Search

We study numerical methods and algorithms for time-dependent fractional-in-space diffusion problems. The considered anomalous diffusion is modelled by the fractional Laplacian (− Δ) α , 0 < α < 1 , following the integral definition. Fractional diffusion is non-local, and the finite element method (FEM) discretization in space leads to a dense stiffness matrix. It is well known that numerically solving such non-local boundary value problems is expensive. Difficulties increase significantly when the problem is time-dependent. The aim of the article is to develop computationally efficient methods and algorithms. There are two main features of our approach. Hierarchical semi-separable (HSS) compression is applied for an approximate solution of the arising linear systems. For time discretization, we use an adaptive forward–backward Euler scheme. The properties of the composite algorithm thus obtained are investigated. In particular, the block representation of HSS compression allowed us to upgrade the HSS solver to efficiently handle varying diagonally perturbed transition matrices corresponding to changing time steps. The contribution of the paper is threefold. The methods are completely constructive, which allows for a clearly structured description of the algorithms. A theoretical estimate of the computational complexity is presented. It shows the advantages of the adaptive time stepping in combination with the HSS solver. Theoretical results are supported by representative numerical experiments. Both sequential and parallel scalability and efficiency are analyzed. The presented results provide convincing proof of the concept of the proposed methods and algorithms. [ABSTRACT FROM AUTHOR]

This paper provides empirically implementable sufficient statistics formulas for optimal nonlinear tax systems in the presence of across-income heterogeneity in preferences, inheritances, income-shifting capabilities, and other sources. We characterize optimal smooth tax systems on income and savings (or other commodities), as well as simpler tax systems. We use familiar elasticity concepts and a novel sufficient statistic for heterogeneity correlated with earnings ability: the difference between across-income variation in savings and the causal effect of income on savings. We apply these formulas to the United States and find that the optimal savings tax is mostly positive and progressive. (JEL E21, G51, H21, H24) [ABSTRACT FROM AUTHOR]

Uncrewed aircraft systems and advanced air mobility are associated with uncertain conditions, such as wind prediction errors, and they may deviate from dedicated airspaces referred to as corridors. However, further studies on these aspects are required. This study focuses on the covariance control for a stochastic discrete-time linear system under correlated uncertainties. A covariance control problem with chance constraints can be formulated as a convex-programming problem. Numerical simulations of uncrewed aircraft systems path planning can be used to compare two control laws: covariance control laws that consider correlated and noncorrelated noise. Numerical simulations were conducted to verify that the covariance control law considering correlated noise generates a trajectory that appropriately satisfies the constraints. Consequently, the effect of considering correlated noise in the covariance control law was clarified. In addition, covariance control has been demonstrated to generate appropriate trajectories for various state constraints. Moreover, numerical simulations indicated that covariance control facilitated the control of uncertainty, and the effectiveness of the covariance control was evaluated. The insights gained from the results of this study can inform enhanced uncertainty management for improving reliability and safety in real-world applications of uncrewed aircraft systems and advanced air mobility. [ABSTRACT FROM AUTHOR]

This article explores the dissipative control for a class of nonlinear DP-CPS (distributed parameter cyber physical system) within a finite-time interval. By utilizing a Takagi-Sugeno (T-S) fuzzy model to represent the system's nonlinear aspects, the studied system is formulated as a class of fuzzy parabolic partial differential equation (PDE). In order to optimize network resources, both the system state and input signal are subjected to quantization using dynamic quantizers. Subsequently, a dynamic state control strategy is proposed, taking into account potential DoS attack. The finite-time boundedness of the fuzzy parabolic PDE is analyzed, with respect to the influence of quantization, through the construction of an appropriate Lyapunov functional. The article then presents the conditions for finite-time dissipative control design, alongside the adjustment parameters for the dynamic quantizers within the fuzzy closed-loop system. Furthermore, the decoupling of interlinked nonlinear terms in the control design conditions is achieved by using an arbitrary matrix. Finally, an example is provided and the simulation results indicate the effectiveness of the dissipative control method proposed. [ABSTRACT FROM AUTHOR]

