and can be easily checked. Three numerical examples are used to show the effectiveness of the obtained results.

A fuzzy min-max neural network based on data core (DCFMN) is proposed for pattern classification. A new membership function for classifying the neuron of DCFMN is defined in which the noise, the geometric center of the hyperbox, and the data core are considered. Instead of using the contraction process of the FMNN described by Simpson, a kind of overlapped neuron with new membership function based on the data core is proposed and added to neural network to represent the overlapping area of hyperboxes belonging to different classes. Furthermore, some algorithms of online learning and classification are presented according to the structure of DCFMN. DCFMN has strong robustness and high accuracy in classification taking onto account the effect of data core and noise. The performance of DCFMN is checked by some benchmark datasets and compared with some traditional fuzzy neural networks, such as the fuzzy min-max neural network (FMNN), the general FMNN, and the FMNN with compensatory neuron. Finally the pattern classification of a pipeline is evaluated using DCFMN and other classifiers. All the results indicate that the performance of DCFMN is excellent.

The global exponential stability is analyzed for a class of high-order Hopfield-type neural networks with time-varying delays. Based on the Lyapunov stability theory, together with the linear matrix inequality approach and free-weighting matrix method, some less conservative delay-independent and delay-dependent sufficient conditions are presented for the global exponential stability of the equilibrium point of the considered neural networks. Two numerical examples are provided to demonstrate the effectiveness of the proposed stability criteria.

In this paper, a new delayed projection neural network with mixed delays is proposed for solving a class of quadratic programming (QP) problems. By the Lyapunov-Krasovskii theory and the linear matrix inequality (LMI) method, the proposed neural network is proved to be convergent to the optimal solution of the QP problems exponentially. The validity of the proposed neural network is verified by two simulation examples.

This paper is concerned with the global asymptotic stability of a class of reaction-diffusion Cohen-Grossberg neural networks with continuously distributed delays. Under some suitable assumptions and using a matrix decomposition method, we apply the linear matrix inequality (LMI) method to propose some new sufficient stability conditions for the reaction-diffusion Cohen-Grossberg neural networks with continuously distributed delays. The obtained results are easy to check and improve upon the existing stability results. Some remarks are given to show the advantages of the obtained results over the previous results. An example is also given to demonstrate the effectiveness of the obtained results.

In this paper, a weighting-delay-based method is developed for the study of the stability problem of a class of recurrent neural networks (RNNs) with time-varying delay. Different from previous results, the delay interval [0, d(t)] is divided into some variable subintervals by employing weighting delays. Thus, new delay-dependent stability criteria for RNNs with time-varying delay are derived by applying this weighting-delay method, which are less conservative than previous results. The proposed stability criteria depend on the positions of weighting delays in the interval [0, d(t)] , which can be denoted by the weighting-delay parameters. Different weighting-delay parameters lead to different stability margins for a given system. Thus, a solution based on optimization methods is further given to calculate the optimal weighting-delay parameters. Several examples are provided to verify the effectiveness of the proposed criteria.

An augmented Lyapunov-Krasovskii functional (LKF) approach is presented to derive sufficient conditions for the existence, uniqueness, and globally exponential stability of the equilibrium point of a class of cellular neural networks with time-varying delays. By dividing the variation interval of the time delay into several subintervals with equal length, a novel vector LKF is introduced and new conditions are obtained based on the homeomorphism mapping principle, free-weighting matrix method, and linear matrix inequality techniques. Since the criteria are involving derivative information of both state and delay, the obtained results are less conservative than some previous ones. Two examples are also given to show the effectiveness of the presented criteria.

The global asymptotic stability problem for a class of reaction-diffusion Cohen-Grossberg neural networks with both time-varying delay and infinitely distributed delay is investigated under Dirichlet boundary conditions. Instead of using the M-matrix method and the algebraic inequality method, under some suitable assumptions and using a matrix decomposition method, we adopt the linear matrix inequality method to propose two sufficient stability conditions for the concerned neural networks with Dirichlet boundary conditions and different kinds of activation functions, respectively. The obtained results are easy to check and improve upon the existing stability results. Two examples are given to demonstrate the effectiveness of the obtained results.

This brief is concerned with the global robust exponential stability of a class of interval Cohen-Grossberg neural networks with both multiple time-varying delays and continuously distributed delays. Some new sufficient robust stability conditions are established in the form of state transmission matrix, which are different from the existing ones. Furthermore, a sufficient condition is also established to guarantee the global stability for this class of Cohen-Grossberg neural networks without uncertainties. Three examples are used to show the effectiveness of the obtained results.

In this paper, several sufficient conditions are established for the global asymptotic stability of recurrent neural networks with multiple time-varying delays. The Lyapunov-Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) approach are employed in our investigation. The results are shown to be generalizations of some previously published results and are less conservative than existing results. The present results are also applied to recurrent neural networks with constant time delays.

In this paper, robust stability problems for interval Cohen-Grossberg neural networks with unknown time-varying delays are investigated. Using linear matrix inequality, M -matrix theory, and Halanay inequality techniques, new sufficient conditions independent of time-varying delays are derived to guarantee the uniqueness and the global robust stability of the equilibrium point of interval Cohen-Grossberg neural networks with time-varying delays. All these results have no restriction on the rate of change of the time-varying delays. Compared to some existing results, these new criteria are less conservative and are more convenient to check. Two numerical examples are used to show the effectiveness of the present results.

In this paper, two sufficient conditions are established for the global asymptotic stability of recurrent neural networks with multiple time varying delays. The Lyapunov-Krasovskii stability theory for functional differential equations and the linear matrix inequality approach are employed in our investigation. Our results are shown to be generalizations of some previously published results and are less conservative than existing results. The present results are also applicable to recurrent neural networks with constant time delays.

A new criterion for the global asymptotic stability of the equilibrium point of cellular neural networks with multiple time delays is presented. The obtained result possesses the structure of a linear matrix inequality and can be solved efficiently using the recently developed interior-point algorithm. A numerical example is used to show the effectiveness of the obtained result.