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This article develops a neuro‐adaptive observer for state and nonlinear function estimation in systems with partially modeled process dynamics. The developed adaptive observer is shown to provide exponentially stable estimation errors in which both states and nonlinear functions converge to their true values. When the neural approximator has an approximation error with respect to the true nonlinear function, the observer can be used to provide an H∞$$ {H}_{\infty } $$ bound on the estimation error. The article does not require assumptions on the process dynamics or output equation being linear functions of neural network weights and instead assumes a reasonable affine parameter dependence in the process dynamics. A convex problem is formulated and an equivalent polytopic observer design method is developed. Finally, a hybrid estimation system that switches between a neuro‐adaptive observer for system identification and a regular nonlinear observer for state estimation is proposed. The switched operation enables parameter estimation updates whenever adequate measurements are available. The performance of the developed adaptive observer is shown through simulations for a Van der Pol oscillator and a single link robot. In the application, no manual tuning of adaptation gains is needed and estimates of both the states and the nonlinear functions converge successfully. [ABSTRACT FROM AUTHOR]

Summary: The problem of interval observer design for systems described by nonlinear models with uncertainties is considered. The problem is solved based on special mathematical technique (the algebra of functions) which allows obtaining solution for systems containing non‐smooth nonlinearities. The relations to design interval observer insensitive or having minimal sensitivity to the disturbance and estimating the prescribed nonlinear function of the state vector of the original system are derived. Theoretical results are illustrated by example. [ABSTRACT FROM AUTHOR]

Summary: This article considers the problem of designing distributed event‐triggered states and unknown disturbances observers for a class of nonlinear interconnected systems where the local state vectors are affected by unknown delays and the nonlinear function satisfying the Lipschitz condition. Distributed observers are designed based on the local input vector and both the local and remote output vectors. Different from previously distributed observers for interconnected systems where the local and remote output vectors are updated continuously, the one in this article uses only information on the local and remote output vectors updating at triggering instants of proposed event‐triggered mechanisms. This indicates that the proposed method in this article is better than the existing ones in saving communication resources while still keeping an acceptable estimation performance. Sufficient conditions for the existence of the proposed distributed observers are established and are formed in a convex optimization problem which can be easily solved by using the MATLAB LMI Control Toolbox. Finally, a numerical example is given to confirm the effectiveness and advantages of the proposed method. [ABSTRACT FROM AUTHOR]

Summary: Nonlinear systems widely exist in real‐word applications and the research for these systems has enjoyed a long and fruitful history, including the system identification community. However, the modeling for nonlinear systems is often quite challenging and still remains many unresolved questions. This article considers the online identification issue of Hammerstein systems, whose nonlinear static function is modeled by a B‐spline network. First, the identification model of the studied system is constructed using the bilinear parameter decomposition model. Second, the online recursive algorithms are proposed to find the estimates using the moving data window and the particle swarm optimization procedure, and show that these estimates converge to their true values with a low computational burden. Numerical examples are also given to test the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper discusses pseudospectra and stability radii for structured nonlinear matrix functions, such as Hermitian, skew‐Hermitian, H‐even, H‐odd, complex symmetric, and complex skew‐symmetric. To compute pseudospectra and stability radii, eigenvalue backward error is required. Hence, we initially present the structured eigenvalue backward error. Subsequently, we compute the structured pseudospectra using the obtained results for the eigenvalue backward error of a class of structured nonlinear matrix functions. Finally, we discuss the stability radii of the above‐structured problems arising in different applications. The paper also generalizes the results on the eigenvalue backward error of matrix polynomials in the literature for the above structures. [ABSTRACT FROM AUTHOR]

This paper provides a new sliding mode control (SMC) approach, by which both the nominal and robust stability associated with a trajectory tracking problem for an uncertain robot manipulator are achieved. More precisely, the new control law consists of linear and nonlinear functions of tracking errors, in which the former is for the nominal stability and the latter is to ensure the robust stability of the resulting closed‐loop systems. The nonlinear function can be interpreted as an extended version of conventional SMC approach, and the reaching phase corresponding to a pregiven sliding surface is shown to be completed in a finite time; the tracking errors arrive at the sliding surface in a finite time and do not deviate from it after the arrival. In the sliding phase, the tracking errors are also ensured to converge to the origin. Finally, some simulation results are given to demonstrate both the theoretical validity and practical effectiveness of the proposed control approach. [ABSTRACT FROM AUTHOR]

The efficiency and dynamic response of air compressors are crucial for stability and lifespan of hydrogen fuel cells. A predictive control scheme with surge‐ and choke‐constrained awareness is proposed to ensure safe and efficient operation of air compressors in this study. The proposed scheme consists of an efficiency enhancement model predictive control (EE‐MPC), and an improved active disturbance rejection control (IADRC). Surge‐ and choke‐constrained awareness is achieved by comparing predicted air flow with surge and choke limitations. Simultaneously, the EE‐MPC is constrained with oxygen excess ratio (OER) and obtains optimal solution by searching active set. The reference flow and supply manifold pressure trajectories for IADRC are generated by EE‐MPC. A designed piecewise differentiable nonlinear smoothing function is embedded in IADRC. The disturbances are estimated for coordinating flow and pressure control. Under China heavy‐duty commercial vehicle test cycle for bus conditions, root‐mean‐squared errors (RMSEs) of flow and pressure are 3.27 g s−1 and 1.88 × 103 Pa, respectively, and the mean efficiency can be enhanced by 13.4% compared to the MPC with fixed OER. Finally, a controller hardware‐in‐the‐loop test is conducted, with flow and pressure RMSEs of 2.48 g s−1 and 4.28 × 103 Pa between the test and simulation, respectively. [ABSTRACT FROM AUTHOR]

