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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 evaluates the accuracy of the Hermitian form of the downfolding procedure using the double unitary coupled cluster (DUCC) ansatz on the benchmark systems of linear chains of hydrogen atoms, H6 and H8. The computational infrastructure employs the occupation-number-representation codes to construct the matrix representation of arbitrary second-quantized operators, allowing for the exact representation of exponentials of various operators. The tests demonstrate that external amplitudes from standard single-reference coupled cluster methods that sufficiently describe external (out-of-active-space) correlations reliably parameterize the Hermitian downfolded effective Hamiltonians in the DUCC formalism. The results show that this approach can overcome the problems associated with losing the variational character of corresponding energies in the corresponding SR-CC theories. [ABSTRACT FROM AUTHOR]

In this article, we show that the collective light–matter strong coupling regime where N molecular emitters couple to the photon mode of an optical cavity can be mapped to a quantum impurity model where the photon is the impurity that is coupled to a bath of anharmonic transitions. In the thermodynamic limit where N ≫ 1, we argue that the bath can be replaced with an effective harmonic bath, leading to a dramatic simplification of the problem into one of the coupled harmonic oscillators. We derive simple analytical expressions for linear optical spectra (transmission, reflection, and absorption) where the only molecular input required is the molecular linear susceptibility. This formalism is applied to a series of illustrative examples, showing the role of temperature, disorder, vibronic coupling, and optical saturation of the molecular ensemble, explaining that it is useful even when describing an important class of nonlinear optical experiments. For completeness, we provide Appendixes A–C that include a self-contained derivation of the relevant spectroscopic observables for arbitrary anharmonic systems (for both large and small N) within the rotating-wave approximation. While some of the presented results herein have already been reported in the literature, we provide a unified presentation of the results as well as new interpretations that connect powerful concepts in open quantum systems and linear response theory with molecular polaritonics. [ABSTRACT FROM AUTHOR]

Synchronization is common in both nature and human physiology, often used to illustrate nonlinear dynamics. Interestingly, one can initiate their comprehension of this phenomenon from pure linear systems. In this Tutorial, we begin with a theoretical exploration of coupled oscillators' dynamic behavior, enabling us to discern and contrast the unique attributes of dissipative coupling as opposed to commonly observed coherent coupling. We then examine synchronization in two dissipative coupled linear systems: one with two pendulums mutually linked via the Lenz effect and the other with two RLC oscillators coupled via a resistor. This Tutorial is designed to serve as a concise starting point for researchers interested in exploring synchronization phenomena using a simplified model driven solely by dissipative coupling. [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]

This paper investigates the robust stabilization problem of linear delay systems with parametric uncertainty. First, by means of the argument principle, a delay‐dependent sufficient condition is derived for designing a feedback controller, with which the closed‐loop system can achieve robust stability. Then, based on the fundamental matrix of the linear delay systems, a constrained optimization problem is formulated for solving the feedback gain matrices. The effectiveness of the proposed method is verified by some simulation results. [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]