This paper presents a thorough robust Class-AB power amplifier design and its application in pressure-mode sensor-on-chip nonlinearity correction. Considering its use in piezoresistive sensing applications, a gain-boosting-aided folded cascode structure is utilized to increase the amplifier's gain by a large amount as well as enhancing the power rejection ability, and a push–pull structure with miller compensation, a floating gate technique, and an adaptive output driving limiting structures are adopted to achieve high-efficiency current driving capability, high stability, and electronic environmental compatibility. This amplifier is applied in a real sensor nonlinearity correction on-chip system. With the help of a self-designed 7-bit + sign DAC and a self-designed two-stage operational amplifier, this system is compatible with nonlinear correction at different signal conditioning output values. It can also drive resistive sensors as small as 300 ohms and as high as tens of thousands of ohms. The designed two-stage operational amplifier utilizes the TSMC 0.18 um process, resulting in a final circuit power consumption of 0.183 mW. The amplifier exhibits a gain greater than 140 dB, a phase margin of 68°, and a unit gain bandwidth exceeding 199.76 kHz. The output voltage range spans from 0 to 4.6 V. The final simulation results indicate that the nonlinear correction system designed in this paper can correct piezoresistive sensors with a nonlinearity of up to ±2.5% under various PVT (Process–Voltage–Temperature) conditions. After calibration by this system, the maximum error in the output voltage is 4 mV, effectively reducing the nonlinearity to 4% of its original value in the worst-case scenario. [ABSTRACT FROM AUTHOR]

In recent years, the simplified computation of position and velocity changes in nonlinear systems using Lie groups and Lie algebra has been widely used in the study of robot localization systems. The unscented Kalman filter (UKF) can effectively deal with nonlinear systems through the unscented transformation, and in order to more accurately describe the robot localization system, the UKF method based on Lie groups has been studied successively. The computational complexity of the UKF on Lie groups is high, and in order to simplify its computation, the Lie groups are applied to the manifold, which efficiently handles the state and uncertainty and ensures that the system maintains the geometric constraints and computational simplicity during the updating process. In this paper, a multi-sensor fusion localization method based on an unscented Kalman filter on manifolds (UKF-M) is investigated. Firstly, a system model and a multi-sensor model are established based on an Autonomous Underwater Vehicle (AUV), and a corresponding UKF-M is designed for the system. Secondly, the multi-sensor fusion method is designed, and the fusion method is applied to the UKF-M. Finally, the proposed method is validated using an underwater cave dataset. The experiments demonstrate that the proposed method is suitable for underwater environments and can significantly correct the cumulative error in the trajectory estimation to achieve accurate underwater localization. [ABSTRACT FROM AUTHOR]

This paper mainly investigates the problem of finite-time H ∞ control for a class of uncertain Markovian jump nonlinear systems (MJNSs) with time-varying delay and generally uncertain transition rates. By constructing the appropriate Lyapunov–Krasovskii functional and free weighting matrices, a novel criterion on finite-time boundedness for the MJNSs with H ∞ performance is derived. We use a special way to deal with the bilinear terms, the mode-dependent state feedback controller is designed to ensure the H ∞ finite-time boundedness of the closed-loop system in the forms of strict linear matrix inequalities. Finally, numerical and practical examples are given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In the fault-tolerant control tasks of nonlinear systems, unmeasurable states, time delay and actuator faults are considered to be the main factors hindering effective controller design and tracking performance improvement. To solve these problems, firstly, a state observer is established to estimate the unmeasurable of the system and the prescribed performance control based on error transformation is presented to maintain system efficiency and reliability. Secondly, the problem of controller design caused by input delay is effectively solved by constructing an auxiliary tracking error and auxiliary system and combining with the well-designed Lyapunov-Krasovskii functionals. Thirdly, the newly employed damping term in the intermediate control law is utilized to compensate for the possibly unlimited number of faults. Then, it is proved that all signals are semi-global practical finite-time stable based on the backstepping technique. Meanwhile, the tracking error can converge to a specified range within finite time. Finally, comparative simulations are presented to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this study, teaching learning-based optimization algorithm (TLBO) has been explored in order abatement (OA) and controller design of the linear time-invariant (LTI) systems. Motivated by various optimization approaches available in the literature, with TLBO's unique computational abilities like fast convergence, simple mathematical steps and gradient free approach, the study aims to determine the unknown coefficients of the abated system (AS) by minimizing the integral square error (ISE) between the higher order system (HOS) and the AS. The efficacy and supremacy of the suggested approach has been demonstrated using six distinct control systems of high order. In order to assess the performance of the proposed method, the obtained results are compared with HOS and lower order system already available in the literature. It reveals that the proposed AS maintains stability and the steady state conditions of the HOS. To further illustrate the practical application of TLBO, a 4th order system has been considered and a proportional-integral (PI) controller is designed using the proposed 2nd order AS. [ABSTRACT FROM AUTHOR]

