Search

Basic multimode impedance analysis, based on the availability of nonequilibrium charge carriers and their delayed return to equilibrium, is employed to assess the state of equivalent circuit representations. This analysis highlights the necessity of surpassing these representations in nonlinear systems with inherent memory, along with their associated advantages and limitations. On the basic grounds of generation and recombination (or trapping) of nonequilibrium carriers and their relaxation times, we show how seeming complexity of frequency-dependent impedance that matches a vast universe of experimental evidences can be reduced to simple combinations of basic microscopic ingredients. Counterintuitive features, such as negative capacitances or unexpected inductances, arise when the results are projected onto linear equivalent circuit representations. This indicates the presence of certain limitations and potential ambiguities in the symbolic representation of "equivalent" circuits. Our approach further provides a microscopic perspective that exposes the linkage of an apparent flux with an apparent inductance dismissing any magnetic essence. [ABSTRACT FROM AUTHOR]

Fermi's golden rule (FGR) offers an empirical framework for understanding the dynamics of spin–lattice relaxation in magnetic molecules, encompassing mechanisms like direct (one-phonon) and Raman (two-phonon) processes. These principles effectively model experimental longitudinal relaxation rates, denoted as T 1 − 1 . However, under scenarios of increased coupling strength and nonlinear spin–lattice interactions, FGR's applicability may diminish. This paper numerically evaluates the exact spin–lattice relaxation rate kernels, employing the extended dissipaton equation of motion formalism. Our calculations reveal that when quadratic spin–lattice coupling is considered, the rate kernels exhibit a free induction decay-like feature, and the damping rates depend on the interaction strength. We observe that the temperature dependence predicted by FGR significantly deviates from the exact results since FGR ignores the higher order effects and the non-Markovian nature of spin–lattice relaxation. Our methods can be easily extended to study other systems with nonlinear spin–lattice interactions and provide valuable insights into the temperature dependence of T1 in molecular qubits when the coupling is strong. [ABSTRACT FROM AUTHOR]

This paper investigates the practical prescribed time tracking for a class of uncertain nonlinear systems based on neural networks and event‐triggered control. Introducing a time‐varying constraint function transforms the original practical prescribed time‐tracking control issue into a tracking error constraint problem. An event‐triggered adaptive control has been proposed, which can effectively reduce the communication burden between the controller and the actuator. Using neural networks to approximate unknown nonlinear functions avoids the differentiation of virtual controllers, thereby reducing the computational burden. In addition, users can independently choose preset time and tracking accuracy without changing the control structure, which remains independent of the initial conditions and any design parameters. Finally, the effectiveness of this method is verified through simulation examples. [ABSTRACT FROM AUTHOR]

In this paper, the model‐free robust control problem is investigated for nonlinear systems with a relaxed condition of initial admissible control. An advanced integral reinforcement learning method is developed, which merges the adaptive network‐based fuzzy inference system (ANFIS) and pre‐training of the initial weights. To loose the condition for choosing the initial control law, pre‐training of initial weights is established by utilizing the ANFIS to provide the information corresponding to the system model, which is applicable to the model‐free issue. Based on the actor‐critic structure, the approximate optimal control law is obtained by employing adaptive dynamic programming. Redesigning the obtained control law, the robust controller can be derived to stabilize the system with the uncertain term. Eventually, two examples are utilized to verify the effectiveness of the constructed algorithm. [ABSTRACT FROM AUTHOR]

Summary: Motivated by existing works on the ℒ1$$ {\mathcal{L}}_1 $$ state‐feedback controller for nonlinear systems, in which the ℒ∞$$ {\mathcal{L}}_{\infty } $$ norm of the output for the worst disturbance with a unit magnitude is required to be bounded by 1, this paper considers an extension of those works to an output‐feedback form. More precisely, the existence of an ℒ1$$ {\mathcal{L}}_1 $$ output‐feedback controller for nonlinear systems is characterized by developing output regulation map and output controlled invariance domain, which are extended versions of the conventional regulation map and controlled invariance domain in the previous works. We first lead to a sufficient condition for the existence of an ℒ1$$ {\mathcal{L}}_1 $$ output‐feedback controller by ensuring the lower‐semicontinuity of the corresponding output regulation map. It is also shown in this paper that there exists an ℒ1$$ {\mathcal{L}}_1 $$ output‐feedback controller only if there exists an output controlled invariance domain. Based on these conditions, we further introduce algorithmic guidelines for verifying the existence of ℒ1$$ {\mathcal{L}}_1 $$ output‐feedback controller. Finally, a numerical example is provided to verify the validity of the overall arguments developed in this paper. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates the adaptive fuzzy backstepping control problem for uncertain discrete‐time nonlinear systems with mismatched disturbances. A novel adaptive fuzzy command filtered backstepping approach is proposed, which can overcome the noncausal problem by using the command filter. The filter errors generated by filter are removed by constructing error compensation mechanism. The fuzzy logic systems are used to approximate the uncertain nonlinear dynamics, and the unknown mismatched disturbances are actively attenuated by using adaptive control technique. Based on the proposed new weighed Lyapunov functions, all the signals in the close‐loop system are proved to be uniformly ultimately bounded. The viability of proposed method is demonstrated by simulation results. [ABSTRACT FROM AUTHOR]

