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This paper solves the group consensus problem of incremental quadratic constraints nonlinear multi-agent systems with semi-Markov switching parameters via a quantity limited controller. The quantity limited controller is designed according to the stationary probability distribution of the system modes, and the number of controllers can be selected from 1 to the number of system modes. Therefore, the controller can be applied in cases where there is a mismatch between the number of system modes and the number of controllers. Next, the more general incremental quadratic constraint is used to handle the nonlinear terms. Finally, in the simulation section, the method of adding topology links is used to implement external equitable partitions of arbitrary topologies, and the validity of the proposed method is verified by a spring damping system. [ABSTRACT FROM AUTHOR]

Type-2 fuzzy neural networks (T2FNNs) have gained popularity due to their processing ability for high uncertainty. However, concerned with the high-dimensional problems of nonlinear systems, the interpretability of individual T2FNNs is weak due to the exponential growth of fuzzy rules. To deal with this problem, an information orientation-based modular T2FNN (IO-MT2FNN) is developed to improve its interpretability in this paper. First, an information entropy-based decomposition method is designed to divide the original input space into three sub-spaces, namely edge, local and global regions. Then, the information with different attributes is separated to provide an unambiguous interpretation. Second, the independent module describing these regions with type-2 fuzzy sets is embedded in the membership function layer of IO-MT2FNN to represent the coupling relationship between regional information in an interpretable way. Third, an information mapping strategy is introduced with low-order Gaussian kernel matrices, instead of a high-order mapping matrix, to extract the features from the allocated information in each module, which enables IO-MT2FNN to achieve a compact topology through dimensionality reduction. Finally, the simulations demonstrate that the proposed IO-MT2FNN can compete with the advanced approaches in terms of interpretability for the prediction of high-dimensional and complex systems. [ABSTRACT FROM AUTHOR]

This paper studies the adaptive event-triggered (AET)-based path following controller design problem for a networked autonomous vehicle, where the limited networked bandwidth, system nonlinearities and uncertainties are considered. The polytopic model is proposed to construct a linear parameter varying (LPV) system for the nonlinear vehicle system. Taking into account the effects of event trigger on the path following performance, an improved AET mechanism is designed to achieve a balance between efficient communication and accurate path following requirements. Sufficient conditions are developed to guarantee that the closed-loop system is exponentially stable with an H ∞ performance index being satisfied. In addition, a co-design method with less conservatism is derived to obtain the event-triggered weight matrix and output feedback controller gain matrix simultaneously. Finally, simulation results verify the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

This paper proposes a novel hierarchical-adaptive threshold abnormal behavior discrimination scheme (HATAD) for Lipschitz nonlinear large-scale systems with disturbances and uncertain dynamics. Two layers of groups of interlinked observers, namely the supervisor and local layers, are designed. The local layer using open loop observers, switching technique, and local controllers is first developed to protect the physical system from the attack effects, where the proposed switching technique can connect the plant to the local controller under the attack conditions. At the supervisor layer, the main controllers and three types of observers are constructed to detect and discriminate the abnormal behaviors and determine the faulty unit. This architecture leads to less restrictive mathematical conditions and analyses, which ensure the stability and the L 2 − L ∞ performance of the estimation error dynamics. To demonstrate the effectiveness of the proposed approach, a simulation study has been conducted on a large-scale system of two units of benchmark continuous stirred tank reactor (C S T R). [ABSTRACT FROM AUTHOR]

This paper investigates the supervisory adaptive safety control problem for uncertain nonlinear systems with unmeasurable states. In order to estimate unknown parameters and unmeasurable states, a supervisory observer framework consisting of a multi-observer bank and a supervisor unit, is proposed based on a dividing rectangles (DIRECT) algorithm. Under a desired accuracy, the parameter estimates converge to near the true parameters within finite-time while the estimation error of the system state converges to a small neighborhood near the origin. Also, an observer robust adaptive control barrier function is constructed to ensure safety for uncertain nonlinear systems by guaranteeing controlled invariance of a time-varying auxiliary set. By adjusting some parameters in the DIRECT algorithm, the time-varying auxiliary set approaches the original safe set, which reduces the conservatism generated by the compression of the safe set. Finally, two examples, including an adaptive cruise control system, are given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposed an event-triggered adaptive fuzzy prescribed time control strategy for a class of nonlinear systems with uncertain external disturbances and unknown virtual control coefficients under prescribed performance. A novel time-domain mapping technique is proposed to transform the prescribed time tracking control problem into an asymptotic convergence problem. An observer is designed to estimate for the external disturbance and fuzzy approximation error of fuzzy logic systems (FLSs). The problem of "explosion of complexity" is addressed by applying dynamic surface control (DSC) technique to backstepping. An adaptive fuzzy event-triggered strategy is designed using the Lyapunov stability theorem. This strategy ensures that, after time-domain mapping, the tracking error asymptotically converges to zero. Additionally, there is no Zeno behavior and all system signals are bounded. Finally, the effectiveness of the proposed scheme is verified through three simulation examples. [ABSTRACT FROM AUTHOR]

The finite-time distributed state estimation (DSE) problems based on sensor network for discrete-time nonlinear systems are considered in this paper. Considering the uncertainty of the target maneuvers, the interactive multiple models (IMM) based distributed estimation framework is established by local filter and consensus fusion. In the proposed distributed algorithm, partial of the output of the system can be collected by some sensors and the sensor network is supposed to be collectively observable. According to the consensus protocol, the final estimate results are obtained by fusing local estimate results of each sensor after the consensus fusion stage. The distributed estimate results can be obtained with finite-time when the consensus fusion step is larger than the diameter of the network, and the convergence rate of estimate error of the proposed distributed estimate algorithm can be guaranteed. Besides, the existence of the lower and upper bounds of the error covariance matrix are proved with some necessary assumptions. Finally, numerical simulation example is given for tracking the target with different maneuvers. [ABSTRACT FROM AUTHOR]