In this paper, a class of linear discrete-time systems with input saturation is studied in a data-driven framework. Firstly, the input-state data are collected to represent the open-loop and closed-loop systems. While the open-loop data-based representation is a result that is parallel to system identification, the closed-loop representation bypasses the system identification and can be used for direct data-driven control law synthesis. Then, by a novel Lyapunov technique, sufficient conditions for system stability are derived, such conditions are independent of system matrices. Moreover, the attraction domain is estimated using two classes of shape reference sets. Finally, two examples are used to test the correctness of the data-driven control laws. [ABSTRACT FROM AUTHOR]

The present study focuses on the master–slave synchronization issue for switched nonlinear time-delay systems based on quantization and switching event-triggered strategy (ETS). The logarithmic quantizer and the switching ETS that is represented by a transition between the periodic sampled-data control and the general continuous ETS are adopted to improve resource utilization and adjust data transmission. According to the event-triggered sampled signal, the synchronization error system with asynchronous switching signal is modeled. In virtue of multiple Lyapunov functional approach, the sufficient conditions are obtained to guarantee the error system is exponentially stable by developing some linear matrix inequalities (LMIs), from which the synchronizing controller is orchestrated. Lastly, the reliability of the proposed methods is illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

For a one dimensional 2-lattice we write down the momentum equation and the equation ruling the shift vector for the dynamic case as a first order system and characterize it in terms of its hyperbolicity. We use similar arguments for problems of increasing difficulty and tackle: one dimensional 3-lattices, three dimensional 2-lattices, three dimensional 3-lattices and finally the most general case of three dimensional (n + 1) -lattices. Our approach is confined to the geometrically and materially linear elastodynamic theory and is valid for generic anisotropic materials that have the multilattice structure. The main finding is that, with the assumptions adopted, the presence of each shift vector is related with zero eigenvalues when the system is written as a first order system. [ABSTRACT FROM AUTHOR]

Summary: We provide rigorous theoretical bounds for Anderson acceleration (AA) that allow for approximate calculations when applied to solve linear problems. We show that, when the approximate calculations satisfy the provided error bounds, the convergence of AA is maintained while the computational time could be reduced. We also provide computable heuristic quantities, guided by the theoretical error bounds, which can be used to automate the tuning of accuracy while performing approximate calculations. For linear problems, the use of heuristics to monitor the error introduced by approximate calculations, combined with the check on monotonicity of the residual, ensures the convergence of the numerical scheme within a prescribed residual tolerance. Motivated by the theoretical studies, we propose a reduced variant of AA, which consists in projecting the least‐squares used to compute the Anderson mixing onto a subspace of reduced dimension. The dimensionality of this subspace adapts dynamically at each iteration as prescribed by the computable heuristic quantities. We numerically show and assess the performance of AA with approximate calculations on: (i) linear deterministic fixed‐point iterations arising from the Richardson's scheme to solve linear systems with open‐source benchmark matrices with various preconditioners and (ii) non‐linear deterministic fixed‐point iterations arising from non‐linear time‐dependent Boltzmann equations. [ABSTRACT FROM AUTHOR]