We propose new results on input‐to‐state stability (ISS) subject to time delays in the input for compact, invariant sets that contain the origin. First, using nonlinear small‐gain theory, we prove a Razumikhin‐type theorem that ensures ISS for sets in the context of functional differential equations with delayed disturbances. Next we demonstrate that this theorem can be used to ensure set ISS for nonlinear systems with input delays and disturbances. In comparison to the existing research on robustness of set ISS with respect to time delays at the input, our results are more general, retain the ISS gain, and do not impose constraints on time delayed states. The advantages of the method are illustrated through two case‐studies on set‐stability for classes of nonlinear oscillators of practical interest. [ABSTRACT FROM AUTHOR]

The traditional Nussbaum‐type functions encounter challenges when extended to systems with multiple unknown control directions, as the coupling between the Nussbaum‐type function and Nussbaum‐type gain may lead to mutual elimination. To address this issue, a novel Nussbaum‐type function is introduced to handle multiple unknown control directions for stochastic systems. The stability of the proposed Nussbaum‐based design can be guaranteed using the Lyapunov analysis. To conserve computational resources, a static composite event‐triggered mechanism is integrated with intermittent feedback in the Nussbaum‐based design. In contrast to conventional event‐triggering mechanisms that depend solely on control signals, the presented design incorporates tracking errors into the event‐triggering conditions. Moreover, to further alleviate computational burdens, we further develop a dynamic composite event‐triggered mechanism. With the overall design scheme, bounded tracking errors and reduced computational burden can be ensured. Simulation examples validate the efficacy of the proposed adaptive Nussbaum composite event‐based robust control design. [ABSTRACT FROM AUTHOR]

An innovative technique for developing fuzzy preview tracking control nonlinear systems using Takagi‐Sugeno (T‐S) fuzzy models is discussed. The design considers robustness against state time‐changing latency, input saturation, and reference tracking. To achieve this, the T‐S fuzzy system was combined with time‐changing latency and input saturation to create an augmented error system, transforming the original fuzzy preview tracking control issue into a stability issue for the augmented error systems. Next, a new fuzzy preview tracking controller was developed by considering the T‐S fuzzy systems' states or outputs, a distinct integrator, and a previewed reference signal to solve the tracking control issue. For the augmented error system's asymptotic stability, new adequate conditions were derived by employing the fuzzy Lyapunov function, small gain theory, and linear matrix inequality (LMI) method. Finally, the proposed method's effectiveness was demonstrated using two numerical examples. [ABSTRACT FROM AUTHOR]

This research explores the efficacy of integrating nonlinear single-degree-of-freedom systems in the vibration control of rod coupling systems. By interlinking two rods with a nonlinear single-degree-of-freedom system as the intermediary, the study employs the Lagrange method (LM) to forecast nonlinear vibrational behaviors. The findings, substantiated by numerical analyses, affirm the precision of LM in gauging the amplitude responses when such a nonlinear system is utilized. The nonlinear dynamics, characterized by intricate vibrational patterns, peak jumping phenomena, and the migration of resonance zones, are induced by the nonlinear single-degree-of-freedom system. By fine-tuning the system's parameters, significant alterations in the vibrational states of the rod coupling system are achievable. This suggests that the application of a nonlinear single-degree-of-freedom system is a viable strategy for modulating vibrations in rod systems. Furthermore, optimal parameterization of this system is proven to effectively dampen vibrations, showcasing its potential as a sophisticated mechanism for vibration suppression in coupled rod configurations. [ABSTRACT FROM AUTHOR]

A rapid stability dimensionality‐augmented state observer (RSDASO) based event‐driven control strategy is presented for the autonomous underwater vehicle (AUV) trajectory tracking issue, addressing state constraints, model uncertainty, limited communication resources and unknown external time‐varying disturbances. The first step is to develop a fast stability extended state observer to estimate the lumped disturbances and unmeasurable states of the system and ensure the estimation error converges in fixed time. Secondly, a fixed‐time AUV trajectory tracking control method is proposed to ensure that the tracking error of the system converges within a fixed time, based on the mentioned observer. Simultaneously, to reduce the communication resource usage by the system, an event‐triggered mechanism (ETM) is included in the control law. Lastly, simulation experiments verify the effectiveness of the process. [ABSTRACT FROM AUTHOR]

This article estimates the reachable set for a class of switched nonlinear positive systems with disturbance. The systems we discussed are homogeneous of degree greater than one and cooperative. Criteria are derived for the existence of a ball where all the solutions of the system converge asymptotically within. Then the results are extended to switched homogeneous positive time‐varying system of degree greater than one and general switched time‐varying system. Finally numerical examples are proposed to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This article addresses the real‐time reachable set problem on nonlinear time‐delay switched singular systems with state jump, which is subject to initial state and peak‐bound disturbance. Initially, based on the system state decomposition method, a state jump lemma is proposed, which combines the nonlinear function and the system state at the switching instant. Then, a real‐time bounded lemma is developed, premised on using the idea of average dwell‐time and analyzing subinterval function changes. Afterwards, the sufficient conditions for estimating the real‐time and nonreal‐time reachable set are established, which ensures that the reachable state of system can be restricted within a real‐time or nonreal‐time closed set. Finally, simulation results of the typical Direct Current boost chopper are performed to exhibit the effectiveness of the devised estimation scheme for the real‐time reachable set of system. [ABSTRACT FROM AUTHOR]