This paper presents a model reference adaptive control (MRAC) system for nonlinear, time-varying, hybrid dynamical plants affected by modeling uncertainties. This system is unique because, in addition to regulating the trajectory tracking error to zero, it allows the user to set the rate of convergence of the tracking error between consecutive resetting events. This proposed result has been possible by leveraging an auxiliary trajectory tracking error dynamics to accelerate convergence of the trajectory tracking error according to the two-layer MRAC framework. The resetting logic of both the reference model and the auxiliary trajectory tracking error dynamics bound variations in the trajectory tracking error due to undesired resetting events in the plant dynamics. The resetting events of the reference and auxiliary model also reduce the trajectory tracking error whenever some dwell-time condition is met. Finally, the resetting logic of both the reference model and the auxiliary trajectory tracking error reduces the control effort at isolated time-instants. Three numerical examples demonstrate the applicability of the proposed result as well as their advantages over alternative adaptive control techniques for nonlinear, time-varying, hybrid dynamical plants as well as classical MRAC. [ABSTRACT FROM AUTHOR]

This paper studies a distributed extended state observer design and dual-side dynamic event-triggered output feedback (DEOF) anti-disturbance control for interconnected systems (ISs) subject to quantization and multi-source disturbances. First, two novel dual-side dynamic event-triggered mechanisms (DETMs) are proposed to alleviate data transmission in both sensor-to-observer (S-O) and controller-to-actuator (C-A) channels. In addition, the DETM in S-O channel is related to the quantization parameter such that a trade-off between triggering frequency and quantization density can be achieved. Second, by using the transmitted system outputs, a distributed extended state observer is constructed to estimate system states and disturbances. Then based on the outputs of distributed extended state observer, a dual-side DEOF H ∞ controller is designed, which can compensate and attenuate two types of disturbances. Subsequently, some sufficient conditions are derived to guarantee system states and estimation errors converge to zero and system output satisfies H ∞ performance. Finally, a numerical simulation is provided to demonstrate the obtained results. • A distributed extended state observer for ISs is designed based on a novel DETM and a logarithmic quantizer. • A DETM containing the quantization parameter is designed such that a trade-off between event-triggered and quantization can be acquired. • A dual-side DETMs in both S-O and C-A channels are proposed to further save communication resources. [ABSTRACT FROM AUTHOR]

This paper suggests a unified tracking control scheme for systems suffering from unknown control direction and preassigned performance requirement. Distinguished from the existing Nussbaum function-based control methods, the presented approach achieves a unified control framework that encompasses the asymptotic or finite-time stability by introducing sliding mode technique when the nonlinear systems suffer from the unknown control direction issue. Two kinds of stabilities can be obtained only via choosing specific functions. Moreover, the suggested control approach can also deal with the changing of control direction. The stability is analyzed, and the total method rigorously guarantees the tracking errors' required performance criterion. The simulation results of the second order inverted pendulum model serve as verification of the proposed method. Furthermore, as an alternative application scenario, the attitude tracking issue of hypersonic vehicles is dealt with by the presented method subjected with the time-varying control coefficient. • The proposed approach achieves a unified control framework under the unknown control direction. • The control approach rigorously guarantees the tracking errors' required performance. • The simulation results serve as verification of the proposed method. [ABSTRACT FROM AUTHOR]

Dynamical modelling for neural systems with direct and indirect connections is to understand how these connections contribute to neural dynamics. Despite recent findings suggesting the existence of indirect connections in neural systems, their dynamical characteristics remain poorly understood. In this paper, we propose a simplified circuit model with indirect interactions inspired by the indirect connection between two neurons, from an energy perspective. Through bifurcation and dynamics analysis, we find that the presented model has a striking resemblance with the classical Hodgkin-Huxley neuronal model. Moreover, stability in a neural network coupled with energy is demonstrated by combining stability analysis and numerical simulation. Our analysis sheds light on the excitability dynamics and multi-stability that can emerge in biophysical systems with nonlinear interactions inspired by the neural systems and highlights the role of energy in propagating electrical activities. • We construct a neuron-inspired circuit model with indirect interactions involving energy. • The neuron-like excitability and bi-stability are identified in the neuron-inspired circuit. • The neuron-inspired circuit can reproduce excitability as same bifurcation mechanism as the HH neuron. • Stability conditions of the neural network are deduced by stability analysis. • Multistability is triggered in the neural network with different coupling matrix. [ABSTRACT FROM AUTHOR]

Pulsation is a universal phenomenon in all disciplines of nonlinear science, which generally exhibit various nonlinear soliton dynamic modes in nonlinear optics. With the emergence of real-time spectral measurement technology, a new phenomenon of optical soliton pulsation, "invisible" soliton pulsation, has gradually attracted researchers' attention. In this paper, by solving the coupled Ginzburg–Landau equation, we have discovered the partially "invisible" pulsation phenomenon of asymmetric soliton molecules (SMs) composed of two unequal-intensity pulses in a normal-dispersion Mamyshev oscillator for the first time. It is indicated that the fluctuation periods of each internal pulse in asymmetric SMs in terms of peak power, energy, and relative phase difference are all four roundtrips. However, the oscillation period of asymmetric SMs energy is two roundtrips, only half of the above period. Further research shows that the oscillation of the relative phase difference between two internal pulses in SMs is related to the variation of their intensity difference, which can also affect the position change of the spectral modulation peak. This work will enrich the research on "invisible" soliton pulsation and is of great significance for promoting the development of nonlinear dissipative systems. • We studied the pulsating dynamics of soliton molecules in a Mamyshev oscillator. • We discovered the partially "invisible" pulsation of asymmetric soliton molecules. • The total energy period of asymmetric soliton molecules is half of each inside pulse. • The "invisible" pulsation is caused by the intensity difference of the inside pulses. [ABSTRACT FROM AUTHOR]