The industrial standard in the design and development process of NVH(Noise Vibration Harshness) characteristic of brakes is the application of Finite Element(FE) models with a high number of degrees of freedom in the range of one or several millions. Nevertheless, parallel experimental investigations are still indispensable. On the other hand, minimal models with, due to the inclusion of the self-excitation process, at least two degrees of freedom are well known to be capable to explain qualitatively phenomena as instability of the desired non-vibrating solution or limit cycle oscillation but are in general very inaccurate in predicting the dynamics of a specific real brake. This is because the underlying physical assumptions are already too restrictive and model parameters (especially those referring to nonlinearities) are widely unknown. To overcome this problem, the data-driven modeling approach SINDy(Sparse Identification of Nonlinear Dynamics) is applied to identify appropriate nonlinear functions for a brake squeal minimal model. A problem thereby is the limited database. It turns out that the naive implementation of the method yielding the lowest possible residuum does not necessarily provide physically meaningful models and results, respectively. Instead, a constrained model that incorporates physical knowledge is used to robustly identify parameters and reproduce realistic dynamic behavior. Thereby, several appropriate models with coexisting limit cycles and stationary equilibrium are identified. In particular, it was found that the angular position of the brake drum has a significant influence on the model parameters and therefore must be taken into account in a model with long-term validity. [ABSTRACT FROM AUTHOR]

This paper focuses on the fuzzy adaptive predefined-time control for fractional-order nonlinear systems with time-varying deferred constraints. First, a modified dynamic surface control technique is introduced to address the problem of computational complexity exposed in the backstepping framework, and the interval type-2 fuzzy logic systems are applied to model the unknown nonlinearities of the systems. Next, a shifting function and the barrier Lyapunov function with variational barrier bounds are formulated to deal with the constraints issue. Particularly, the constraint conditions can be satisfied within a predetermined time, even if they are transgressed initially. Furthermore, a switching threshold event-triggered controller is devised to balance the control energy and communication resources. With the help of the predefined-time stability criterion, it is proven that the presented predefined-time event-triggered controller can ensure that all the signals involved in the closed-loop system are bounded and the tracking error fluctuates to a small neighborhood of the origin in a predefined-time interval. Finally, two simulation examples are provided to confirm the effectiveness of the put-forward control algorithm. [ABSTRACT FROM AUTHOR]

This paper presents an extensive investigation into the state feedback stabilization, observer design, and observer-based controller design for a specific category of nonlinear Hadamard fractional-order systems. The research extends the conventional integer-order derivative to the Hadamard fractional-order derivative, offering a more universally applicable method for system analysis. Furthermore, the traditional Lipschitz condition is adapted to a one-sided Lipschitz condition, broadening the range of systems amenable to analysis using these techniques. The efficacy of the proposed theoretical findings is illustrated through several numerical examples. For instance, in Example 1, we select an order of derivative r = 0.8; in Example 2, r is set to 0.9; and in Example 3, r = 0.95. This study enhances the comprehension and regulation of nonlinear Hadamard fractional-order systems, setting the stage for future explorations in this domain. [ABSTRACT FROM AUTHOR]

This paper investigates the tracking problem of fractional-order multi-agent systems. Both the order and parameters of the leader are unknown. Firstly, based on the positive system approach, the asymptotically stable criteria for incommensurate linear fractional-order systems are derived. Secondly, the models of incommensurate heterogeneous multi-agent systems are introduced. To cope with incommensurate and heterogeneous situations among followers and the leader, radial basis function neural networks (RBFNNs) and a discontinuous control method are used. Thirdly, the consensus criteria are derived by using the Vector Lyapunov Function method. Finally, a numerical example is presented to illustrate the effectiveness of the proposed theoretical method. [ABSTRACT FROM AUTHOR]