The classical PID (proportional‐integral‐derivative) control is the most basic and widely used control algorithm in engineering systems by far. Whether PID control can effectively deal with coupled multiagent uncertain nonlinear dynamics is well worth investigating. In this article, a class of PID controlled multiagent stochastic systems with coupled uncertain dynamics is considered, where the control input is nonaffine. Each agent has its own regulation objective, and only has access to its own regulation error information for PID feedback. First, a PID parameter set will be constructed explicitly based on some prior knowledge about the nonlinear functions, such that the overall multiagent system can be stabilized globally in the mean square sense, as long as the PID parameters are chosen from the constructed set. Moreover, the regulation error will be proven to have an upper bound proportional to the noise intensity along the reference signal. Furthermore, it will be shown that the regulation error of each agent can be arbitrarily small by choosing the PID parameters suitably large. Finally, the theoretical results will be verified by simulations. [ABSTRACT FROM AUTHOR]

The current investigation address a novel generalized elasto‐thermodiffusion model for a thermoelastic porous half‐space incorporating the nonlocal stress theory proposed by Eringen. Modeling of the problem is performed by adopting Moore‐Gibson‐Thompson (MGT) thermoelasticity theory defined in an integral form of a common derivative on a slipping interval, well known as the memory‐dependent derivative. The bounding plane of the medium is subjected to time‐dependent thermal and chemical shocks and there is no change in the volume fraction field. Laplace transform and the Fourier transform techniques have been adopted to represent the analytical solutions in the transformed domain. The distributions of the physical fields such as the temperature, stress, chemical potential, mass concentration and the volume fraction field were found in the real space‐time domain adopting suitable numerical scheme based on the Fourier series expansion. According to the discussion of the computational results and the respective graphical representations, the prominent role of different parameters such as the effect of nonlocality, effect of void and thermodiffusion is analyzed. Moreover, the superiority of a nonlinear kernel function compared to a linear form is also reported. [ABSTRACT FROM AUTHOR]

To solve the difficulties in threshold selection and poor performance under low signal‐to‐noise ratio (SNR) conditions in existing spectrum sensing algorithms, a graph‐based spectrum sensing algorithm using nonlinear function regulation was proposed. The idea was to add a specific nonlinear transformation between the normalisation and quantization steps of the existing signal‐to‐graph converter (SGC). If the autocorrelation function of the observed signal selected as the input fed to SGC, the nonlinear function has the ability to adjust the uniformity of its probability distribution, increasing the probability of the observed signal being transformed into a complete graph under the alternative hypothesis, whereas remaining a noncomplete graph under the null hypothesis. Thus transformed the graph‐based spectrum sensing into a complete graph‐detection problem. Based on the theory of dispersive ordering, a theoretical analysis of the mechanism by which nonlinear transformations affect graph connectivity was conducted. The simulation results showed that the detection performance of the proposed algorithm was superior to that of existing graph‐based spectrum sensing algorithms. When SNR was −7 dB, the detection probability of the proposed algorithm exceeded 95%. Moreover, among the existing graph‐based spectrum sensing algorithms, the proposed algorithm exhibited the lowest computational complexity apart from the block range‐based method. [ABSTRACT FROM AUTHOR]

Summary: An impedance control scheme is proposed for a Stewart‐structure‐based wheel‐legged robotic system to strengthen the dynamic attitude adjustment stability in wheel motion. The wheel‐leg, which is driven by electrical cylinders in the Stewart structure, is analyzed in kinematics and dynamics. The rotation in the axial direction of every electric cylinder is calculated to improve the accuracy of the kinematic model. To fulfill the impedance demands, a passive structure with 6 degrees of freedom (DOF) is modeled. The mass of the mechanism has a coupling effect on the impedance model for each DOF, which is a nonlinear function. As motion decoupling in the workspace has been completed for the Stewart structure, an impedance control strategy with inner‐loop position tracking is employed. An extended state observer (ESO) is designed to estimate the disturbances arising from the nonlinear coupling effects. Based on the ESO observation outputs, an active disturbance rejection control that explicitly handles the workspace limit is designed with guaranteed practical stability. By reducing force interaction and body vibration, the wheel‐legged robotic system keeps wheel motion stability on uneven roads. Multiple comparative experimental results are presented to validate the stability and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, the distributed containment control schemes are presented for a class of nonlinear heterogeneous high‐order fully actuated multi‐agent systems. First, for each follower, the reference trajectory generator is constructed by using the output information of the neighbor agents. Then, the distributed containment controllers are designed for the system with known nonlinear system function matrices and control gain matrices. Further, since the existence of modeling errors and other uncertain factors, the obtained system model is often not accurate enough, that is, the system function matrix and control gain matrix are actually unknown nonlinear matrices. To tackle these obstacles, we employ the radial basis function neural network method to approximate the unknown nonlinear system function matrices and skillfully construct the controllers combined with the adaptive technology to eliminate the effects of the unknown control gain matrices. The developed control strategies can guarantee that the containment control can be realized and the containment errors can be adjusted to arbitrary precision. In the end, the simulation results on the electromechanical system and robotic system demonstrate the availability and effectiveness of the provided schemes. [ABSTRACT FROM AUTHOR]

Summary: This article addresses the issue of bipartite containment tracking for nonlinear strict feedback multi‐agent systems (MASs) with disturbances and measurement uncertainties. To provides a better performance against strong disturbance, a coordination transformation is applied such that all the nonlinear functions, controller disturbances and measurement uncertainties are lumped into a single disturbance signal in the last state equation. Then, the lumped disturbance is compensated through a novel disturbance rebuilding method. Moreover, in order to get better control performance, state constraints are also considered through a nonlinear transformation function (NTF). Different from traditional methods dealing with the state constraint problems, the NTF method can avoid using any discontinuous Lyapunov function. Finally, an adaptive finite‐time distributed controller is established via the disturbance estimates, backstepping technique and fuzzy logic system (FLS). The performance of the controller is illustrated by a simulation example in which the bipartite containment formation of followers is realized in a practical finite time. [ABSTRACT FROM AUTHOR]