Understanding and controlling neural network synchronization is crucial for neuroscience in revealing brain functions and addressing neurological disorders. This study explores the innovative use of dynamic learning of synchronization (DLS) technology to enhance synchronization within neuronal networks. Using the Hodgkin-Huxley model across various network topologies, including Erdős-Rényi random graphs, small-world, and scale-free networks, it dynamically adjusts external electrical excitation to study its effects on network synchrony. To further demonstrate the universality of DLS technology, this study also validates the main results using larger-scale networks and the Izhikevich and FitzHugh-Nagumo models. The research quantifies the enhancement of synchrony through DLS, using root-mean-square error (RMSE) and synchronization factors as metrics. Findings show that DLS effectively boosts network synchrony by dynamically adjusting external excitation in response to node differences, significantly in both small-world and scale-free networks, irrespective of synaptic connections. Furthermore, DLS demonstrates potential for targeted synchronization enhancement in specific region of network. This paper highlights DLS technology's effectiveness in modulating external excitation to improve complex neural network synchrony, providing new insights into neural synchronization and information transmission. • A dynamic learning of synchronization (DLS) technique is proposed. • Our DLS technique can improve neural network synchrony by adjusting external electric stimulation in real-time. • The study evaluates DLS effects across different network structures by using Hodgkin-Huxley model. • DLS offers potential for targeted synchronization enhancement in specific parameters region of network. [ABSTRACT FROM AUTHOR]

In this paper, we concentrate on the exponential stabilization of stochastic nonlinear systems. Different from the single event-triggering mechanism in traditional deterministic/stochastic control systems, based on two stopping time sequences, we propose a double-event-triggering mechanism (DETM) to update control signals and make two different controls switch in order. Also, this novel DETM allows aperiodic time updating and guarantees a positive lower bound on the inter-event times. Together with this DETM, we introduce a switching control law that consists of a primary control and a secondary control for a non-switched stochastic system to obtain the exponential stabilization and boundedness results. Finally, an illustrative example with simulation figures is provided to demonstrate the obtained results. • A novel switching control is first established for a non-switched stochastic system. • The switching control generalizes the traditional periodic and aperiodic intermittent controls. • We first extend the single event-triggering mechanism to a double-event-triggering mechanism. • Zeno phenomenon is effectively avoided under the double-event-triggering mechanism. • Exponential stabilization and boundedness problems of stochastic nonlinear systems are solved. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a decentralized Event-Triggered fault-tolerant echo-state network (ESN) direct adaptive controller for uncertain interconnected nonlinear systems in pure-feedback form. The proposed controller addresses input saturation, actuator faults, external disturbances, and unavailable states for measurement. Unlike the existing works in the literature that adapts the ESN weights using the tracking error, our method employs the control error that is estimated using a fuzzy inference system, to derive the adaptation laws. The complexity explosion typically seen with recursive back-stepping and Dynamic Surface Control (DSC) designs is completely avoided. Our control scheme addresses four types of state-dependent actuator faults: bias, drift, loss of accuracy, as well as loss of effectiveness. The ESNs approximate unknown ideal control laws, while robust terms are added to enhance the stability of the closed-loop system. Stability analysis ensures that tracking errors converge, in finite time, to a small compact set near the origin due to the strictly positive real (SPR) property. Simulation results of a quadrotor UAV and a mathematical system are presented. A comparative analysis is performed with another approach to emphasize the effectiveness of the proposed method. • An ESN adaptive controller is proposed for interconnected pure-feedback unknown nonlinear systems with finite-time stability. • The input saturation, actuators faults, triggering events and complexity explosion are dealt with using state transformation. • The adaptive laws of the ESN are derived for the first time using control-errors instead of tracking-errors. • The parameters of the adaptive laws are highly reduced due to the use of only one ESN regardless of system's order. [ABSTRACT FROM AUTHOR]

This paper studies the distributed state estimation problem for nonlinear systems with random transmission delays and transmission failures, and proposes a novel sequential hybrid consensus filtering algorithm. The covariance intersection method is used to reach consensus over priors, and the consensus on measurements is used to fuse the innovation information, which makes the proposed algorithm robust to transmission failures. A compensation scheme is proposed when there are one-step transmission delays. The consensus weight of the delayed information is derived, and with the compensation term, the local estimation accuracy is improved. Rather than waiting for all information from neighboring nodes, the proposed algorithm is implemented sequentially once information from a neighboring node is received during the consensus step. The rigorous theoretical performance analysis is presented, and the proposed algorithm is tested numerically on a single target tracking problem and a distributed navigation of satellite cluster problem. [ABSTRACT FROM AUTHOR]

Practical time-varying formation-containment tracking (TVFCT) issue for nonlinear multi-agent systems with general noise is researched in this paper. A neuro-adaptive practical TVFCT protocol is put forward, where neural networks (NNs) and parameter adaptive laws are developed for estimating the nonlinearities and compensating the upper bound of the time-varying formation (TVF) condition, respectively. Leaders are expected to achieve the predetermined TVF and followers are driven to move into the formation structure confined by leaders simultaneously. The whole formation position depends on the desired trajectory produced by a virtual-leader. General noise rather than white noise is investigated in the multi-agent systems. The noise-to-state-practically stability in probability (NSPS-P) criteria can be guaranteed by employing the Lyapunov theories combined random differential equations (RDEs). Numerical simulation results reveal the effectiveness of the developed protocols. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the p th moment exponential stability of impulsive random delayed nonlinear systems (RDNS) with average-delay impulses. Utilizing the average impulsive interval, average impulsive delay, and the Lyapunov method, we present several criteria for p th exponential stability in these systems under a novel condition, diverging from previous literature. Additionally, we explore the effects of delayed impulses, analyzing both destabilizing and stabilizing impulses. Our findings reveal the dual effects of time delay in impulses, which can potentially destabilize a stable system or stabilize an unstable one. • The p th moment exponential stability is investigates for impulsive RDNS. • Established stability criteria for impulsive RDNS with average-delay impulses. • Both continuous dynamics and impulses take time delay into account. • Average delayed impulses can stabilize unstable systems or destabilize stable ones. [ABSTRACT FROM AUTHOR]