This article addresses the problem of adaptive fault‐tolerant event‐triggered control (ETC) for time‐varying delay switched nonlinear systems (SNSs) with actuator and sensor failures. First, in order to address the unknown actuator failures, a fault compensation coefficient is introduced. Then, a mode‐dependent state observer is established to estimate the unknown states. The unknown nonlinear function is approximated by the usage of fuzzy logic systems (FLS). In addition, the Lyapunov–Krasovskii functions are utilized to discuss the influence of time‐varying delays. Then, an adaptive fuzzy fault‐tolerant ETC and a novel event‐triggering mechanism (ETM) are derived. It is proved that the proposed fault‐tolerant controller can ensure that all states of the closed‐loop system (CLS) are semi‐globally uniformly ultimately bounded (SGUUB) by average dwell time (ADT) constraints and the Zeno phenomenon can be excluded. Results of two simulation examples verify that the proposed control method is effective. [ABSTRACT FROM AUTHOR]

This article focuses on the adaptive output feedback control problem for a class of uncertain nonlinear systems under unknown actuator and sensor faults. In contrast to existing works, we consider unknown time‐varying discontinues faults and loosen their conservative conditions on nonlinear functions. First, since there is just inaccurate output information is available, an observer based on dynamic gain is conceived to reconstruct state variables that cannot be measured. Second, the dynamic gain is introduced into the design of virtual controller by coordinate transformation, and is employed to construct Lyapunov function to handle unknown parameters. On the other hand, a new global output feedback control algorithm is proposed by utilizing dynamic gain which improves the flexibility of parameters selection on the premise of ensuring stability. Based on the Lyapunov stability theory, the resulting closed‐loop system is proved strictly all signals are global bounded. Finally, a simulation example is presented to illustrate the efficiency of the proposed control algorithm. [ABSTRACT FROM AUTHOR]

Composite observer based finite time control of nonlinear systems in case of multiple disturbances is studied in this article, wherein the disturbances contain two parts, the first type is the harmonic disturbance with modeling errors, and all other disturbances are classified as the second type, known as lumped disturbances. To give estimation of the harmonic disturbance and the lumped disturbances, a disturbance observer (DO) and the extended state observer are constructed, respectively. On this basis, a finite‐time elegant anti‐disturbance controller is presented by combing DO‐based control, active disturbance rejection control, backstepping technique and the finite time command filter method. Eventually, it is proved that the design method put forward in this article is correct and feasible. [ABSTRACT FROM AUTHOR]

This article is concerned with the trajectory tracking control problem for the nonlinear systems in the sense of the predefined settling time and accuracy. In contrast with the existing works, we focus on the cases where the system dynamics, its bounding functions, the unmatched disturbances, and the time‐varying parameters are totally unknown; the derivatives of the desired trajectory are not required to be available. They significantly challenge the identification and/or approximation‐based control solutions. To overcome this obstacle, a novel robust prescribed performance control approach via state feedback is put forward in this article. It not only ensures the natural satisfaction of the specific initial condition but also realizes a full‐time performance specification for trajectory tracking. Furthermore, for the case of unmeasured state variables, an output‐feedback control approach is further derived by adopting an input‐driven filter and conducting trivial changes on the design procedure. Moreover, both approaches exhibit significant simplicity, without the needs for parameter identification, function approximation, disturbance estimation, derivative calculation, or command filtering. Three simulation studies are conducted to clarify and verify the above theoretical findings. [ABSTRACT FROM AUTHOR]

This article addresses the global regulation by periodic event‐triggered output feedback control for a class of feedforward nonlinear systems. Particularly, the considered systems suffer from parameter uncertainties and unknown measurement sensitivity, which entail integrating advanced compensation strategies within the event‐triggered framework. To this end, a time‐varying gain is devised to tackle uncertain nonlinearities as well as the sampling error. Subsequently, a novel periodic event‐triggered output feedback controller is constructed based on the delicate choice of design parameters. Notably, the proposed control scheme is able to avoid the continuous monitoring of the system behavior, and guarantee that all closed‐loop system states are globally bounded and ultimately converge to zero. Finally, a practical example is given to illustrate the main results. [ABSTRACT FROM AUTHOR]

Summary: This paper designs an interval observer for switched nonlinear partial differential equation (PDE) systems. Initially, persistent dwell‐time switching rules are used to model switched PDE systems with fast and slow switching phenomena. Next, for unobservable systems caused by uncertainties, the interval observer for the target PDE systems is proposed by utilizing unknown but bounded information of the initial states, boundary conditions, external disturbances, and measurement noises. Subsequently, by utilizing the estimated state's upper and lower bounds, an interval observer‐based control strategy is devised to stabilize the studied systems, and sufficient conditions to ensure the stability of the target systems and the observation error dynamics are provided. Furthermore, the designed interval observer is employed to detect sensor failures in the presence of various uncertainties. Finally, two examples, including the lithium‐ion battery's temperature estimation and fault detection, are utilized to demonstrate the effectiveness of the obtained methods. [ABSTRACT FROM AUTHOR]