It is well known that unknown modeling errors cannot be avoided in practice. Such unmeasured uncertainties are usually denoted as unknown nonlinear functions that exist in every channel of the system equation. This paper aims to develop an output feedback adaptive control scheme by constructing state estimation filters to address such unknown modeling errors. In the controller design, these uncertainties caused by modeling errors will be accumulated to the last step for compensation. Unknown parameters existing in the upper bound functions of unknown nonlinear functions and system parameters are estimated synchronously based on tuning function approaches. It is shown that the designed output feedback controller can ensure the stability and tracking performance of the closed‐loop system, and the transient performance in terms of a truncated norm is also established. [ABSTRACT FROM AUTHOR]

In studies of infectious disease prevention, the level of protective efficacy of medicinal products such as vaccines and prophylactic drugs tends to vary over time. Many products require administration of multiple doses at scheduled times, as opposed to one‐off or continual intervention. Accurate information on the trajectory of the level of protective efficacy over time facilitates informed clinical recommendations and implementation strategies, for example, with respect to the timing of administration of the doses. Based on concepts from pharmacokinetic and pharmacodynamic modeling, we propose a non‐linear function for modeling the trajectory after each dose. The cumulative effect of multiple doses of the products is captured by an additive series of the function. The model has the advantages of parsimony and interpretability, while remaining flexible in capturing features of the trajectories. We incorporate this series into the Andersen‐Gill model for analysis of recurrent event time data and compare it with alternative parametric and non‐parametric functions. We use data on clinical malaria disease episodes from a trial of four doses of an anti‐malarial drug combination for chemoprevention to illustrate, and evaluate the performance of the methods using simulation. The proposed method out‐performed the alternatives in the analysis of real data in terms of Akaike and Bayesian Information Criterion. It also accurately captured the features of the protective efficacy trajectory such as the area under curve in simulations. The proposed method has strong potential to enhance the evaluation of disease prevention measures and improve their implementation strategies. [ABSTRACT FROM AUTHOR]

An adaptive event‐triggered control issue based on command filter and dynamic surface control is studied for switched nonlinear systems with full state time‐varying constraints in this article. To handle state constraints, the nonlinear mapping conversion technique is used. Radial basis function neural networks (RBFNNs) are utilized to approximate unknown nonlinear continuous functions. Adaptive control algorithm is designed based on command filtered backstepping technology. Novel even triggered control is constructed for two different cases in the switching interval. Furthermore, all signals in the switched system are proved to be semi‐globally uniformly ultimate bounded (SGUUB) by the aid of dynamic surface control method under arbitrary switching. Meanwhile, all states do not violate the preset constraints and Zeno phenomenon is avoided. The validity of the presented approach is confirmed through a numerical simulation result. [ABSTRACT FROM AUTHOR]

This article is concerned with event‐triggered adaptive tracking control design of strict‐feedback nonlinear systems, which are subject to input saturation and unknown control directions. In the design procedure, a smooth nonlinear function is employed to approximate the saturation function so that the controller can be designed under the framework of backstepping. The Nussbaum gain technique is employed to address the issue of the unknown control directions. A predetermined time convergent performance function and a nonlinear mapping technique are introduced to guarantee that the tracking error can converge in the predetermined time with a fast convergence rate and a high accuracy. Then the event‐triggered adaptive prescribed performance tracking control strategy is proposed, which not only ensures the boundedness of all the closed‐loop signals and the convergence of tracking error but also reduces the communication burden from the controller to the actuator. At last, the simulation study further tests the availability of the proposed control strategy. [ABSTRACT FROM AUTHOR]

Feedback‐controlled chemical reaction networks (FCRNs) are indispensable for various biological processes, such as cellular mechanisms, patterns, and signaling pathways. Through the intricate interplay of many feedback loops (FLs), FCRNs maintain a stable internal cellular environment. Currently, creating minimalistic synthetic cells is the long‐term objective of systems chemistry, which is motivated by such natural integrity. The design, kinetic optimization, and analysis of FCRNs to exhibit functions akin to those of a cell still pose significant challenges. Indeed, reaching synthetic homeostasis is essential for engineering synthetic cell components. However, maintaining homeostasis in artificial systems against various agitations is a difficult task. Several biological events can provide us with guidelines for a conceptual understanding of homeostasis, which can be further applicable in designing artificial synthetic systems. In this regard, we organize our review with artificial homeostasis systems driven by FCRNs at different length scales, including homogeneous, compartmentalized, and soft material systems. First, we stretch a quick overview of FCRNs in different molecular and supramolecular systems, which are the essential toolbox for engineering different nonlinear functions and homeostatic systems. Moreover, the existing history of synthetic homeostasis in chemical and material systems and their advanced functions with self‐correcting, and regulating properties are also emphasized. [ABSTRACT FROM AUTHOR]