This paper investigates command filter-based adaptive neural network (NN) minimal learning practical fixed-time control for stochastic nonlinear systems with prescribed performance and actuator faults. The considered system is in a high-order nonstrict-feedback stochastic structure with unknown dynamics and external disturbances. By combining NN with minimal learning parameter method, the need for prior knowledge of nonlinear functions is eliminated, and the number of weights' updating laws for the NN is reduced to one, regardless of the system's order and number of neural nodes. This reduction significantly decreases the computational burden. Additionally, a unique property of the Gaussian basis function of NNs is applied to solve the algebraic loop problem of the nonstrict-feedback structure. A novel event-triggered control mechanism is proposed to save communication resources. In order to surmount the "explosion of complexity" and "singularity" problems, a novel fixed-time command filter is suggested, and then, a modified compensation mechanism is proposed to mitigate the errors that emerge from command filters. Furthermore, to improve the transient and steady-state performance of the tracking error, a prescribed performance function is taken into account. Via the Lyapunov stability theory, it will be shown that the developed adaptive backstepping control scheme, guarantees that the closed-loop system signals are bounded in probability in a fixed time, that the convergence time is independent of the initial value, and the tracking error remains within the decaying prescribed performance bounds all the time. Finally, the effectiveness and practicability of the theoretical results are verified by a practical simulation example. [ABSTRACT FROM AUTHOR]

This paper investigates the zonotope-based interval estimation problem for event-triggered nonlinear systems with incrementally quadratic constraint and unknown-but-bounded uncertainties from process disturbance and measurement noise. Considering the restricted communication bandwidth, an event-triggered communication protocol is deployed in the sensor-to-observer channel, based on which an event-triggered observer is constructed for nonlinear systems having incremental quadratic constraints. A co-design method of nonlinear observer and event-triggered protocol is obtained to ensure the stability and ℓ ∞ index of the estimation error dynamic. Based on the designed event-triggered observer, a zonotope-based interval estimation algorithm is designed for the purpose of giving the intervals enclosing admissible values of system state. The mean value extension coalesce into natural interval extension is utilized to deal with the nonlinear transformation of system, and the enclosing zonotope of ellipsoid is introduced to tackle the extra uncertainties induced by event-triggered protocol. Lastly, the results of a simulation on a hyper-chaotic Chen system are provided to confirm the validity of the presented methodology. [ABSTRACT FROM AUTHOR]

This paper addresses the optimized leader–follower consensus control problem of nonlinear canonical dynamic multi-agent system (MAS). Since every agent is modeled in high-order dynamic, they contain the various state variables having derivative relations. Consequently, to attain the optimized consensus control, backstepping technique and reinforcement learning (RL) are combined together. In the first backstepping step, the virtual control is formulated to have the consensus error term consisting of neighbor agents' output states. In the last backstepping step, since the nonlinearity dynamic is arisen, the optimized actual control is derived by performing the critic-actor RL. It is worth mentioning that, in the traditional RL optimal control, the critic and actor updating laws are obtained by performing the gradient descent algorithm to square of the approximated Hamilton–Jacobi-Bellman (HJB) equation, which includes multiple nonlinearity items, as a result, the algorithm is very intricate. However, in this optimized consensus control, since the RL training laws are yielded in the light of negative gradient of a simple positive function that is relevant to the HJB equation, its algorithm is very simple. At the same time, it can also avoid the persistence excitation conditions. Finally, theory and simulation confirm the validity of this optimized consensus method. [ABSTRACT FROM AUTHOR]

This paper uses a prescribed-time event-triggered approach to explore the control of uncertain strict-feedback nonlinear systems with output constraints and an unknown time-varying control gain. The proposed method utilizes a universal barrier Lyapunov function (BLF) to ensure compliance with the output constraints. Furthermore, a technique known as congelation of variables is employed to handle the unknown time-varying control gain. Approximating the unknown dynamics using radial basis function neural network (RBFNN), a neural prescribed-time controller is designed based on the backstepping approach. Additionally, the event-triggered mechanism is employed to conserve computational and communication resources. With this scheme, all signals are guaranteed to converge to a compact set within the prescribed time frame. Finally, numerical simulations are presented to illustrate the effectiveness of the proposed algorithm. • The RBFNN is employed to approximate the uncertain dynamics. • A time-varying BLF is introduced to address the constraints on the tracking error. • The unknown control gain is tackled by a method known as congelation of variables. • A prescribed-time event-triggered approach achieves the controller design. [ABSTRACT FROM AUTHOR]

This paper studies the sliding-mode surface (SMS)-based approximate optimal control issue for a class of nonlinear multiplayer Stackelberg-Nash games (MSNGs). First, considering different roles of the players in MSNGs, a hierarchical decision-making process is expressed as designing different cost functions for the leader and the followers. Therein, the leader makes its decision preferentially with consideration of all followers, while each follower responds optimally to leader's strategy simultaneously via Nash games. Then, based on the sliding mode control technology, a novel robust control policy is proposed to solve the coupling Hamilton–Jacobi equations of nonlinear MSNGs. Subsequently, SMS-based critic network is utilized to approximate optimal control inputs for all players. Based on the Lyapunov stability theory, it is strictly proven that all signals of the closed-loop nonlinear systems are uniformly ultimately bounded. Finally, the effectiveness of the proposed method is demonstrated via a simulation example. • The Stackelberg-Nash game (SNG) has one leader and multiple followers. • The SMC method is combined with optimal control design for SNG. • The robust control scheme applies only a critic network. [ABSTRACT FROM AUTHOR]

This paper considers the problem of fuzzy logic adaptive fixed-time control for nonlinear switched system. Different from existing research results on fixed-time control, the system functions are completely uncertain in this paper. The approximation error will cause Lyapunov function not to be negative definite. To address this problem, a new criterion of fixed-time stability is developed at first. Based on this fixed-time theory, a fuzzy logic control method is proposed by using backstepping technique. The proposed adaptive laws in this paper do not satisfy a series of linear differential equations but nonlinear ones. Simulation results verify the feasibility of presented algorithms. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of dynamic event-triggered output feedback tracking control for a class of $p$ -normal nonlinear systems with unknown growth rate. To cope with the unknown growth rate imposed on the system nonlinearities, a dynamic gain technique is introduced and a constructive coordinate transformation is given. On the other hand, an event-triggered strategy combining with the dynamic gain is proposed such that the triggering threshold can be adjusted in an adaptive manner. With the help of the proposed event-triggered strategy, a dynamic event-based output feedback controller is developed to ensure that all signals of the closed-loop system are bounded while the tracking error converges to a small neighborhood of the origin. Moreover, it is proved that the Zeno behavior is excluded in the presence of nonsmooth controller. Two examples, including an induction heater circuit system and a numerical example, are provided to indicate the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

