Robust stability of Boolean networks with data loss and disturbance inputs.

This study discusses the robust stability problem of Boolean networks (BNs) with data loss and disturbances, where data loss is appropriately described by random Bernoulli distribution sequences. Firstly, a BN with data loss and disturbances is converted into an algebraic form via the semi-tensor product (STP) technique. Accordingly, the original system is constructed as a probabilistic augmented system, based on which the problem of stability with probability one for the original system becomes a set stability with probability one for the augmented system. Subsequently, certain criteria are proposed for the robust stability of the systems. Moreover, an algorithm is developed to verify the robust set stability of the augmented system based on truth matrices. Finally, the validity of the obtained results is demonstrated by an illustrative example.

A novel stability criterion and precise control for linear time delay systems based on regional configuration of the poles.

This paper presents the concept of region stability and provides criteria for region stability of linear time delay systems, which can reveal the dynamic and steady-state performance of the systems more precisely. Corresponding design schemes for stabilization and tracking control that can accurately control various performance of time delay systems have also been explored. First, in the light of the connection between the poles and the dynamic properties of the system, the concept of region stability is given to describe the finer dynamic behavior of time delay systems. The criteria for the region stability are also presented. Second, the region stabilization methods are investigated, which can ensure that the system satisfies a certain dynamic performance by setting the eigenvalues in a certain convex region. Third, a precise tracking control of the linear time delay systems is addressed as an application of region stabilization. It can control the steady state performance and transient response of the tracking signal more precisely. Finally, three instances are provided to display the superiority of the new method for the performance indexes of the linear time delay systems.

Sampled-data exponential consensus of multi-agent systems with Lipschitz nonlinearities.

In this paper, the exponential consensus of leaderless and leader-following multi-agent systems with Lipschitz nonlinear dynamics is illustrated with aperiodic sampled-data control using a two-sided loop-based Lyapunov functional (LBLF). Firstly, applying input delay approach to reformulate the resulting sampled-data system as a continuous system with time-varying delay in the control input. A two-sided LBLF which captures the information on sampled-data pattern is constructed and the symmetry of the Laplacian matrix together with Newton-Leibniz formula have been employed to obtain reduced number of decision variables and decreased LMI dimensions for the exponential sampled-data consensus problem. Subsequently, an aperiodic sampled-data controller was designed to simplify and enhance stability conditions for computation and optimization purposes in the proposed approach. Finally, based on the controller design, simulation examples including the power system are proposed to illustrate the theoretical analysis, moreover, a larger sampled-data interval can be acquired by this method than other literature, thereby conserving bandwidth and reducing communication resources.

Reachable set estimation and stochastic sampled-data exponential synchronization of Markovian jump neural networks with time-varying delays.

In this paper, the stochastic sampled-data exponential synchronization problem for Markovian jump neural networks (MJNNs) with time-varying delays and the reachable set estimation (RSE) problem for MJNNs subjected to external disturbances are investigated. Firstly, assuming that two sampled-data periods satisfy Bernoulli distribution, and introducing two stochastic variables to represent the unknown input delay and the sampled-data period respectively, the mode-dependent two-sided loop-based Lyapunov functional (TSLBLF) is constructed, and the conditions for the mean square exponential stability of the error system are derived. Furthermore, a mode-dependent stochastic sampled-data controller is designed. Secondly, by analyzing the unit-energy bounded disturbance of MJNNs, a sufficient condition is proved that all states of MJNNs are confined to an ellipsoid under zero initial condition. In order to make the target ellipsoid contain the reachable set of the system, a stochastic sampled-data controller with RSE is designed. Eventually, two numerical examples and an analog resistor-capacitor network circuit are provided to show that the textual approach can obtain a larger sampled-data period than the existing approach.

H∞ master-slave synchronization for delayed impulsive implicit hybrid neural networks based on memory-state feedback control.

This paper investigates the H∞ master-slave synchronization problem for delayed impulsive implicit hybrid neural networks based on memory-state feedback control. By developing a more holistic stochastic impulse-time-dependent Lyapunov-Krasovskii functional and dealing with the nonlinear neuron activation function, the stochastic admissibility and prescribed H∞ performance index for the synchronization error closed-loop system are achieved. In addition, the desired mode-dependent memory-state feedback synchronization controller is acquired in the form of linear matrix inequalities. The free-weighting matrix technique is adopted to remove the inherent limitation of time-varying delay derivative for the implicit delayed systems, and the derivative of time-varying delay is relaxed enough to be greater than 1. The simulation of genetic regulatory network in bio-economic system is given to verify validity of the derived results.

Dynamic event-triggered adaptive finite-time consensus control for multi-agent systems with time-varying actuator faults.