Summary: This paper addresses the problem of adaptive robust safety‐critical control (ARSCC) for switched systems, where the safety of subsystems is not necessary. A novel ARSCC framework and an executable algorithm are presented to solve the ARSCC problem by finding a switching signal and controllers of subsystems. To estimate uncertainties, a novel switched piecewise‐constant adaptive law is presented, which guarantees a pre‐computable estimation error boundary. A single barrier function (SBF) method is proposed to ensure safety of switched systems with uncertainties, where the safety of subsystems is satisfied only in some subregion of a given safe set, instead of the whole safe set. Based on the SBF method, a novel state‐dependent switching law possessing different dwell times for different subsystems, is established to orchestrate the switching among potentially unsafe subsystems. As a special case of the SBF method, a common barrier function method is presented to achieve safety of switched systems with uncertainties under switching signals with given dwell times. In addition, some sufficient conditions are derived to obtain safety and asymptotic stability for switched systems with uncertainties by combining SBF and single Lyapunov function. Finally, a switched RLC circuit system is given to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

The adaptive neural tracking fault‐tolerant control problem is considered for nonlinear non‐affine switched systems with sensor faults via dynamic surface control (DSC) technique under arbitrary switchings within predefined‐time interval. During the controller design process, the non‐affine formation strictly processed so that the implicit control signals can be transformed into explicit ones. The introduction of hyperbolic tangent function to design the control signal eliminates the singularity at the same time, but also avoids the tedious discussion of the segmentation function to solve the singularity. Considering Lyapunov stability theorem, an adaptive fault tolerant control approach is presented, which means that the settling‐time can be programmed by the user practical specification under arbitrary switching, the predefined time boundedness of all closed‐loop signals can be ensured, and the influence of sensor faults can be compensated. The effectiveness of the presented method is verified via simulation results. [ABSTRACT FROM AUTHOR]

Summary: The paper is devoted to the prescribed finite time attitude control for quadrotors. A novel prescribed finite time function is introduced, which is independent of initial conditions and design parameters. And a switched prescribed finite time controller is firstly designed, such that the quadrotor can not only converge to the desired attitude in a prescribed time, but also guarantee the stability of the quadrotor after the settling time. Simultaneously, it effectively avoids chattering issues at the controller's switching points. Finally, the simulation comparisons are carried out between the proposed control strategy and infinite time, finite time, traditional prescribed finite time control schemes to demonstrate the superiority of the developed controller. [ABSTRACT FROM AUTHOR]

To meet the demand for estimating actuator and sensor faults simultaneously in a class of repetitive nonlinear time‐delay systems, this paper proposes a novel fault estimation strategy based on an iterative learning scheme. Firstly, an iterative‐learning‐based fault estimation law is designed to estimate actuator faults while system is free of sensor failures. Both the fixed initial shift and random one are taken into consideration. Secondly, a novel sensor fault observer is proposed based on an augmented state variable which consists of original system state and sensor fault signal; output compensation strategy is also provided to ensure the iterative‐learning‐based actuator fault estimation method is effective considering the existence of sensor failures. In addition, theorems based on λ$$ \lambda $$‐norm and linear matrix inequality are provided to determine values or ranges of gain matrices and parameters in proposed sensor fault observer and iterative‐learning‐based actuator fault estimation law. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Fluctuation dynamics of an experimentally measured observable offer a primary signal for nonequilibrium systems, along with dynamics of the mean. While universal speed limits for the mean have actively been studied recently, constraints for the speed of the fluctuation have been elusive. Here, we develop a theory concerning rigorous limits to the rate of fluctuation growth. We find a principle that the speed of an observable's fluctuation is upper bounded by the fluctuation of an appropriate observable describing velocity, which also indicates a tradeoff relation between the changes for the mean and fluctuation. We demonstrate the advantages of our inequalities for processes with non-negligible dispersion of observables, quantum work extraction, and the entanglement growth in free fermionic systems. Our results open an avenue toward a quantitative theory of fluctuation dynamics in various non-equilibrium systems encompassing quantum many-body systems and nonlinear population dynamics. Fluctuation dynamics of an observable offers a primary signal for understanding non-equilibrium statistical mechanics. Here, the author derives a principle that the speed of an observable's fluctuation is upper bounded by the fluctuation of an observable describing velocity, which is valid for various non-equilibrium systems from quantum many-body systems to nonlinear population dynamics. [ABSTRACT FROM AUTHOR]

In this work, a control strategy based on fuzzy sliding mode control (FSMC) is applied to effectively manage the large-amplitude chaotic vibrations exhibited by a simply supported beam. The analysis considers the nonlinear beam structure, which is subjected to an external load. Hamilton's principle is employed, and the equations of motion are derived for the studied structure. The 3rd Galerkin discretization is employed to derive the ordinary differential governing equation of the structure. A control strategy is presented to decrease the response of the obtained multidimensional system. The vibration of a one-dimensional system is compared with that of the derived multidimensional system. As shown throughout the study, a multidimensional nonlinear system of the structure must be considered for accurate dynamic estimation. By using the recurrent neural network (RNN) model, we can accurately predict chaotic motion and effectively apply control strategies to suppress chaotic motion. The efficacy and suitability of the employed control strategy have been demonstrated by controlling chaos in the beam's multidimensional system. [ABSTRACT FROM AUTHOR]