Nowadays, alternative gravity is a crucial tool for addressing some enduring observational problems, such as the dark universe. Additionally, they can be used to advance the results of general relativity in astrophysics. Wormholes, or imagined passageways through spacetime, have the potential to revolutionize interstellar transport and cosmic interconnection. In the present work, the existence and characteristics of wormhole solutions in the context of the non‐linear function of f(Q)$f(\mathcal {Q})$ gravity are investigated. A typical characteristic of maintaining wormholes is the presence of exotic stuff that defines the energy conditions (ECs). The authors looked at the ECs that must be met and analyzed how the f(Q)$f(\mathcal {Q})$ function affects the energy‐momentum requirements for maintaining the wormholes open. For a comprehensive understanding of wormhole geometries, we also studied the embedding diagram and volume integral quantifier. Nowadays, alternative gravity is a crucial tool for addressing some enduring observational problems, such as the dark universe. Additionally, they can be used to advance the results of general relativity in astrophysics. Wormholes, or imagined passageways through spacetime, have the potential to revolutionize interstellar transport and cosmic interconnection. In the present work, the existence and characteristics of wormhole solutions in the context of the non‐linear function of f(Q)$f\!(\mathcal{Q})$ gravity are investigated. A typical characteristic of maintaining wormholes is the presence of exotic stuff that defines the energy conditions (ECs). The authors looked at the ECs that must be met and analyzed how the f(Q)$f\!(\mathcal{Q})$ function affects the energy‐momentum requirements for maintaining the wormholes open. For a comprehensive understanding of wormhole geometries, we also studied the embedding diagram and volume integral quantifier. [ABSTRACT FROM AUTHOR]

We consider the asymptotic nonlinear stability of viscous shock profiles for an initial‐boundary value problem of the scalar conservation laws with an artificial heat flux satisfying Cattaneo's law in the negative half line ℝ−=(−∞,0)$$ {\mathrm{\mathbb{R}}}_{-}=\left(-\infty, 0\right) $$ with Dirichlet boundary condition. When the nonlinear flux function is assumed to be strictly convex and the unique global entropy solution of the corresponding Riemann problem of the resulting scalar conservation laws consists of shock wave with negative speed, it is shown in this paper that the large time behavior of its global smooth solutions can be precisely described by the suitably shifted viscous shock profiles, where the time‐dependent shift function is uniquely determined by both the boundary value and the initial data. We also show that the shift function converge to a constant time asymptotically. Our analysis is based on weighted L2−$$ {L}^2- $$energy method. [ABSTRACT FROM AUTHOR]

In this study, the Atangana–Baleanu fractional derivative in the Caputo type (as a kind of non‐local and non‐singular derivative) is used to define a new class of stochastic fractional integro‐differential equations. A projection method (more precisely, a Galerkin approach) based on the piecewise Chebyshev cardinal functions is developed to solve these stochastic fractional equations. To construct this method, the operational matrices of fractional and stochastic integrals of these basis functions are obtained and used in the established method. By approximating the solution of the problem with a finite expansion of the expressed basis functions (in which the expansion coefficients are unknown), a system of algebraic equations is obtained. By solving this system, the expansion coefficients and subsequently the solution of the original stochastic fractional problem are obtained. The convergence analysis of the proposed method is investigated, theoretically and numerically. The accuracy of the established procedure is illustrated by solving several numerical examples. [ABSTRACT FROM AUTHOR]

This paper proposes a new secure distributed estimation for cyber‐physical systems against adversarial attacks with noisy input. To mitigate the effect of attacks, a novel distributed attack detection based on a reliable reference estimation obtained by temporal convex combination is proposed. Furthermore, for more effective and robust performance, an adaptation rule to adjust convex combination weights is presented, in which the generalized correntropy method with nonlinear loss function and stochastic gradient descent are utilized. Besides, to eliminate input noise, a bias‐compensation method in local adaptation of the secure distributed estimation is proposed. Simulations show superior dynamic and real‐time adaptability of the proposed algorithm under complex attacking scenarios. [ABSTRACT FROM AUTHOR]

A new analytic model for calculating of the air‐gap flux density (AGFD) of surface‐mounted permanent magnet synchronous machines (SMPMSMs) is presented. This proposed model is capable to taking into account the effects of magnetic saturation, armature reaction and stator slots opening. Furthermore, the real form of air‐gap distribution and spatial distribution of flux density of the PM poles are considered. The armature reaction effect is modeled using phasor diagram analysis of the motor as a function of the load torque, the armature current amplitude, power factor and the inverse air gap length. Also, saturation phenomenon predicted using the new non‐linear proposed function in connection with the armature reaction effects and the properties of the lamination material. It is shown that the proposed model capable to predicting acceptably the air gap flux density waveform of the SMPMSMs at lagging and leading power factors and with the load torque variation. The presented analytical approach is verified by the two‐dimensional finite‐element analysis (FEA) results. [ABSTRACT FROM AUTHOR]

The paper expounds the question of echo state network‐based fixed‐time adaptive tracking control for a type of multi‐input multi‐output nonlinear strict‐feedback system with input delayed saturation. Based on the feature that echo state network can obtain better estimation performance at lower computational cost, it is utilized to approximate the unknown nonlinear function in the controller design course. By constructing an auxiliary system, a time‐delay system with input saturation is eliminated. Moreover, command filtering techniques can be applied to avoid the "complexity explosion" problem in the backstepping method. Then, the closed‐loop system is attested to be semi‐global practical fixed‐time stable. In the end, a simulation shows the valid scheme. [ABSTRACT FROM AUTHOR]