In this study, the adaptive finite-time leader-following consensus control for multi-agent systems (MASs) subjected to unknown time-varying actuator faults is reported based on dynamic event-triggering mechanism (DETM). Neural networks (NNs) are used to approximate unknown nonlinear functions. Command filter and compensating signal mechanism are introduced to alleviate the computational burden. Unlike the existing methods, by combining adaptive backstepping method with DETM, a novel finite time control strategy is presented, which can compensate the actuator efficiency successfully, reduce the update frequency of the controller and save resources. At the same time, under the proposed strategy, it is guaranteed that all followers can track the trajectory of the leader in the sense that consensus errors converge to a neighborhood of the origin in finite time, and all signals in the closed-loop system are bounded. Finally, the availability of the designed strategy is validated by two simulation results.

Improved disturbance observer-based fixed-time adaptive neural network consensus tracking for nonlinear multi-agent systems.

This paper is concerned with the problem of fixed-time consensus tracking for a class of nonlinear multi-agent systems subject to unknown disturbances. Firstly, a modified fixed-time disturbance observer is devised to estimate the unknown mismatched disturbance. Secondly, a distributed fixed-time neural network control protocol is designed, in which neural network is employed to approximate the uncertain nonlinear function. Simultaneously, the technique of command filter is applied to fixed-time control, which circumvents the "explosion of complexity" problem. Under the proposed control strategy, all agents are enable to track the desired trajectory in fixed-time, and the consensus tracking error and disturbance estimation error converge to an arbitrarily small neighborhood of the origin, meanwhile, all signals in the closed-loop system remain bounded. Finally, a simulation example is provided to validate the effectiveness of the presented design method.

Disturbance Observer-Based Adaptive Neural Network Output Feedback Control for Uncertain Nonlinear Systems.

This article is devoted to the output feedback control of nonlinear system subject to unknown control directions, unknown Bouc-Wen hysteresis and unknown disturbances. During the control design process, the design obstacles caused by unknown control directions and Bouc-Wen hysteresis are eliminated by introducing linear state transformation and a new coordinate transformation, which avoids using the Nussbaum function with high-frequency oscillation to deal with the issue. Besides, to settle the issue caused by the unknown disturbances, a novel nonlinear disturbance observer is designed, which has the characteristics of simple structure, low coupling, and easy implementation. Especially, a compensation item is constructed to offset the redundant items generated in the backstepping design process. Simultaneously, using the neural network and backstepping technology, an output feedback controller is devised. The controller ensures that all closed-loop signals are bounded, and the system output, state observation error, and disturbance observation error converge to a small neighborhood of the origin. Finally, to illustrate the effectiveness of the proposed scheme, simulation verification is carried out based on a numerical example and a Nomoto ship model.

Discontinuous Event-Triggered Control for Local Stabilization of Memristive Neural Networks With Actuator Saturation: Discrete- and Continuous-Time Lyapunov Methods.

In this article, the local stabilization problem is investigated for a class of memristive neural networks (MNNs) with communication bandwidth constraints and actuator saturation. To overcome these challenges, a discontinuous event-trigger (DET) scheme, consisting of the rest interval and work interval, is proposed to cut down the triggering times and save the limited communication resources. Then, a novel relaxed piecewise functional is constructed for closed-loop MNNs. The main advantage of the designed functional consists in that it is positive definite only in the work intervals and the sampling instants but not necessarily inside the rest intervals. With the aid of extended reciprocally convex combination lemma, generalized sector condition, and some inequality techniques, two local stabilization criteria are established on the basis of both the discrete- and continuous-time Lyapunov methods. The proposed analysis technique fully takes advantage of the looped-functional and the event-trigger mechanism. Moreover, two optimization schemes are, respectively, established to design the control gain and enlarge the estimates of the admissible initial conditions (AICs) and the upper bound of rest intervals. Finally, some comparison results are given to validate the superiority of the proposed method.

Multi-Instant Observer Design of Discrete-Time Fuzzy Systems via An Enhanced Gain-Scheduling Mechanism.

This article is concerned with developing a featured multi-instant Luenberger-like observer of discrete-time Takagi-Sugeno fuzzy systems with unmeasurable state variables, that is, not only to reduce the conservatism but also (at the same time) to alleviate the computational complexity over the recent approach reported in the literature. Contrary to previous approaches, an enhanced gain-scheduling mechanism is proposed for constructing much abundant working modes by online evaluating the updated variation information of normalized fuzzy weighting functions across two adjacent sampling instants and, thus, a different group of observer gain matrices with less conservatism is designed in order to employ the exclusive features for each working mode. Moreover, all the redundant terms containing both surplus and unknown system information are discriminated and removed in this study and, thus, the required computational complexity is reduced to a certain extent than the counterpart one. Finally, numerical examples are provided to illustrate the superiority of the developed approach.

Multi-Instant Gain-Scheduling Fuzzy Observer of Discrete-Time Takagi-Sugeno Systems and Its Application: An Efficient Balanced Matrix Approach.