This paper focuses on the observer-based fault-tolerant control problem for the discrete-time nonlinear systems with the perturbation and the fault signals. First, the nonlinear term with perturbation is put into the local nonlinear part so that the nonlinear system with perturbation can be described as an interval type-1 (IT1) T-S fuzzy system. Then, based on the unknown input observer technology, the IT1 T-S fuzzy fault estimation (FE) observer scheme is presented to obtain the real-time FE information and decouple the local nonlinear part from the estimation error system, where the design complexity and the computational burden are reduced simultaneously. Second, based on the real-time FE information, an FE-based interval type-2 (IT2) T-S fuzzy fault-tolerant control scheme is presented to achieve the compensation for the influence of the fault signal and the stabilization for the system. Different from the traditional methods, a mixed design scheme, which is based on the IT1 T-S fuzzy fault estimation observer method and the IT2 T-S fuzzy fault-tolerant controller method, is proposed in this paper. This strategy can not only reduce the computational burden, but also obtain a less conservative result. Finally, the effectiveness of the mixed design approach is illustrated by an example. [ABSTRACT FROM AUTHOR]

This paper focuses on the security cluster synchronization (CS) of coupled genetic oscillator networks (GONs) with parameters mismatch under denial-of-service (DoS) attacks. Firstly, a model of DoS attacks on the control channel of GONs is established. Then, in order to achieve secure CS of GONs under DoS attacks, a pinning partial impulsive control (PPIC) strategy is proposed for the first time. Compared with the existing pinning impulsive control and partial impulsive control, the PPIC control method only controls part of the molecules of part of the genetic oscillators, so it has better performance in saving control cost. Moreover, we design an algorithm to obtain sufficient conditions for secure CS and the DoS attacks duration ratio that the system can tolerate. In addition, when the system is immune to DoS attacks, it can still achieve CS under PPIC. Finally, two numerical examples based on MATLAB software are presented to demonstrate the effectiveness of the results. The secure synchronization region is obtained, and the convergence efficiency of error systems under PPIC and pinning impulsive control is compared in the simulation. • Compared with the existing results, this article considers security cluster synchronization of genetic oscillator networks under DoS attacks and the DoS attacks duration ratio that the system can tolerate is also obtained, which is more practical. In addition, this article also considers the parameters mismatch and nonlinear coupling of the system, which is more complex to study. • The pinning partial impulsive control (PPIC) strategy is proposed for the first time in this paper, which combines the pinning impulsive control and the partial impulsive control, and can further reduce the control cost of the system. The convergence efficiency of error systems under PPIC and pinning impulsive control is compared in the simulation. • A new algorithm for achieving secure security cluster synchronization of genetic oscillator networks under DoS attacks is designed. On the premise of realizing secure cluster synchronization, the relationship between the DoS attacks duration ratio, the average impulsive interval, the impulsive strength and the proportion of the controlled molecules is obtained, and the secure synchronization region is given in the simulation. [ABSTRACT FROM AUTHOR]

This paper suggests a novel limit cycle control technique, based on the finite-time stability scheme, for producing sustained oscillations in a class of nonlinear complex systems. The considered systems are constrained to input dead-zone and saturation simultaneously and suffer from non-vanishing perturbations due to model uncertainties, and external disturbances. For this purpose, an innovative sliding manifold is proposed based on the topology of the wanted limit cycle which provides the conditions for developing the finite time stability concept for limit sets. With the aid of the finite-time command filter and the cooperation of the sliding mode control (SMC) method with the backstepping technique, a robust controller is constructed which guarantees the finite-time convergence of phase trajectories of the closed-loop system toward the wanted limit cycle. This leads to the creation of sustained oscillations, with the desirable amplitude and frequency, in the system's output. The stability analysis is proved based on the Lyapunov approach through the set stability concept. Finally, the effectiveness of the suggested methodology is confirmed by a variety of simulations. • This paper presents a finite-time limit cycle controller for nonlinear systems with input dead-zone and saturation, simultaneously. • Since the attractive limit cycle is a positive limit set, the set stability approach is used. • The sliding surface is designed according to the shape of the desired limit cycle. • The effectiveness of the proposed method is validated by providing simulation results. [ABSTRACT FROM AUTHOR]

This paper investigates the fixed-time consensus control problem for a class of nonlinear multiagent systems (MASs) based on dynamic event-triggered mechanism. In contrast to the already-existing fixed-time control schemes, which cannot address the singularity problem, by constructing a virtual signal and using inequality technology, a new processing method is provided to solve such a problem. In addition, a novel fixed-time nonlinear filter that converges in a fixed time is introduced, which effectively solves the "explosion of complexity" problem existed in backstepping. Moreover, to improve the utilization of resources, an event-triggered mechanism with internal dynamic variables is proposed. It is worth noting that some existing static event-triggered mechanisms are special cases of the dynamic ones. On this basis, an effective fixed-time event-triggered control scheme is developed for MASs, which minimizes the data transmission as much as possible while ensuring the system performance. More importantly, the scheme can ensure the convergence of the system in a fixed time. Finally, simulation results are shown to support the validity of the developed approach. • Compared with the early results that may lead to the singularity problem, a practical fixed-time stability theory is introduced in this paper, which not only guarantees the convergence of MASs in fixed time, but also avoids the above problems in early results. • A novel fixed-time nonlinear filter is presented in this paper, which can not only solve the problem of "explosion of complexity", but also ensure that the designed nonlinear filter converges in a fixed time. • The controller developed herein is updated if only if the dynamic event-triggered condition is satisfied, which reduces the computational and communication burden, that is, the lower bound on inter-execution time in previous results is no greater than that in this paper. [ABSTRACT FROM AUTHOR]

This paper solves the problem about the practical fixed-time consensus for heterogeneous nonlinear multiagent systems (MASs) with one-order dynamic models. First, the event trigger functions are introduced to reduce the communication burden of the network. And the adaptive laws are present which aim to deal with the instability caused by the uncertain parameters. By combining them, the control input is designed to make the system practical fixed-time consensus. Then we prove the boundedness of the variables and there is no Zeno phenomenon in the discussed systems under the control scheme. Comparing with the existing works, this paper focus on the distribute uncertain heterogeneous nonlinear MASs, has a practical fixed-time consensus and takes a balance between communication burden and accuracy. Finally, a comparison experiment is illustrated. [ABSTRACT FROM AUTHOR]