Summary: In this paper, the adaptive control is investigated by switching linear controllers for a class of nonlinear parameterized systems with multiple unknown control directions. Parametric uncertainties entering the state equations nonlinearly can be fast time‐varying or jumping at unknown time instants, the bounds of the parametric uncertainties are not required to know a priori and the multiple control directions are unknown. Our proposed adaptive controller is a switching type controller. First, sufficient conditions for designing an adaptive stabilizer are derived. Then, a switching‐type adaptive controller is designed, in which a linear controller with two undetermined design parameters to be tuned is recursively designed by adding a power integrator, and a switching mechanism is proposed to tune these parameters online for compensating the multiple unknown control directions and the unknown bounds of the parametric uncertainties. The undetermined design parameters are based on the upper bound estimation of the unknown parameters existing not only in the nonlinear functions but also in the control directions functions. The proposed adaptive controller globally asymptotically stabilizes the system in the sense that, for any initial conditions, the state converges to the origin while all the signals of the closed‐loop system are bounded. Finally, an example is given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Nonlinearity manipulation based on electromagnetic (EM) metasurfaces has always been a hot topic, which is an important part of communication and radar systems. However, most of the existing transmission metasurfaces are mainly focused on linear processing on the incident EM waves. In this article, a reprogrammable nonlinear transmission metasurface is proposed for spatial waves using active power amplifiers. An ultrathin and compact metasurface is designed, fabricated, and measured, to achieve reprogrammable functions on the nonlinear transmissions. For EM incidence, the metasurface can not only amplify the magnification of small signals, but also control high‐energy signals nonlinearly, whose magnification is determined by different bias voltages. The simulation and experimental results show good consistency, which verifies the feasibility of the proposed method. This work can find potential applications in signal gain compression and construction of nonlinear units of diffractive deep neural networks. [ABSTRACT FROM AUTHOR]

This article studies the adaptive state‐feedback control problem of output‐constrained stochastic high‐order nonlinear systems with stochastic integral input‐to‐state stability (SiISS) inverse dynamics. A key nonlinear transformation function is constructed to convert the original output‐constrained stochastic nonlinear system into an equivalent form without any output constraint. By subtly using the SiISS small‐gain condition and fully extracting the characteristics of system nonlinearities, two new control design and analysis methods are developed to guarantee that the closed‐loop system has an almost surely unique solution, all the closed‐loop signals are bounded almost surely, and the equilibrium point is stable in probability without the violation of output constraint. A simulation result is provided to show the effectiveness of this control method. [ABSTRACT FROM AUTHOR]

In this paper, we consider a piezoelectric beam model with nonlinear source terms and investigate the interaction between a viscoelastic damping and a nonlinear frictional damping. Under general assumptions on the relaxation function and the nonlinear feedback, we establish explicit formulae for the energy decay rates of this system and prove that the energy decays at a rate dictated by the weaker damping. Our results substantially improve some earlier related results in the literature. [ABSTRACT FROM AUTHOR]

This article investigates the adaptive fault‐tolerant tracking control problem for nonlinear systems with prescribed performance and input dead‐zone. First, a new composite variable is constructed by using the characteristics of actuator fault and input dead‐zone for the modeling purpose. Second, an adaptive neural network observer is designed to estimate the system states in the presence of inaccurate feedback information. Third, the proposed control strategy effectively counteracts the effects of sensor failure and unknown nonlinear functions, which makes the tracking error confined within the performance boundary and all the signals of the closed‐loop system semi‐globally uniformly ultimately bounded. Finally, an application oriented example is provided to demonstrate the effectiveness of the proposed control algorithm. [ABSTRACT FROM AUTHOR]

This paper presents a study of the cooperative optimal swarm control problem for two‐order multi‐agent systems with partially unknown nonlinear functions. Unlike traditional approaches that consider a single error, this paper proposes to use multi‐order errors in the performance index function to achieve optimal control performance. Additionally, different proportional coefficients are assigned to illustrate the varying influences of each sequence error, and a two‐order cooperative (TOC)performance index function is designed. To address the influence of unknown nonlinear functions, a swarm control system based on sliding mode control with an actor‐critic network is constructed, which increases the applicability of the proposed method to a variety of dynamic models. Furthermore, to alleviate the computational pressure caused by the multi‐order errors in the TOC performance index function, a new reinforcement learning (RL)‐based sliding mode swarm controller is designed. The stability of the proposed controller is demonstrated using the Lyapunov function. Finally, the control model and control rate are applied to a quadrotor unmanned aerial vehicle system, and simulation results demonstrate that the multi‐agent systems can effectively achieve swarm control. Impact Statement: This paper proposes a reinforcement learning‐based sliding mode control strategy for the cooperative optimal swarm control problem, where the nonlinear functions of two‐order multi‐agent systems are only partially known. In addition, we also propose a cooperative performance index function, which takes into account multi‐order errors for optimizing the performance. This contribution is significant for research in sliding mode control strategies and error co‐optimization. [ABSTRACT FROM AUTHOR]

Here, a gradient‐based neural network (GNN) model is constructed for solving the discrete periodic Lyapunov matrix equation (DPLME) associated with discrete‐time linear periodic systems. In practical applications, the recurrent neural network model should not only converge rapidly, but also be able to tolerate noise. However, the influence of noise on GNN models was seldom considered in the past. In order to improve the convergence and robustness of the GNN model, a novel type of non‐linear activation function is applied to the GNN model. Compared with the traditional activation functions, the activation function used here makes the GNN model to achieve fixed‐time convergence. Besides, when disturbed by bounded noise, the unique positive definite solution of the DPLME can still be obtained by using the GNN model. Finally, simulation experiment is performed to verify the effectiveness and superiority of the proposed GNN model. [ABSTRACT FROM AUTHOR]