In this article, the asynchronous control problem of switched linear systems with all unstable modes under denial‐of‐service (DoS) attacks is studied. First, the upper bound of the sampling period, which can be easily calculated based on the scenario where all modes are unstable, is obtained under a periodic sampling control strategy. Second, by constructing an appropriate discrete multiple linear quadratic Lyapunov function, an asynchronous control scheme in the form of linear matrix inequalities is devised. To ensure the stability of switched systems under DoS attacks, a sufficient condition for the total duration and frequency of DoS attacks is established. It is shown that the switched system can tolerate DoS attacks up to a certain limit while maintaining exponential stability, and this result is applicable even when all subsystems are unstable. Finally, numerical examples and a comparative study are presented to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the approximate controllability of control problems governed by evolution hemivariational inequalities in super-reflexive Banach spaces by preassuming the approximate controllability of the associated linear system. We first show that the original problem is connected with a differential inclusion problem involving the Clarke subdifferential operator, and then we prove the approximate controllability of the original problem via the approximate controllability of the differential inclusion problem. The paper offers a unique solution to a challenge introduced by assuming the underlying space X as a super-reflexive Banach space, which presents issues of convexity due to the nonlinear nature of the duality map involved in the expression of the control. Such issues are not present when X is a separable Hilbert space. Therefore, the paper's novelty is its successful resolution of the convexity problem, paving the way for approximate controllability of the evolution hemivariational inequality in which X is a super-reflexive Banach space. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the method of solving partial differential equations (PDEs) using artificial neural network (ANN) structures, which have been actively applied in artificial intelligence models. The ANN model for solving PDEs offers the advantage of providing explicit and continuous solutions. However, the ANN model for solving PDEs cannot construct a conventionally solvable linear system with known matrix solvers; thus, computational speed could be a significant concern. We study the implementation of the multigrid method, developing a general concept for a coarse-grid correction method to be integrated into the ANN-PDE architecture, with the goal of enhancing computational efficiency. By developing a reduced form of the multigrid method for ANN, we demonstrate that it can be interpreted as an equivalent representation of the classic multigrid expansion. We validated the applicability of the proposed method through rigorous experiments, which included analyzing loss decay and the number of iterations along with improvements in terms of accuracy, speed, and complexity. We accomplished this by employing the gradient descent method and the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method to update the gradients while solving the given ANN systems of PDEs. [ABSTRACT FROM AUTHOR]

ABSTRACT Inspired by the efficiency of Anderson acceleration (AA) and the fact that its un‐truncated version is essentially equivalent to the generalized minimal residual method (GMRES) for solving linear systems, in this study, the preconditioned alternating Anderson acceleration Richardson (PA3R) approach is proposed as an acceleration framework, and its relationship to AA and GMRES is examined from a spectrum perspective. Next, the convergence condition of the PA3R approach is demonstrated to be ‖M−1N‖<1$$ \left\Vert {M}^{-1}N\right\Vert <1 $$ (where A=M−N$$ A=M-N $$ is the splitting of system matrix A∈ℂn×n$$ A\in {\mathrm{\mathbb{C}}}^{n\times n} $$) for a general system matrix, which always holds for the mature splitting iteration methods. This new approach is applied to four well‐established splitting methods to solve complex symmetric linear systems. Furthermore, the optimal relaxation parameters are investigated, showing that the eigenvalue distribution region of the iteration matrices of the resulting methods are approximately half of that of the original methods. The numerical results indicate that for examples with dimensions exceeding 4 million, the use of the PA3R approach results in a significant efficiency improvement especially in terms of CPU time compared with the non‐PA3R version. [ABSTRACT FROM AUTHOR]

This study focuses on the analytical identification and quantification of one type of spurious responses in the context of response history analysis. The spurious response is caused by linear interpolation of input loads. Through analytical derivations and numerical simulations, it is shown that the identified spurious response is fully caused by the interpolation and can significantly affect both damping and inertial forces. Furthermore, the spurious response is not bounded, thus, resistance-based designs could potentially be non-conservative. The findings are applicable to (non-)linear MDOF systems. To address this issue and improve the quality of numerical results, remedies and recommendations are proposed. [ABSTRACT FROM AUTHOR]

The advantages and disadvantages of application of Padé approximants to regression analysis with two independent covariates are discussed. The main difficulty of using Padé function is nonlinearity of data fitting. Possible approaches to overcoming the problem are discussed. New formulation of residuals is suggested in the method of least squares. It leads to a system of linear equations in case of rational functions. The possibility of using ridge regularization technique to avoid overfitting is demonstrated in this approach. To illustrate the efficiency of the suggested method, several practical cases from physics and reliability theory are considered. [ABSTRACT FROM AUTHOR]

Results on continuous dependence on parameters, as well as on regularization, of solutions to linear systems of parabolic partial differential equations of second order with delay are given. One of the main features is that the topology on the zero order and delay coefficients is the weak-* topology on an L ∞ space, whereas the assumptions on the second- and first-order coefficients are slightly stronger. This is important in the context of generation of linear skew-product dynamical systems by such equations. [ABSTRACT FROM AUTHOR]