In this paper, the resilient distributed filtering problem is studied for time-varying nonlinear multi-rate systems (TVNMRSs) with integral measurements over sensor networks, where the lifting technology is utilized during the analysis of the TVNMRSs. In order to reduce unnecessary data transmissions, the memory-event-triggered communication mechanism (METCM) is adopted to determine whether the sensor nodes communicate with each other. The purpose of this paper is to design a resilient distributed filtering method such that, for all multi-rate sampling, integral measurements, filter gain fluctuations and METCM, an upper bound on the filtering error covariance is guaranteed and minimized subsequently by choosing the appropriate filter gains. Besides, a sufficient condition with rigorous theoretical proof is provided to discuss the uniform boundedness of the upper bound on the filtering error covariance. In the end, the simulations with comparative experiments are made to demonstrate the effectiveness of proposed resilient distributed filtering algorithm based on METCM. • The METCM is used to regulate the communication among sensor nodes. • A new resilient distributed filtering scheme with recursive characteristic is proposed. • A sufficient condition is given to ensure the uniform boundedness of upper bound on the filtering error covariance. [ABSTRACT FROM AUTHOR]

This paper introduces a co-design approach for fault detection and time-varying formation control for a series of nonlinear leader-following multi-agent systems under stochastic switching directed topology. The random environmental fluctuations are described by a Markov chain. Utilizing relative output information, fault detection observers are developed not only to estimate system states but also to construct a robust residual signal, capable of detecting multiple faulty agents simultaneously in the presence of external perturbations. The paper provides sufficient conditions to guarantee the uniform ultimate boundedness in probability of the formation error and the H ∞ performance for fault detection. Precise identification of potential faulty agents is achieved by evaluating the residual signal and logical reasoning. The effectiveness of formation control and the efficiency of the proposed joint design approach are demonstrated by a set of tailless fighter airplanes. [ABSTRACT FROM AUTHOR]

This paper investigates a technical problem, that is, how to apply the backstepping to obtain an event-triggered controller for multiple-input multiple-output (MIMO) nonlinear systems. If the controller is set to be triggered, then all virtual controls are also forcibly triggered synchronously since this controller incorporates all virtual controls. That indicates the virtual controls applied to the control operation are event-triggered and discontinuous. As a result, the control design and performance analysis may become more complicated for such event-triggered systems. Therefore, this paper presents a prescribed-time fuzzy adaptive event-triggered control strategy for MIMO nonlinear systems. A new event-triggered mechanism is constructed for updating the actual controller and all virtual controls, and the nonlinear impulsive dynamics approach is employed for tackling the difficulties arising from the discontinuity of the virtual controls. Moreover, the Lyapunov stability analysis approach for nonlinear impulsive system is utilized to determine the performance of the controlled system. The good tracking performance is accomplished by selecting the proper design parameters. Ultimately, the feasibility and validity of the developed control strategy is supported by simulation. [ABSTRACT FROM AUTHOR]

Fractional order nonlinear systems with saturated delayed impulses and short-term memory is investigated in this paper. Models in this paper are described by piecewise Caputo derivative. First, sufficient conditions for local exponential stability are derived based on the fractional order Lyapunov function method and saturated control theory. Then, the optimization model to estimate the domain of attraction is built, which is constrained by some LMIs. Third, the application of synchronization for fractional order complex dynamical networks via distributed saturated delayed impulsive control is studied. Finally, two numerical examples are given to illustrate the effectiveness of the theoretical results. • According to the impulsive control theory and fractional order calculus, some linear matrix inequalities(LMIs) based sufficient conditions for local exponential stability are derived for fractional order nonlinear systems with short memory. Both delay and saturation have been considered in the impulsive effects. • The domain of attraction is estimated by building an optimization model, which is also transformed to a solvable optimization problem, furthermore, the control gain matrix can be computed by solving the optimization problem. • The analysis is extended to fractional order complex dynamical networks with distributed impulsive method. The impulsive synchronization criteria are derived, which are related to the parameters of nodes' dynamics, the general algebraic connectivity and impulsive interval, etc. Then, the optimization problem with constraints formed as LMIs is built. [ABSTRACT FROM AUTHOR]

In the existing efficient robust model predictive control (ERMPC) algorithms (see e.g. [14,31,32]), through offline optimization and online lookup table calculation, a fixed state feedback control law or a linear interpolated control law is applied to a system when the system state lies between two adjacent polyhedrons, which undoubtedly will result in conservativeness of the controller. Faced with this issue, an improved ERMPC algorithm is proposed in this paper, which considers the nonlinearity between the state feedback control laws with respect to polyhedrons and the norm distance from system state to origin, and can provide continuously variable state feedback control law varying with the state. First, a set of polyhedral parameters and their corresponding state feedback control law sequences are obtained offline by solving a set of LMIs optimization problems. Next, for each state feedback control law sequence, a nonlinear fitting function is established offline between the state feedback control law and its serial number. Then a simplified lookup table is constructed offline to save memory space and shorten online computation time of the controller. According to the simplified lookup table and information of the norm distance from system state to origin, we online establish the coordinate of current state in the nonlinear fitting curve for getting current feedback control law, which changes continuously with the state. The proposed ERMPC algorithm is successfully applied to an actual fast-responding linear one stage inverted pendulum (LOSIP) system to verify its effectiveness. [ABSTRACT FROM AUTHOR]