A new method is developed for finding exact solitary wave solutions of a generalized Korteweg–de Vries equation with p$p$‐power nonlinearity coupled to a linear Schrödinger equation arising in many different physical applications. This method yields 22 solution families, with p=1,2,3,4$p=1,2,3,4$. No solutions for p>1$p>1$ were known previously in the literature. For p=1$p=1$, four of the solution families contain bright/dark Davydov solitons of the 1st and 2nd kind, obtained in recent literature by basic ansatz applied to the ordinary differential equation (ODE) system for traveling waves. All of the new solution families have interesting features, including bright/dark peaks with (up to) p$p$ symmetric pairs of side peaks in the amplitude and a kink profile for the nonlinear part in the phase. The present method is fully systematic and involves several novel steps that reduce the traveling wave ODE system to a single nonlinear base ODE for which all polynomial solutions are found by symbolic computation. It is applicable more generally to other coupled nonlinear dispersive wave equations  as well as to nonlinear ODE systems of generalized Hénon–Heiles form. [ABSTRACT FROM AUTHOR]

We study the Schrödinger-Poisson type system: { − Δ u + λ u + (μ 11 ϕ u − μ 12 ϕ v) u = 1 2 π ∫ 0 2 π | u + e i θ v | p − 1 (u + e i θ v) d θ in R 3 , − Δ v + λ v + (μ 22 ϕ v − μ 12 ϕ u) v = 1 2 π ∫ 0 2 π | v + e i θ u | p − 1 (v + e i θ u) d θ in R 3 , where 1 < p < 3 with parameters λ , μ i j > 0. Novel approaches are employed to prove the existence of a positive solution for 1 < p < 3 including, particularly, the finding of a ground state solution for 2 ≤ p < 3 using established linear algebra techniques and demonstrating the existence of two distinct positive solutions for 1 < p < 2. The analysis here, by employing alternative techniques, yields additional and improved results to those obtained in the study of Jin and Seok (2023) [14]. [ABSTRACT FROM AUTHOR]

The consensus problem of a multi-agent system with nonlinear second-order underactuated agents is addressed. The essence of the approach can be outlined as follows: the output is redesigned first so that the agents attain the minimum-phase property. The second step is to apply the exact feedback linearization to the agents. This transformation divides their dynamics into a linear observable part and a non-observable part. It is shown that consensus of the linearizable parts of the agents implies consensus of the entire multi-agent system. To achieve the consensus of the original system, the inverse transformation of the exact feedback linearization is applied. However, its application causes changes in the dynamics of the multi-agent system; a way to mitigate this effect is proposed. Two examples are presented to illustrate the efficiency of the proposed synchronization algorithm. These examples demonstrate that the synchronization error decreases faster when the proposed method is applied. This holds not only for the states constituting the linearizable dynamics but also for the hidden internal dynamics. [ABSTRACT FROM AUTHOR]

This article introduces a novel two-step fifth-order Jacobian-free iterative method aimed at efficiently solving systems of nonlinear equations. The method leverages the benefits of Jacobian-free approaches, utilizing divided differences to circumvent the computationally intensive calculation of Jacobian matrices. This adaptation significantly reduces computational overhead and simplifies the implementation process while maintaining high convergence rates. We demonstrate that this method achieves fifth-order convergence under specific parameter settings, with broad applicability across various types of nonlinear systems. The effectiveness of the proposed method is validated through a series of numerical experiments that confirm its superior performance in terms of accuracy and computational efficiency compared to existing methods. [ABSTRACT FROM AUTHOR]

This article studies a data-driven prescribed performance platooning control method for nonlinear connected automated vehicle systems (CAVs) under aperiodic denial-of-service (DoS) attacks. Firstly, the dynamic linearization technique is employed to transform the nonlinear CAV system into an equivalent linearized data model. Secondly, to improve the system's transient performance, a prescribed performance transformation (PPT) scheme is proposed to transform the constrained output into the unconstrained one. In addition, an attack compensation mechanism is designed to reduce the adverse impact. Combining the PPT scheme and the attack compensation mechanism, the data-driven adaptive platooning control scheme is proposed to achieve the vehicular tracking control task. Lastly, the merits of the developed control method are illustrated by an actual simulation. [ABSTRACT FROM AUTHOR]

In the transition from traditional electrical energy generation with mainly linear sources to increasing inverter-based distributed generation, electrical power systems' power quality requires new monitoring methods. Integrating a high penetration of distributed generation, which is typically located in medium- or low-voltage grids, shifts the monitoring tasks from the transmission to distribution layers. Compared to high-voltage grids, distribution grids feature a higher level of complexity. Monitoring all relevant nodes is operationally infeasible and costly. State estimation methods provide knowledge about unmeasured locations by learning a physical system's non-linear relationships. This article examines a new flexible, close-to-real-time concept of harmonic state estimation using synchronized measurements processed in a neural network. A physics-aware approach enhances a data-driven model, taking into account the structure of the electrical network. An OpenDSS simulation generates data for model training and validation. Different load profiles for both training and testing were utilized to increase the variance in the data. The results of the presented concept demonstrate high accuracy compared to other methods for harmonic orders 1 to 20. [ABSTRACT FROM AUTHOR]