The problem of relaxed state estimation of discrete-time Takagi-Sugeno fuzzy systems is studied by constructing a novel multi-instant gain-scheduling fuzzy observer. First, a multi-instant gain-scheduling mechanism with a single adjustable parameter is given for the first time in order to produce more reasonable switch modes over previous results reported in recent literature. Second, for every switch mode, a batch of specified observer gain matrices is determined by developing an efficient balanced matrix approach so that the updated values of adjacent normalized fuzzy weighting functions can be flexibly exploited. Since the implied information of each specific switch mode is capable of being absorbed and utilized more thoroughly by the aid of the refined higher-order balanced matrices, the conservatism can be prominently reduced at the price of consuming extra computational burden within the allowable range. Finally, two benchmark examples are provided to test and verify the progressiveness of our proposed approach.

Novel Adaptive Event-Triggered Fuzzy Command Filter Control for Slowly Switched Nonlinear Systems With Constraints.

This article addresses the adaptive fuzzy control problem for switched nonlinear systems with state constraints. The unified barrier function (UBF) is introduced to solve the time-varying state constraints, which removes the feasibility conditions. By integrating command filter into backstepping control to avoid the "explosion of complexity." In addition, a novel event-triggered strategy is designed to deal with the asynchronous switching between subsystems and controllers without limiting the maximum asynchronous time, and mitigate the communication burden. Also, a new threshold function is introduced to overcome the difficulty of discontinuous triggering error at the switching instants. Then, by combining the improved admissible edge-dependent average dwell-time (AED-ADT) method with Lyapunov stability analysis, it is proved that all system signals are bounded and do not violate the predefined constraints under given switching rule. Finally, the numerical simulation results verify the superiority of the proposed algorithm, and the algorithm is applied to a ship maneuvering system.

Output feedback H∞ control for singular hybrid systems with partly unknown transition rates and input saturation.

This paper investigates dynamic output feedback H∞ control for singular Markovian jump systems with partly unknown transition rates and input saturation. Necessary and sufficient conditions that singular Markovian jump system satisfies stochastic admissibility and H∞ performance index are successfully deduced in terms of linear matrix inequalities under the two different conditions of completely known transition rates and partly unknown transition rates. Mode-dependent dynamic output feedback controller is designed to ensure that the closed-loop singular Markovian jump system satisfies stochastic admissibility and H∞ performance index. Novel set invariant condition is proposed, and it not only provides an estimate of the attractive domain of the closed-loop system but also allows the analysis of performance outside the stability region within this invariant set. Furthermore, the estimation of the attraction domain comes down to the determination of the largest contractively invariant ellipsoid satisfying the necessary and sufficient conditions and the novel set invariant condition, and it is solved as an optimization problem with linear matrix inequality constraints. Finally, the effectiveness and utility of the proposed method are verified by a numerical example and an oil catalytic cracking process.

Event-Triggered Adaptive Tracking With Guaranteed Transient Performance for Switched Nonlinear Systems Under Asynchronous Switching.

This article presents an event-triggered neural-network (NN) tracking control scheme, capable of ensuring transient performance for switched nonlinear systems. A mode-dependent event-triggered communication mechanism (MDETCM) is designed, and this significantly saves communication resources without limiting the number of switches between two consecutive triggering instants. Meanwhile, to solve the impact of asynchronous switching on system performance, the information of the switching signal is considered into the event-triggered mechanism (ETM). Also, by introducing a normalized function transformation and a tan-type barrier function, the transient performance is regarded as a tracking error constraint without considering the initial conditions of system output and reference signal required in traditional prescribed performance bound (PPB) control. At the same time, the improved admissible edge-dependent average dwell time (AED-ADT) method is cleverly connected with adaptive backstepping control, and a state-feedback tracking algorithm is proposed, under which all closed-loop signals are bounded and the transient performance of the controlled plant is ensured. Finally, the superiority of the proposed scheme is demonstrated through numerical studies, and the control scheme is available for a single-link robot.

Event-Triggered-Based Distributed Consensus Tracking for Nonlinear Multiagent Systems With Quantization.

In this article, an observer-based adaptive neural network (NN) event-triggered distributed consensus tracking problem is investigated for nonlinear multiagent systems with quantization. In the first place, the limited capacity of the communication channel between agents is considered. The event-trigger mechanism and dynamic uniform quantizers are set up to reduce information transmission. The next NN is utilized to handle the unknown nonlinear functions. Finally, in order to estimate the unmeasurable states, an NN-based state observer is designed for each agent by using a dynamic gain function. To settle the difficulty caused by the coupling effects of event-triggered conditions and the scaling function in dynamic uniform quantizers and observers, a distributed control protocol with estimated information of its neighbors is designed, which ensures distributed consensus tracking of the nonlinear multiagent systems without incurring the Zeno behavior. The effectiveness of the control protocol is illustrated by a simulation example.