Cardiovascular disease (CVD) stands as a prominent contributor to human mortality. Electrocardiogram (ECG) represents a widely adopted noninvasive method employed by clinicians to detect and diagnose CVDs. Nonetheless, conventional ECG‐based detection approaches for cardiac disorders tend to be time‐consuming and inefficient, necessitating the need for more effective solutions. Recent studies have highlighted the effectiveness of the echo state network (ESN) in detecting abnormal ECG patterns. However, traditional ESN models often face challenges such as unstable training and convergence difficulties due to variations in the range of reservoir state values. To address this issue, this study introduces a novel approach called the normalized echo state network (NESN). The NESN method normalizes the states of all neurons within the reservoir before applying the nonlinear activation function. In our study, we conducted performance evaluations of the proposed model using the MIT‐BIH arrhythmia database. We performed a synergistical analysis to investigate the impact of reservoir parameters on the network performance. The experimental results demonstrated promising outcomes, with an accuracy of 99.1% and an F1‐score of 96.4%. Specifically, for detecting abnormal ECG patterns, our model achieved a sensitivity of 90.2%, a positive predictive value of 96.6%, and a specificity of 99.8%. These results highlight the superior performance of our classifier compared to most traditional mainstream heartbeat detection methods and ring topology ESN model. [ABSTRACT FROM AUTHOR]

Summary: In this article, the adaptive event‐triggered control issue is researched for a kind of switched nonlinear interconnected systems subject to unknown backlash‐like hysteresis and control coefficients. The fuzzy logic systems (FLSs) are employed to approximate the unknown nonlinear functions. To deal with the unknown control coefficients, the Nussbaum method and adaptive control are introduced. The proposed event‐triggered controller can effectively lessen the communication burden, meanwhile, the Zeno behavior is eliminated. It is guaranteed that the system outputs can track the reference signals and all the system signals are semi‐globally uniformly ultimately bounded (SGUUB). Finally, the simulation results verify the effectiveness of this control scheme. [ABSTRACT FROM AUTHOR]

Distributed observer is an effective tool to deal with leader‐following control problems. This article investigates the fully predefined‐time distributed observer (FPTDO) design problem of a generalized second‐order strict‐feedback nonlinear leader system. Firstly, given the system parameters and the upper bounds of the system nonlinearities, an FPTDO is proposed to provide the state estimates. Secondly, considering that the time‐varying system parameters and nonlinear functions of the leader system are unknown to each follower, an FPTDO is developed to estimate the time‐varying system parameters, nonlinearities and full state of the leader. The proposed FPTDOs exhibit the following advantages: (1) the observation errors converge to zero within a finite time that is predefined by only one design parameter independent of the initial conditions; (2) the designs of the FPTDOs do not require any information of the communication topology (Laplacian matrix); and (3) the exact models of the nonlinear functions are not required by each follower. Finally, simulation examples are given to demonstrate the effectiveness of the proposed FPTDOs. [ABSTRACT FROM AUTHOR]

In computational practice, most attention is paid to rational approximations of functions and approximations by the sum of exponents. We consider a wide enough class of nonlinear approximations characterized by a set of two required parameters. The approximating function is linear in the first parameter; these parameters are assumed to be positive. The individual terms of the approximating function represent a fixed function that depends nonlinearly on the second parameter. A numerical approximation minimizes the residual functional by approximating function values at individual points. The second parameter's value is set on a more extensive set of points of the interval of permissible values. The proposed approach's key feature consists in determining the first parameter on each separate iteration of the classical nonnegative least squares method. The computational algorithm is used to rational approximate the function x−α,0<α<1,x≥1$$ {x}^{-\alpha },\kern0.3em 0<\alpha <1,\kern0.3em x\ge 1 $$. The second example concerns the approximation of the stretching exponential function exp(−xα),0<α<1$$ \exp \left(-{x}^{\alpha}\right),0<\alpha <1 $$ at x≥0$$ x\ge 0 $$ by the sum of exponents. [ABSTRACT FROM AUTHOR]

This note is devoted to the analysis of adaptive sliding mode control of H∞$$ {}_{\infty } $$/passivity of semi‐Markov jump discrete‐time uncertain singular systems. We consider the constraints of parameter uncertainties, unknown nonlinear functions, and external disturbances throughout the model. Firstly, a novel mode‐independent sliding mode surface is constructed, then the sliding mode dynamic equation under the equivalent controller is obtained. Secondly, by introducing virtual points, several sufficiency criteria are derived for the sliding mode dynamic ensuring H∞$$ {}_{\infty } $$/passive performance and stochastic admissibility with linear matrix inequalities form. Thirdly, the state trajectory can be driven into a switching band containing the origin by adaptive sliding mode control techniques. Finally, the effectiveness of our findings is demonstrated by comparing existing strategies with three simulation examples. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates the finite‐time formation tracking control problem for nonholonomic multirobot systems with inputs quantization. The fuzzy logic systems (FLSs) and adaptive method are introduced to approximate unknown nonlinear functions and parameters. Multirobot needs to keep safe and effective communicating range, the barrier function and prescribed performance method are employed to ensure collision avoidance and connectivity maintenance. Then, in order to make each robot more precisely and quickly track referenced leader's trajectory and consider the finite channel bandwidth in practical applications, the travel range of robots can be maintained at more secure region and formation can operate normally within the given bandwidth. By combining the command filter and finite‐time theory, a novel decentralized finite‐time formation asymptotic tracking (FTFAT) control strategy is further proposed based on inputs quantization technology, it guarantees that all signals are bounded and the formation tracking errors asymptotically converge to zero in finite‐time. Finally, the practicability of FTFAT strategy is demonstrated absolutely for nonholonomic multirobot systems. [ABSTRACT FROM AUTHOR]