In order to enhance the detection of maritime vessel targets, considering the causal relationship between the motion of vessels and their wakes, as well as the characteristics of ship wakes such as large diffusion range and distinctive features, this paper proposes a data-driven method based on Dynamic Mode Decomposition (DMD) for detecting and analyzing ship wakes in sea surface videos. The method, named Multi-dimensional Dynamic Mode Decomposition (MDDMD), segments the video sequence into smaller blocks and analyzes them at various resolution levels, effectively addressing the data analysis issues of large and complex systems. The MDDMD algorithm not only extracts key dynamic features but also reveals the intrinsic structure of the system at different scales, providing new perspectives for the in-depth understanding of nonlinear systems. Comparative experimental results with existing DMD and PCA algorithms demonstrate that the MDDMD algorithm has higher accuracy and robustness in ship wake detection. This study offers valuable insights for ship wake detection under complex maritime conditions and holds potential for practical application in the field of maritime surveillance. [ABSTRACT FROM AUTHOR]

Summary: In this article, for switched nonlinear time‐delay multi‐agent systems (MASs) under directed graphs, an adaptive event‐triggered (ET) consensus problem is investigated. Each agent's switching signal is allowed to be arbitrary and asynchronous. To save communication resources, an adaptive ET consensus strategy is designed. In addition, the Pade approximation approach is introduced to transform the system into an input delay‐free system. A Lyapunov–Krasovskii functional is employed to analyze the effect of time‐varying delays on system stability. It is proved that the consensus errors of switched NMASs are bounded, and the Zeno behavior does not exist. Finally, the presented strategy's effectiveness is verified by simulation results. [ABSTRACT FROM AUTHOR]

Summary: In this article, for non‐parameterized nonlinear continuous (NPNC) multiple‐input multiple‐output (MIMO) systems, two combined iteration‐domain and time‐domain adaptive iterative learning control (ILC) algorithms are proposed to track iteration‐varying reference trajectories repetitively over a finite time interval. Different from the general requirement in adaptive control community that the control gain matrices of the controlled systems are real symmetric and positive‐definite, only the nonsingular property of the control gain matrices is assumed. Moreover, there are just two adaption parameters and one adaption parameter involved in the proposed two adaptive ILC algorithms respectively such that the computation load and memory‐space are greatly saved. A simulation example is utilized to illustrate the effectiveness of the two proposed adaptive ILC algorithms with less adaption parameters. [ABSTRACT FROM AUTHOR]

Summary: This work presents an approach to control a type of stochastic cascade nonlinear systems, which involve external disturbances and nonlinear terms. The external disturbances under the consideration are not measurable and regarded as extended states. The proposed method addresses the problem of unmeasured states and external disturbances by introducing an extended state observer (ESO). Based on the above work, a new stochastic nonlinear system including ESO is established. To ensure the stability and boundedness of the system, an adaptive output feedback controller is designed by using stochastic integrated input‐to‐state stability and backstepping design technique. This controller guarantees that all the states remain almost surely bounded and globally asymptotically stable in probability. Simulation experiments are conducted to validate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

Under the influence of sensor saturation and packet dropout, this paper is concerned with the fault detection (FD) problem for a class of nonlinear systems with two additive time‐varying delay components. In the addressed measurement model, the sensor is assumed to have two communication channels, which can contribute to improving the probability of successfully delivering the measurements. A FD filter is designed to generate residual signals, and the sufficient criteria are established to ensure the stochastic finite‐time stability (SFTS) of the residual system with H∞$$ {H}_{\infty } $$ performance constraint by constructing new Lyapunov‐Krasovskii functionals. Based on the established criteria, the explicit expression of the desired FD filter is obtained via solving a set of linear matrix inequalities (LMIs). Finally, the usefulness of the proposed FD scheme is verified by a simulation example. [ABSTRACT FROM AUTHOR]

Control of nonlinear systems in the presence of model mismatch and system constraints is quite challenging. To address the issue, this work proposes an adaptive Gaussian process-based real-time optimisation (AGP-RTO) control framework. Specifically, the control law consists of two components, a feedforward tracking control law and an uncertainty compensation control law. Because GP has high flexibility to capture complex unknown functions by using very few parameters and it inherently handles measurement noise, this work utilises the GP as an alternative to estimate the mismatch between the real plant and the approximated model. During every RTO execution, the GPs adaptively update the predictions of the model mismatch, then the predictions are embedded into a nonlinear optimisation problem for the correction of the model cost and constraint functions, which yields the uncertainty compensation control law. The proposed AGP-RTO framework ensures that the Karush-Kuhn-Tucker (KKT) conditions determined by the model match those of the plant upon convergence. Compared to many direct adaptive control methods, AGP-RTO does not rely on a high gain for fast adaptation and hence it improves the robustness of the closed-loop system. Compared to the modifier adaptation (MA) method, AGP-RTO avoids the plant-gradient estimation by using the finite difference scheme, besides it trains the GP models offline, which speeds up online evaluation and improves the applicability and efficacy of real-time control. Comparisons are carried out to illustrate the superiority of the AGP-RTO. [ABSTRACT FROM AUTHOR]