This paper develops a new dual ML-ADHDP method to solve the optimal consensus problem (OCP) of a class of heterogeneous discrete-time nonlinear multi-agent systems (MASs) with unknown dynamics and time delay. A hierarchical and distributed control strategy is used to transform the original problem into nonlinear model reference adaptive control (MRAC) problems and an OCP of virtual linear MASs. For the nonlinear MRAC problems, a new multi-layer action-dependent heuristic dynamic programming (ML-ADHDP) method is developed to overcome the unknown dynamics and neural network estimation errors, which has higher control accuracy. In order to solve the OCP of virtual linear MASs and improve the convergence speed, a new multi-layer performance index is proposed. Then the ML-ADHDP method is used to solve the coupled Hamiltonian–Jacobi–Bellman equation and obtain the optimal virtual control. Theoretical analysis proves that the original MASs can achieve Nash equilibrium, and simulation results show that the developed dual ML-ADHDP method ensures better convergence speed and higher control accuracy of original MASs. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive fuzzy fixed time control scheme is developed for stochastic pure-feedback nonlinear systems with full state constraints. The mean value theorem is exploited to deal with the problem of nonaffine appearance in the systems and transform the structure of pure-feedback to the structure of strict-feedback. The barrier Lyapunov functions are constructed to guarantee that all states in the systems maintain within the prescribed constraints and the fuzzy logic systems are employed to approximate unknown nonlinear functions at each step. Then, an adaptive fuzzy fixed time controller is constructed by utilizing backstepping technique, which guarantees that all the signals in the considered systems are semiglobally uniform ultimately bounded in a fixed time. Finally, the validity of the proposed fixed time control scheme is verified via a simulation example. [ABSTRACT FROM AUTHOR]

Non-uniform rational B-splines (NURBS) are a convenient way to integrate CAD software and analysis codes, saving time from the operator and allowing efficient solution schemes that can be employed in the analysis of complex mechanical problems. In this paper, the Isogeometric Boundary Element Method coupled with Bézier extraction of NURBS and conventional BEM are used for analysis of 2D contact problems under cyclic loads. A node-pair approach is used for the analysis of the slip/stick state. Furthermore, the extent of the contact area is continuously updated to account for the nonlinear geometrical behaviour of the problem. The Newton–Raphson's method is used for solving the non-linear system. A comparison to analytical results is presented to assess the performance and efficiency of the proposed formulation. Both BEM and IGABEM show good agreement with the exact solution when it is available. On most examples, they are equivalent with some advantage for IGABEM, though the former is slightly more accurate in some situations. This is probably due to the smoothness of NURBS not being able to describe sharp edges on tractions. As expected, IGABEM incurs in higher computational cost due to the basis being more complex than conventional Lagrangian polynomials. [ABSTRACT FROM AUTHOR]

This paper investigates the input-to-state stability (ISS) and integral input-to-state stability (iISS) of switched stochastic nonlinear systems with time delays and random impulses. Different from the existing researches on ISS and iISS, random impulses with both high intensity and density are taken into account. More practically, these impulses are of different stochastic characteristics with respect to different subsystems, and may also occur in coincidence with the subsystem switching instants. The upper bound of the time-derivative operator of Lyapunov function is assumed to be time-varying and mode-dependent, and some sufficient conditions for the ISS and iISS properties of this presented switched stochastic nonlinear systems are established by employing Lyapunov-Razumikhin technique and comparison principle. Finally, several numerical examples are adopted to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

The event-triggered security control and fault detection for nonlinear systems, in which the output signals are wirelessly transmitted to the control and detection module, is investigated in this paper. In particular, quantization before data transmission and deception attacks during data transmission are considered. To ease the data transmission pressure of wireless networks, a dynamic event-triggered protocol is proposed. Specifically, the triggering threshold changes in accordance with the system state. A stochastic sequence is introduced for modelling the time of occurrence of cyber-attacks within an insecure communication environment. By taking the dynamic event-triggered protocol, signal quantization and randomly occurring deception attacks into account, an integrated dynamic output feedback controller and fault detection filter module is developed. With the proposed design, stochastic stability is obtained, while the expected levels of security control performance and detection performance are also guaranteed. Novel algorithms are proposed for determining the parameters of the controller, filter and dynamic event-triggered protocol. A practical example is given to demonstrate the effectiveness of the proposed design idea. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive neural control scheme is proposed for a class of unknown nonlinear systems with unknown sensor hysteresis. The radial basis function neural networks are employed to approximate the unknown nonlinearities and the backstepping technique is implemented to construct controllers. The difficulty of the control design lies in that the genuine states of the system are not available for feedback, which is caused by sensor hysteresis. The proposed control scheme eventually ensures the practical finite-time stability of the closed-loop system, which is proved by the Lyapunov theory. A numerical simulation example is included to verify the effectiveness of the developed approach. [ABSTRACT FROM AUTHOR]

The finite-time event-triggered H ∞ fuzzy output feedback control problem is investigated in this paper for a class of nonlinear systems. The considered nonlinear system is first modeled by an interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy system with the modeling errors. A state observer and an event-triggered mechanism are then designed by using the sampled estimating states and measured output signals. Based on the designed state observer and event-triggered mechanism, an observer-based finite-time event-triggered H ∞ fuzzy controller is developed. The sufficient conditions of guaranteeing the finite-time stability of the addressed system are established in the framework of linear matrix inequalities (LMIs). Furthermore, a computational algorithm of solving observer and controller gain matrices is given in terms of the established sufficient conditions. Finally, a practical simulation example is provided to demonstrate the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

In the paper, a novel input-constrained H ∞ fault-tolerant control approach is developed by using sliding mode control technology and event-triggered reinforcement learning (RL) algorithm. To reduce or even eliminate the impacts of the time-varying actuator failures, a properly sliding mode control strategy is proposed for the controlled system, while the event-triggered H ∞ control scheme is established via RL algorithm for the equivalent sliding mode dynamics. By utilizing a single neural network (NN), the Hamilton–Jacobi–Bellman (HJB) equation can be solved approximately, thereby gaining time-triggered worst-case disturbance law, as well as event-triggered optimal control policy. Besides, it is unnecessary to given a initial stabilizing control input in the learning process of neural networks (NNs) in this paper. Moreover, the Lyapunov stability principle is applied to guarantee that the controlled system is uniformly ultimately bounded (UUB). Finally, to verify the feasibility and efficient performance of the developed approach, three simulations are carried out. [ABSTRACT FROM AUTHOR]