The direct current (DC)‐link voltage control of the flywheel energy storage system plays an important role in realizing high‐quality grid connection. With the traditional proportional‐integral control, the DC‐link voltage cannot track its reference value quickly and smoothly when the flywheel energy storage system switches from the charging stage to other working stages. Therefore, a DC‐link voltage control strategy for the flywheel energy storage system based on active disturbance rejection control is proposed in this paper to deal with this issue. The DC‐link voltage and its differential value are considered as the state variables in this strategy. The internal and external disturbances, such as load power, switching loss, and parameter uncertainty, are regarded as an expanded state. By inputting the voltage error and the observed disturbance into the nonlinear state feedback control law, the rapidity and anti‐interference of the DC‐link voltage control are ensured under different States of Charge of the flywheel energy storage system. Then, the coefficient freezing method is used to analyze the effects of the disturbance observation bandwidth by nonlinear gain and pole position changes. The DC‐link voltage can track the reference value over a wider frequency range of disturbances. By configuring the appropriate observer structure parameters, the disturbance observation bandwidth under the nonlinear function gain variation is always higher than the expected bandwidth. The effectiveness of the proposed control strategy is verified by simulation results at last. [ABSTRACT FROM AUTHOR]

This article studies the fault‐tolerant control for linear systems with disturbances through sliding mode scheme. Compared with the existing results, by means of a nonlinear sliding function with an exponential term, a reduced‐order sliding motion can be obtained while the reaching phase of conventional sliding mode control is eliminated. On the other side, with the help of an exponentially decaying barrier Lyapunov functions, a continuous sliding mode algorithm is established. Within the proposed framework, the trajectories of closed‐loop systems can be forced to a prescribed practical sliding surface, and then, both the transient as well as steady‐state performances are guaranteed despite the occurrence of abrupt actuator faults. Under the Lyapunov direct method, a sufficient condition is derived such that the sliding motion is uniformly bounded with time‐varying performance constraints. Finally, an electric amplidyne system is considered to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]

We propose a generalization of a model with age of infection in a heterogeneous environment. Firstly, we give the well‐posedness of the model and prove that the solutions are bounded and positive. The difficult mathematical issue in this research is that the model is partially degenerate, and the solution map is not compact. In addition, we construct a global attractor of a bounded set to establish the existence of total trajectory. Moreover, we define the principal eigenvalue associated with a principal eigenvalue problem to give a relation with the basic reproduction number R0$$ {R}_0 $$ and this value. By assuming that R0<1$$ {R}_0<1 $$, then the infection‐free steady‐states E0$$ {E}^0 $$ is globally asymptotically stable. Furthermore, for R0>1$$ {R}_0>1 $$ and by using the persistence results, we prove the existence of endemic steady‐states E∗$$ {E}^{\ast } $$, and by constructing an appropriate Lyapunov function, we show that E∗$$ {E}^{\ast } $$ is globally asymptotically stable. Lastly, we validate our theoretical analysis by giving some numerical graphics. [ABSTRACT FROM AUTHOR]

This article investigates the robust adaptive guaranteed cost tracking (RAGCT) control problems for two class of high‐order nonlinear systems with time‐varying uncertainties. A special nonlinear function, named as the local smooth nonlinear function, is introduced, which is crucial for our controller design. Then, using the function and the recently proposed high‐order fully actuated (HOFA) system approaches, a novel RAGCT controller for HOFA system with time‐varying uncertainty is designed, which guarantees the global boundedness of the closed‐loop system within finite time. Then, based on the result about the above HOFA system, the RAGCT controller for a class of strict‐feedback systems with high‐order form and time‐varying uncertainties is obtained, which also guarantees that the closed‐loop system is globally bounded within finite time. Most importantly, two designed controllers can preset arbitrarily the upper bounds of cost functions characterizing the tracking performance independent of the system initial values and the time‐varying uncertainties, which optimizes greatly the system tracking performance, and is difficult to achieve by using existing guaranteed cost control methods. Finally, two simulation examples including one‐link manipulator are provided to show the effect and the practicability of our proposed control method. [ABSTRACT FROM AUTHOR]

Based on the theories of sliced inverse regression (SIR) and reproducing kernel Hilbert space (RKHS), a new approach RDSIR (RKHS‐based Double SIR) to nonlinear dimension reduction for survival data is proposed. An isometric isomorphism is constructed based on the RKHS property, then the nonlinear function in the RKHS can be represented by the inner product of two elements that reside in the isomorphic feature space. Due to the censorship of survival data, double slicing is used to estimate the weight function to adjust for the censoring bias. The nonlinear sufficient dimension reduction (SDR) subspace is estimated by a generalized eigen‐decomposition problem. The asymptotic property of the estimator is established based on the perturbation theory. Finally, the performance of RDSIR is illustrated on simulated and real data. The numerical results show that RDSIR is comparable with the linear SDR method. Most importantly, RDSIR can also effectively extract nonlinearity from survival data. [ABSTRACT FROM AUTHOR]

Summary: This article discusses the adaptive neural tracking control issue for a flexible manipulator system with time‐varying full‐state constraints. First, the flexible manipulator system is modeled using partial differential equations with boundary conditions. Second, neural network techniques are used to deal with unknown nonlinear functions. Based on the backstepping technique, an adaptive neural boundary controller is developed that effectively suppresses the effects of input saturation. Moreover, the construction of the asymmetric time‐varying barrier Lyapunov function guarantees that the full‐state constraints of the system are met and that the closed‐loop system signals remain bounded. Finally, simulations are performed, and the results demonstrate the efficacy of the proposed approach. [ABSTRACT FROM AUTHOR]

Nowadays, the accurate prediction of strength properties of cementitious materials containing nano‐ and micro‐silica (NS–MS) remains an open question because of the highly nonlinear function of its constituents on the porosity. In the present study, a combined framework is developed by integrating ant colony optimization (ACO), particle swarm optimization (PSO), and biogeography‐based optimization (BBO) with the artificial neural network (ANN) to predict compressive and flexural strengths of cement mortar in two different forms of ignoring (ANNII) and considering (ANNIII) the porosity as an input parameter. This procedure is accomplished considering the porosity effect on the strengths and implementing an experimental program containing 32 mixes (960 specimens) with different NS–MS contents at various ages. Macro‐ and micro‐structural analyses showed that NS–MS caused more decreased pore structure, and thus this situation increases strength properties compared to their separate use. Also, MBBO‐MOANNIII results indicated an improvement in convergence speed and model accuracy compared to other models. This improvement is because of considering the porosity. [ABSTRACT FROM AUTHOR]