In this paper, we consider the cooperative robust output regulation problem for a class of nonlinear multi-agent systems over jointly connected switching networks. First, by attaching each subsystem with an input driven filter, we obtain an extended system. Second, by integrating the distributed observer approach and the distributed internal model approach, we convert the cooperative output regulation problem of the original system into a distributed robust stabilisation problem of an augmented error system which is also a multi-agent system. Finally, we solve the original problem by stabilising the augmented error system via a distributed output feedback control law. [ABSTRACT FROM AUTHOR]

The paper presents output feedback control of a class of two-time-scale nonlinear systems. State feedback control for two-time-scale system is converted into output feedback via two high-gain observers. The high-gain observers are designed for reduced-order, quasi-steady-state, and boundary layer models of the two-time-scale system. Analyses reveal three-time-scale structure of the closed-loop system. Convergence of the closed-loop system is guaranteed under sufficient conditions. Simulation results of control of inverted pendulum on a cart illustrate the application of the proposed methodology. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive tracking control strategy based on multi-dimensional Taylor network (MTN) is proposed for a class of stochastic nonlinear state-constrained systems with input delay. Firstly, to avoid constraint violation, the adaptive backstepping approach and barrier Lyapunov function (BLF) are combined in a unified framework. Then, a suitable auxiliary system with the same order as the considered system is constructed to deal with the effect of input delay. In addition, MTN is used to estimate unknown nonlinear functions during the design of the controller. Furthermore, with the help of the Lyapunov stability theorem, the controller presented in this paper can guarantee that all the closed-loop signals are bounded in probability, the system states remain in the defined compact sets, the output signal can track the reference signal successfully, and the tracking error is bounded by the expected bound. Finally, two examples are given to verify the effectiveness of the designed scheme. [ABSTRACT FROM AUTHOR]

This paper studies the finite-time output tracking problem for a class of nonlinear sandwich systems with sandwiched dead-zone function and input actuator saturation constraint. To achieve the goal, a systematic adaptive backstepping controller is proposed based on the practical finite-time stability criterion which guarantees the output tracking even if the dead zone and saturation constraints occur, simultaneously. In the control approach to confine the system output to a predefined set, the barrier Lyapunov function is utilised. To cope with the problem of 'explosion of complexity', a finite-time command filter is also employed. Furthermore, the values of the unknown parameters are estimated by appropriate adaptive laws. The finite-time stability of the closed-loop system is proved based on the Lyapunov approach which ensures the boundedness of all signals. Finally, the efficiency and applicability of the proposed method are confirmed by providing the simulation results for the hydraulic servo press system. [ABSTRACT FROM AUTHOR]

In this paper, an interval multiobserver is designed for nonlinear systems subject to unknown but bounded disturbances and measurement noises. The behavior of discrete nonlinear systems is described by an uncoupled multimodel. Linear Matrix Inequalities (LMIs) are formulated to study the stability of the proposed systems and to ensure the cooperativity dynamic of the observation errors. An augmented system is introduced to apply a tracking control where the control gains are obtained by pole placement. Finally, a numerical example is proposed to verify the efficiency of the interval multiobserver in state estimation and to prove the performance of the control strategy to follow the desired trajectory. [ABSTRACT FROM AUTHOR]

When it comes to practical engineering, there is a high likelihood of shafts developing slant cracks due to torque transmission. These cracks exhibit breathing characteristics, repeatedly opening and closing under gravity and radial forces. To diagnose rotor systems with breathing slant cracks, the nonlinear output frequency response functions (NOFRFs) method is introduced. Firstly, a dynamic model of rotor systems with breathing slant cracks is established, and the system's frequency spectra are obtained by solving the model with different crack angles, depths, and positions. Secondly, the NOFRFs values at different orders are derived based on the NOFRFs theory. The simulation results display increased nonlinear characteristics with crack angle and depth. The system's nonlinear characteristics are stronger when cracks are closer to the disk. The G 3 (j ω F) ¯ value for the first-order is sensitive to crack angles, the G 4 (j 2 ω F) ¯ value for the second-order is sensitive to crack depths, and the G 4 (j 4 ω F) ¯ value for the fourth-order is sensitive to crack positions. As a result, the NOFRFs response at different orders can detect variations in angles, depths, and positions of the breathing slant crack. Finally, experiments are conducted on a rotor system with breathing slant cracks, and the results match those of the simulation, indicating that the NOFRFs method is feasible for identifying breathing slant cracks. [ABSTRACT FROM AUTHOR]

This paper considers the event‐triggered adaptive fuzzy bipartite containment control problem for switched nonlinear multi‐agent systems (MASs) with actuator attacks. To handle the completely unknown nonlinear functions in the considered system, fuzzy logic systems (FLSs) are applied to approximate the unknown nonlinear functions. In addition, an adaptive bipartite containment control approach is designed to deal with the actuator attacks, which can reduce the burden of communication. According to the designed adaptive bipartite containment control scheme, it is shown that all the signals are semi‐globally uniformly ultimately bounded (SGUUB), and all the outputs of the followers achieve the bipartite consensus and finally enter the convex set spanned by leaders' in the presence of actuator attacks. Eventually, a simulation example is presented to illustrate the availability of the developed strategy. [ABSTRACT FROM AUTHOR]