Adaptive Fuzzy Event-Triggered Control for High-Order Nonlinear Systems With Prescribed Performance.

This article focuses on the design of a novel adaptive fuzzy event-triggered tracking control approach for a category of high-order uncertain nonlinear systems with prescribed performance requirements, in which a high-order tan-type barrier Lyapunov function (BLF) is employed to handle and analyze the output tracking error, fuzzy systems are adopted to identify the totally unknown nonlinear functions, and only one gain function rather than parameter estimation functions is designed to cancel out all unknowns appearing in fuzzy systems. As a result, complicated calculations are avoided and a structured simple control is achieved. The proposed controller not only ensures that the tracking error is always within a predefined region but also reduces the communication burden from the controller to the actuator. Finally, comparison simulations are presented to verify the effectiveness of the proposed control schemes.

Quantized Interval Type-2 Fuzzy Control for Persistent Dwell-Time Switched Nonlinear Systems With Singular Perturbations.

This article investigates the problem of quantized fuzzy control for discrete-time switched nonlinear singularly perturbed systems, where the singularly perturbed parameter (SPP) is employed to represent the degree of separation between the fast and slow states. Taking a full account of features in such switched nonlinear systems, the persistent dwell-time switching rule, the technique of singular perturbation and the interval type-2 Takagi-Sugeno fuzzy model are introduced. Then, by means of constructing SPP-dependent multiple Lyapunov-like functions, some sufficient conditions with the ability to ensure the stability and an expected H∞ performance of the closed-loop system are deduced. Afterward, through solving a convex optimization problem, the gains of the controller are obtained. Finally, the correctness of the proposed method and the effectiveness of the designed controller are demonstrated by an explained example.

Adaptive Fuzzy Event-Triggered Control for Single-Link Flexible-Joint Robots With Actuator Failures.

This article studies the finite-time tracking control problem for the single-link flexible-joint robot system with actuator failures and proposes an adaptive fuzzy fault-tolerant control strategy. More precisely, the issue of "explosion of complexity" is successfully solved by incorporating the command filtering technology and the backstepping method. The unknown nonlinearities are identified with the help of the fuzzy logic system. An event-triggered mechanism with the relative threshold strategy is exploited to save communication resources. Furthermore, the proposed control design can guarantee that the tracking error converges to a small neighborhood of origin within a finite time by taking full advantage of the finite-time stability theory. Finally, the simulation example is presented to further verify the validity of the proposed control method.

Sampled-Data Synchronization of Stochastic Markovian Jump Neural Networks With Time-Varying Delay.

In this article, sampled-data synchronization problem for stochastic Markovian jump neural networks (SMJNNs) with time-varying delay under aperiodic sampled-data control is considered. By constructing mode-dependent one-sided loop-based Lyapunov functional and mode-dependent two-sided loop-based Lyapunov functional and using the Itô formula, two different stochastic stability criteria are proposed for error SMJNNs with aperiodic sampled data. The slave system can be guaranteed to synchronize with the master system based on the proposed stochastic stability conditions. Furthermore, two corresponding mode-dependent aperiodic sampled-data controllers design methods are presented for error SMJNNs based on these two different stochastic stability criteria, respectively. Finally, two numerical simulation examples are provided to illustrate that the design method of aperiodic sampled-data controller given in this article can effectively stabilize unstable SMJNNs. It is also shown that the mode-dependent two-sided looped-functional method gives less conservative results than the mode-dependent one-sided looped-functional method.

Robust Sampled-Data Control for Switched Complex Dynamical Networks With Actuators Saturation.

In this article, an aperiodic sampled-data control problem is investigated for polytopic uncertain switched complex dynamical networks subject to actuator saturation. Due to the constraint on the upper bound of the sampling interval being no greater than the dwell time, the issue concerning the asynchronization between the sampled-data controller mode and the system mode is hence considered to be caused by subsystems that may switch in a sampling interval. By considering the sampling interval without switching and the sampling interval with switching, the parameters-dependent loop-based Lyapunov functionals are constructed, respectively. With the help of the constructed functional, mean-square exponential stability criteria for the error polytopic uncertain switched complex dynamical networks are presented under the definition of average dwell time. Furthermore, based on the stability criteria, the asynchronous aperiodic sampled-data controller is designed for polytopic uncertain switched complex dynamical networks subject to actuator saturation. The polytopic uncertain switched complex dynamical networks can be guaranteed to exponentially synchronize with the target node based on the proposed stability conditions and aperiodic sampled-data controller design method. Finally, by transforming the proposed theoretical conditions into the LMI-based objective optimization problem, the domain of attraction of polytopic uncertain switched complex dynamical networks is estimated. An example based on switched Chua's circuit is applied to verify the effectiveness of the proposed method.