For a given finite subset S of a compact Riemannian manifold (M,g) whose Schouten curvature tensor belongs to a given cone, we establish a necessary and sufficient condition for the existence and uniqueness of a conformal metric on M\S such that each point of S corresponds to an asymptotically flat end and that the Schouten tensor of the conformal metric belongs to the boundary of the given cone. As a by‐product, we define a purely local notion of Ricci lower bounds for continuous metrics that are conformal to smooth metrics and prove a corresponding volume comparison theorem. © 2022 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

This article investigates the tracking control problem of adaptive fault‐tolerant control (AFTC) for a class of strict‐feedback nonlinear systems with actuator/sensor faults and unmatched disturbances. The sensor/actuator faults include bias, drift, loss of accuracy, and loss of effectiveness. Our main control objective is to investigate an adaptive fault‐tolerant control algorithm with the help of tuning functions, adaptive control technology, fuzzy logic systems (FLSs) and so on. For unknown nonlinear functions and fault items, FLSs and adaptive control technology are utilized to approximate them. Furthermore, over‐parameterization problem existed in the backstepping‐based controller design is solved by introducing the tuning functions. Theoretical analysis proves that our proposed AFTC scheme can ensure that all the signals in the closed‐loop system are bounded and the tracking error remains within a small range of zero even if a series of faults mentioned above occur. In the end, the simulation results show that the presented AFTC strategy is feasible and effective. [ABSTRACT FROM AUTHOR]

This study presents a near‐optimal learning‐based approach for sliding‐mode control of uncertain nonsquare nonlinear systems subject to output constraints. To achieve a compromise between safety and optimality, a reinforcement learning algorithm is proposed to compute the near‐optimal values of the sliding manifold coefficients. In the reinforcement learning algorithm, only measured input‐output data obtained by experiments or simulations are employed. Furthermore, the presented method does not require partial knowledge of the system dynamics to initialize the reinforcement learning process. By employing the tuned sliding vector, an adaptive fuzzy sliding‐mode control (AFSMC) input, including a fuzzy term and a robust term, is generated. The fuzzy term is used to approximate an unknown nonlinear function and the robust term is designed for mismatch compensation. To guarantee that the output constraints are not violated, the adaptation laws for obtaining the fuzzy singletons and the bounds of the approximation errors are designed based on the barrier Lyapunov functions (BLF) theorem. The closed loop asymptotic stability is theoretically analyzed in the article, while the effectiveness of the method is assessed in simulation. [ABSTRACT FROM AUTHOR]

In this article, we are concerned with the input‐to‐state practical stability (ISpS) of nonautonomous nonlinear infinite‐dimensional systems. Sufficient conditions of ISpS are provided based on Lyapunov functions and a nonlinear inequality. We characterize ISpS in terms of uniform practical asymptotic gain property. We show that for a class of admissible inputs the existence of an ISpS‐Lyapunov function implies the ISpS of a system in Banach spaces. These results are used to study the input‐to‐state practical stability of a certain class of nonautonomous semilinear evolution equations. Furthermore, we provide a small‐gain theorem for nonautonomous nonlinear interconnected systems. An example is used to illustrate the application of the developed method. [ABSTRACT FROM AUTHOR]

The highly accurate state estimation of nonlinear systems is needed in many different application fields. In many existing nonlinear filters, the uncompensated nonlinear approximation error and widely used numerical sampling methods both seriously affect the estimation accuracy and numerical stability. In this paper, based on the variational Bayesian framework, a novel iterative nonlinear filter consisting of forward modeling and inverse estimation is proposed. In the forward modeling stage, a linear Gaussian regression process with distributed variational parameters (VPs) is designed to fit the whole nonlinear measurement likelihood. The distributed VPs consider both first and second moments information, so as to compensate for approximation error from the whole likelihood perspective, instead of only the nonlinear function approximation, which can further improve the accuracy of Bayesian posterior update. In the linear Gaussian regression process, the original nonlinear measurement function (NMF) is just viewed as a prior and no longer directly participates in the modeling of the measurement likelihood. Hence, in the inverse estimation stage, when maximizing the evidence lower bound to update the posteriors of the state and VPs, we can obtain closed‐form solutions without numerical sampling methods to approximate the integral of NMF required in many existing methods, which can guarantee numerical stability. Moreover, to avoid the random setting of hyperparameters and to block the propagation of the accumulated error, we propose two rules, estimation and lower bound consistencies, to conduct the hyperparameters' initialization at the beginning of iteration at each sampling time and also derive an optimization method to update hyperparameters during iteration. Finally, the performance of our proposed method is demonstrated in the nonlinear orbital estimation problems. [ABSTRACT FROM AUTHOR]

This paper studies the problem of the adaptive control of nonlinear impulsively coupled complex networks. Firstly, a class of adaptive controllers are designed for the nonlinear impulsive differential equations, where the nonlinear function can be decomposed into matching condition and mismatching condition. Secondly, combining with Lasalle invariant set theorem, Schur complement theorem and some inequality techniques, we consider the synchronization of impulsively coupled complex networks via the general adaptive control. Moreover, this paper proposes the pinning adaptive synchronization results for impulsive dynamical complex networks. Finally, the proposed results are verified by some examples in which simulations are available for comparison. [ABSTRACT FROM AUTHOR]