This paper proposes a new type of echo state network called Long‐Term Memory Enhanced Echo State Network (LTME‐ESN). By extending the ideas of the forget gate and the input gate from the LSTM, LTME‐ESN modifies the equation for updating the state in a Leaky Integral Echo State Network (Leaky‐ESN). By regulating the accumulation of information, the construction of extended periods of dependency between states may be delayed, allowing for adaptive management of the data transported from the previous state to the present one. In order to optimize parameters by using Stochastic Gradient Descent (SGD), this research presents a necessary condition for LTME‐ESN to meet the properties of the echo state network. The study uses low‐frequency sinusoidal, high‐frequency sinusoidal, and chaotic time series to demonstrate the model's efficiency. Simulations show that LTME‐ESN outperforms Leaky‐ESN in prediction accuracy and variation. [ABSTRACT FROM AUTHOR]

In this paper, a proposed echo state network (ESN) model called F‐ESN is based on methane topology. Due to the neurons in the reservoir of the ESN model being random and sparsely connected, the stability of the system structure could be better, and the prediction accuracy could be higher. To solve this issue, the reservoir's neuronal connectivity is modified to a certain methane structure. A master neuron governs each little unit and communicates with the others to pass information. In addition, MFO optimized by adaptive dynamic operators is used to optimize the three parameters of ESN : leakage rate (a)$ (a)$, spectral radius of the connection weight matrix (ρ)$ (\rho)$, and input scale factor (sin)$ (s^{in})$. To verify the effectiveness of the proposed method, low‐frequency sin time series, high‐frequency SIN time series, and MG time series are simulated. The experimental results show that the methane topology can further improve the prediction accuracy of leakage echo state networks. [ABSTRACT FROM AUTHOR]

In this paper, the adaptive fuzzy finite‐time tracking control problem is studied for a class of non‐strict feedback high‐order time‐delay systems with unknown dead‐zone. The fuzzy logic systems are introduced to approximate the uncertain nonlinear functions in the system. The Lyapunov–Krasovskii (L–K) functional technology is used to compensate for the unknown time delays. In addition, based on the backstepping technique and finite‐time theory, an adaptive fuzzy finite‐time tracking controller is designed to ensure that the closed‐loop system is semi‐global practical finite‐time stability, and the tracking error can converge to a small neighbourhood around the origin within a finite time. Finally, the rationality of the proposed method is verified by simulation results. [ABSTRACT FROM AUTHOR]

We consider the nonlinear elliptic system $$\begin{align*} \left\{ \begin{array}{ll} u \in W_{0}^{\frac{N}{N-1}}(\Omega): & -\textrm{div}(M(x)\nabla u) + u = -\textrm{div}(u\,M(x)\,\nabla\psi) + f(x),\\ \displaystyle \psi \in W_0^{1,2}(\Omega): & -\textrm{div}(M(x)\nabla \psi) + \psi = R(u) + E(x)\,\nabla\psi, \end{array} \right. \end{align*}$$ { u ∈ W 0 N N − 1 (Ω) : − div (M (x) ∇u) + u = − div (u M (x) ∇ψ) + f (x) , ψ ∈ W 0 1 , 2 (Ω) : − div (M (x) ∇ψ) + ψ = R (u) + E (x) ∇ψ , where Ω is a bounded, open subset of $ \mathbb {R}^N $ R N , $ N \geq ~3 $ N ≥ 3 ; $ M(x) $ M (x) is a coercive, symmetric matrix with $ L^{\infty }(\Omega) $ L ∞ (Ω) coefficients; $ f(x) $ f (x) and $ E(x) $ E (x) belong to some Lebesgue space, and $ R(s) $ R (s) is a continuous function such that $$\begin{align*} 0 \leq R(s)\leq |s|^{\theta}, \quad \mbox{for}\ \theta { \lt } \frac{2}{N}. \end{align*}$$ 0 ≤ R (s) ≤ | s | θ , for θ < 2 N. Using a duality technique, we prove existence of at least a weak solution $ (u,\psi) $ (u , ψ). Moreover, if N=3 or N=4, we prove under stronger assumptions on $ f(x) $ f (x) and $ E(x) $ E (x) that the solution u belongs to $ W_0^{1,2}(\Omega) $ W 0 1 , 2 (Ω). [ABSTRACT FROM AUTHOR]

The variable selection of high dimensional nonparametric nonlinear systems aims to select the contributing variables or to eliminate the redundant variables. For a high dimensional nonparametric nonlinear system, however, identifying whether a variable contributes or not is not easy. Therefore, based on the Fourier spectrum of density-weighted derivative, one novel variable selection approach is developed, which does not suffer from the dimensionality curse and improves the identification accuracy. Furthermore, a necessary and sufficient condition for testing a variable whether it contributes or not is provided. The proposed approach does not require strong assumptions on the distribution, such as elliptical distribution. The simulation study verifies the effectiveness of the novel variable selection algorithm. [ABSTRACT FROM AUTHOR]