ABSTRACT Among randomized numerical linear algebra strategies, so‐called sketching procedures are emerging as effective reduction means to accelerate the computation of Krylov subspace methods for, for example, the solution of linear systems, eigenvalue computations, and the approximation of matrix functions. While there is plenty of experimental evidence showing that sketched Krylov solvers may dramatically improve performance over standard Krylov methods, especially when combined with a truncated orthogonalization step, many features of these schemes are still unexplored. We derive a new sketched Arnoldi‐type relation that allows us to obtain several different new theoretical results. These lead to an improvement of our understanding of sketched Krylov methods, in particular by explaining why the frequently occurring sketched Ritz values far outside the spectral region of A$$ A $$ do not negatively influence the convergence of sketched Krylov methods for f(A)b$$ f(A)b $$. Our findings also help to identify, among several possible equivalent formulations, the most suitable sketched approximations according to their numerical stability properties. These results are also employed to analyze the error of sketched Krylov methods in the approximation of the action of matrix functions, significantly contributing to the theory available in the current literature. [ABSTRACT FROM AUTHOR]

ABSTRACT This article addresses the asynchronous guaranteed cost control (GCC) problems for interval type‐2 (IT2) fuzzy continuous‐time Markov jump systems (C‐TMJSs) with quantization and non‐consecutive transmission. A dynamic event‐triggered mechanism (ETM) for IT2 fuzzy C‐TMJSs is designed to address the limited bandwidth and communication burden, which incorporates mode‐dependent thresholds and weighting matrices. An asynchronous IT2 fuzzy guaranteed cost controller possessing unmatched premise variable information is developed to stabilize the considered system, achieving desired GCC performance. The relationship between system mode and controller mode is described by the hidden Markov model (HMM). A quantizer is employed to quantize the signal prior to transmission to the next node, modeled as a stochastic quantization utilizing the HMM. Furthermore, an improved mode‐dependent and fuzzy‐dependent Lyapunov function is constructed for stability analysis, and the conditions of optimal GCC performance are derived. Finally, two examples are performed to validate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper addresses the event-triggered H ∞ control for switched linear systems without stable subsystems. A novel event-triggered-based switching strategy is designed to remove the requirement of real-time availability of system state which is a prerequisite for the traditional min-switching law to work. Instead, we only need to check the switching conditions at the discrete triggering instants, and unfavorable asynchronous switching behavior is also avoided. However, under the designed switching strategy, the value of the Lyapunov function may be increasing during the active interval caused by the possibility of the mismatch between the min-switching and triggering. To handle this challenge, we then construct an improved two-side looped-functional, which is also event-triggered-based and can remove conservative nonincreasing requirements of multiple Lyapunov functions. Sufficient conditions with less conservative for the considered switched linear systems to be asymptotically stable with H ∞ performance are obtained. Besides, Zeno phenomenon of both switching and triggering is also avoided. Finally, two examples are exploited to verify the applicability and effectiveness of the developed method. [ABSTRACT FROM AUTHOR]

Kaczmarz algorithm is an iterative projection method for solving system of linear equations that arise in science and engineering problems in various application domains. In addition to classical Kaczmarz, there are randomized and parallel variants. The main challenge of the parallel implementation is the dependency of each Kaczmarz iteration on its predecessor. Because of this dependency, frequent communication is required which results in a substantial overhead. In this study, a new distributed parallel method that reduces the communication overhead is proposed. The proposed method partitions the problem so that the Kaczmarz iterations on different blocks are less dependent. A frequency parameter is introduced to see the effect of communication frequency on the performance. The communication overhead is also decreased by allowing communication between processes only if they have shared non‐zero columns. The experiments are performed using problems from various domains to compare the effects of different partitioning methods on the communication overhead and performance. Finally, parallel speedups of the proposed method on larger problems are presented. [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 paper delves into the output feedback control of systems with dual multi‐memoryless channels, where the data packets transmitted from the sensor to the controller (S/C) and from the controller to the actuator (C/A) are suffered from two different multi‐parallel Markovian fading channels. Two new multi‐state Markovian chains are introduced, by which the multiple fading channels system is transformed into a new jumping parameter system. Then a stochastic maximum principle is given along with an optimal state feedback controller for the case that the state is known. When the state is unknown, a Markov jump linear estimator is designed by using the completing square method. In this case, an output feedback controller is obtained by substituting the real system state with its estimation. Meanwhile, the separation principle is shown. Finally, the validity of these methods is verified by simulation examples. [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]