In this paper, the locally fixed-time and globally fixed-time $\mathcal {H}_{\infty }$ control problems for the port-controlled Hamiltonian (PCH) systems are investigated via the interconnection and damping assignment passivity-based control (IDA-PBC) technique. Compared with finite-time stabilization, where the convergence time of the closed-loop system's states relies on the initial values, the settling time of fixed-time stabilization can be adjusted to achieve desired equilibrium point regardless of initial conditions. The concepts of fixed-time $\mathcal {H}_{\infty }$ control, fixed-time stability region (or region of attraction), and fixed-time stability boundary are presented in this paper, and the criterions of globally fixed-time attractivity of a prespecified locally fixed-time stability region are obtained. Combining the locally fixed-time stability of an equilibrium point and the globally fixed-time attractivity of a prespecified fixed-time stability region, the globally fixed-time $\mathcal {H}_{\infty }$ control problem of PCH system is effectively solved. Two novel control laws are designed to deal with the globally fixed-time $\mathcal {H}_{\infty }$ control problem, and the conservativeness in estimating the settling time is also briefly discussed. An illustrative example shows that the theoretical results obtained in this paper work very well in the fixed-time $\mathcal {H}_{\infty }$ control design for PCH systems. [ABSTRACT FROM AUTHOR]

This paper investigates the probabilistic-constrained distributed filtering problem for a class of nonlinear stochastic systems with state constraints and cyber attacks. The considered cyber attacks are periodic denial-of-service (DoS) attacks which are modeled by a kind of periodic pulse-width-modulated (PWM) jamming signals. Different from some existing works, by using the proposed filter design method, the probability of the filtering error exceeding a threshold can be guaranteed below a certain level quantitatively. Furthermore, in order to economize the limited bandwidth resources, an event-triggered communication scheme (ETS) is designed for the data transmission. The aim of the problem addressed is to design a time-varying distributed filters such that: 1) the probability of the filtering error restricted to a given ellipsoid is larger than a specified value; and 2) the obtained ellipsoid threshold is minimized in the sense of matrix norm at each time point. To achieve this purpose, a recursive linear matrix inequality method is utilized and sufficient conditions are derived. Moreover, the filter parameters are explicitly determined in terms of the solution to certain matrix inequalities. Finally, the reliability and applicability of the proposed distributed filtering strategy are demonstrated by an illustrative example. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of event-triggered $\mathcal {H}_{\infty }$ control for continuous Takagi-Sugeno fuzzy systems with repeated scalar nonlinearities. A feasible stability solution is first proposed based on the fuzzy-rule-dependent Lyapunov functional methods and positive definite diagonally dominant matrix techniques, which not only reduces the conservativeness of the resulting closed-loop dynamic system, but also ensures the concerned fuzzy system is asymptotically stable with a specified $\mathcal {H}_{\infty }$ disturbance attenuation performance. Then, sufficient conditions are presented for the existence of admissible state-feedback controller, and the cone complementarity linearization approach is employed to convert the non-convex feasibility problem into a sequential minimization one subject to linear matrix inequalities, which can be validly solved by employing standard numerical software. In the end, a numerical example and a Chua’s chaotic circuit system are provided to show the applicability of the proposed theories. [ABSTRACT FROM AUTHOR]

This paper investigates the adaptive fuzzy output feedback event-triggered control problem for a class of switched nonlinear systems with sensor faults. Due to that the unknown nonlinearities of the systems are more general and the sensor undergoes faults, the considered problem is difficult to be addressed by existing schemes. Therefore, fuzzy logic systems are employed to approximate unknown nonlinear terms and a fault compensation coefficient is introduced to compensate for the effect of sensor failures. Then, a state observer is established for estimating unmeasured states. By choosing a suitable common Lyapunov function, an adaptive fuzzy output feedback fault-tolerant event-triggered controller is derived. It is proven that the proposed scheme can guarantee that the system output tracks the desired trajectory effectively, all states of the resulting closed-loop system are semi-globally uniformly ultimately bounded, and the Zeno phenomenon is excluded. Finally, two simulation examples, which include a switched RLC circuit system and a numerical example, are presented to show the the effectiveness of the proposed strategy. [ABSTRACT FROM AUTHOR]

In this paper, nonlinear control for dealing with a class of uncertain nonlinear systems is discussed according to operator-based coprime factorization method. In detail, firstly, for guaranteeing internal-output stability of nominal nonlinear systems with left factorization, a simple and effective design scheme is proposed with a weak assumption. Simultaneously, based on the proposed scheme, the given nominal nonlinear systems are proved to be coprime. Secondly, tracking performance of the considered systems is obtained by designing a suitable Bezout identity without complicated calculation on the obtained left factorization. Thirdly, with respect to the considered nonlinear system, when it comes to appear perturbation, different adverse effects resulting from different perturbation are considered to guarantee robust stability. For the two different cases, two suffcient conditions using inherent characteristics are proposed for guaranteeing robust stability. Finally, two examples are shown to confirm effectiveness of the proposed design scheme of this paper. [ABSTRACT FROM AUTHOR]

This paper focuses on the problem of finite-time stabilization for a class of high-order nonlinear systems with output constraint and zero dynamics. The systems under investigation possess two remarkable features: the output is restricted in a pre-specified region arising from the demand of practical operation, and inherent nonlinearities include nonlinear growth rate of high-order and low-order together with unmeasurable dynamic uncertainties. This paper proposes a continuous controller by means of a new tangent function and a serial of nonnegative integral functions with sign functions, and the controller ensures the adjustability of convergent speed of system state, which is faster than the counterpart of traditional finite-time stabilizers. The novelty is attributed to a perspective to applying the fast finite-time stability in partial state feedback control design in the case when the output is restricted. Finally, a numerical example is presented to demonstrate the effectiveness of the theoretical result. [ABSTRACT FROM AUTHOR]

In this paper, the synchronization problem for networked nonlinear agents with time-varying control gain is studied under a synchronous periodic data sampling framework. To achieve synchronization, both the state-dependent and time-dependent event-triggered protocols are proposed. The effectiveness of these protocols is justified by Lyapunov stability theorem based on rigorous mathematical proof, facilitated by a delayed differential inequality with time-dependent parameters. Instead of specifying a lower bound for the control gain, as others usually suggested, our criteria rely on its time-average and thus allow higher flexibility in controller design. Numerical simulations are also presented to confirm the reaching of synchronization and demonstrate the wide applicability of the proposed protocols. [ABSTRACT FROM AUTHOR]