In this article, an H∞$$ {H}_{\infty } $$ optimal preview repetitive control (OPRC) scheme is proposed to deal with the disturbance attenuation problem for continuous‐time linear systems with external unknown disturbance and input delay. A general bounded L2$$ {L}_2 $$ gain is applied to the H∞$$ {H}_{\infty } $$ OPRC tracking control problem by introducing a function with discounted performance. First, an augmented system containing system state equation, tracking error dynamics, and modified repetitive control output equation is constructed, which is then transformed into a non‐delayed one by state transformation. Next, the OPRC controller is given and the game algebraic Riccati equation (GARE) is derived by transforming the H∞$$ {H}_{\infty } $$ tracking problem into a 2‐player zero‐sum game problem to give a Nash equilibrium solution of the associated min–max optimization problem. Besides, a value iteration (VI) algorithm is introduced to optimize the solution of continuous time GARE and ensure its convergence. Furthermore, the bounded‐input bounded‐output stability of the closed‐loop system is obtained by giving an upper bound on the discount factor. Finally, the numerical simulation example is provided to illustrate the effectiveness of the proposed method. [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]

We consider a linear system based on a population dynamics model dependent on age, space and nonlocal boundary conditions. Note that our population dynamics model is a four‐step model with a second derivative with respect to the age variable and a second derivative with respect to the space variable. Population growth at each stage depends on time and space. We prove the uniqueness and existence of a positive solution by combining the Galerkin's variational method and the Banach's fixed point theorem. [ABSTRACT FROM AUTHOR]

Much is understood about 1-dimensional spin chains in terms of entanglement properties, physical phases, and integrability. However, the Lie algebraic properties of the Hamiltonians describing these systems remain largely unexplored. In this work, we provide a classification of all Lie algebras generated by the terms of 2-local spin chain Hamiltonians, or so-called dynamical Lie algebras, on 1-dimensional linear and circular lattice structures. We find 17 unique dynamical Lie algebras. Our classification includes some well-known models such as the transverse-field Ising model and the Heisenberg chain, and we also find more exotic classes of Hamiltonians that appear new. In addition to the closed and open spin chains, we consider systems with a fully connected topology, which may be relevant for quantum machine learning approaches. We discuss the practical implications of our work in the context of variational quantum computing, quantum control and the spin chain literature. [ABSTRACT FROM AUTHOR]

Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this work, we propose a novel method for solving linear systems. Our approach leverages binary optimization, making it particularly well-suited for problems with large condition numbers. We transform the linear system into a binary optimization problem, drawing inspiration from the geometry of the original problem and resembling the conjugate gradient method. This approach employs conjugate directions that significantly accelerate the algorithm's convergence rate. Furthermore, we demonstrate that by leveraging partial knowledge of the problem's intrinsic geometry, we can decompose the original problem into smaller, independent sub-problems. These sub-problems can be efficiently tackled using either quantum or classical solvers. Although determining the problem's geometry introduces some additional computational cost, this investment is outweighed by the substantial performance gains compared to existing methods. [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]

ABSTRACT In this article, the resilient event‐triggered control issue for switched linear systems with the bounded disturbance is explored under the aperiodic denial‐of‐service (DoS) attacks. Unlike the discussions on asynchronous behavior caused by network transmission/DoS attacks, configure a copy of predictor at controller module to avert the negative impacts of asynchronous switching. Subsequently, by establishing a resilient event‐triggered strategy (RETS) to eliminate invalid sampling during DoS attacks intervals, the waste of network resources is reduced. Besides, a sufficient condition is derived to ensure the input‐to‐state stability (ISS) for the close‐loop switched systems under DoS attacks. The results indicate that the switched systems can resist a certain degree of DoS attacks under the average dwell time (ADT) constrained by DoS attacks frequency and duration. In addition, Zeno behavior is eliminated by calculating the lower bound of the triggering intervals. Finally, the availability of theoretical approach is verified through a numerical simulation. [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]