In engineering practice, the nonlinear vibration effect can easily lead to chaos in the system, which will not only reduce the performance of the system but also lead to premature fatigue of components, control failure, and increased safety risks. In view of the core position of the robotic arm in modern industry, this study relies on the robotic arm brake system to explore the theoretical basis of integrated viscoelastic materials as a vibration isolation layer. By analyzing the dynamic characteristics of the friction braking system with fractional differential terms, it aims to provide a new perspective for understanding and controlling the chaotic phenomena of a class of nonlinear friction systems. Firstly, we construct a model of a friction system and analyze its dynamic characteristics in detail. The self-excited vibration of the system under disturbance is studied. The relationship between amplitude and frequency is calculated by a nonlinear approximate analytical algorithm, and the accuracy of this relationship is verified by a numerical algorithm. Then, we compare the differences between non-fractional systems and fractional systems. It is found that with the increase in the fractional order term, the vibration amplitude of the system decreases significantly, which helps to reduce the nonlinear characteristics generated by the friction system and narrow the range of unstable solutions. Secondly, we also study the influence of parameter coefficients on the amplitude–frequency characteristics and analyze the local static bifurcation characteristics through singularity theory. Finally, we study the dynamic bifurcation behavior under different parameter perturbations and find that the change in system parameters will lead to the alternation of periodic motion and chaotic motion. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model of the GMA(Generalized Mass Action) system for a class of microbial continuous fermentation processes is proposed, and the mathematical properties of the GMA system are discussed. A two-stage method is proposed to determine the parameter values of the GMA system. First, the GMA system is rewritten. In the first stage, the logarithmic transformation and linear least square method are used to solve the parameter identification problem of the rewritten system. In the second stage, a system of linear equations is solved. The parameters in the original GMA system are then identified by the two-stage method. Compared with the error results of existing literature [5,6,10,20,22,25], smaller error values have been achieved. This shows that our proposed GMA system can better describe the microbial continuous fermentation process. To determine the optimal operating condition of the microbial continuous fermentation process, a steady-state optimization model is established by maximizing the volume yield of 1, 3-propanediol. Considering the power function structure of the steady-state optimization model, we further transform it into a problem with a linear objective and multiple linear constraints. The transformed problem can be easily solved by the presented interior point algorithm. The optimization results show that the maximum volume yield of 1, 3-propanediol has increased to 403.4028 mmol/$ (\mathrm{L} \cdot \mathrm{h}) $. This result can provide a theory guide for the practical production of 1, 3-propanediol. [ABSTRACT FROM AUTHOR]

A wide class of two‐component evolution systems is constructed admitting an infinite‐dimensional Lie algebra. Some examples of such systems that are relevant to reaction–diffusion systems with cross‐diffusion are highlighted. It is shown that a nonlinear evolution system related to the Ricci flow on warped product manifold, which has been extensively studied by several authors, follows from the above‐mentioned class as a very particular case. The Lie symmetry properties of this system and its natural generalization are identified and a wide range of exact solutions is constructed using the Lie symmetry obtained. Moreover, a special case is identified when the system in question is reducible to the fast diffusion equation in one space dimension. Finally, another class of two‐component evolution systems with an infinite‐dimensional Lie symmetry that possess essentially different structures is presented. [ABSTRACT FROM AUTHOR]

Wave propagation in the form of fronts or kinks, a common occurrence in a wide range of physical phenomena, is studied in the context of models defined by their Hamiltonian structure. Motivated, for dispersive wave evolution equations such as a strongly nonlinear model of two‐layer internal waves in the Boussinesq limit, by the symmetric properties of a class of front‐propagating solutions, known as conjugate states or solibores, a generalized formulation based purely on the dispersionless reduction of a system is introduced, and a class of undercompressive shock solutions, here referred to as "Hamiltonian shocks," is defined. This analysis determines whether a Hamiltonian shock, representing locally a kink for the parent dispersive equations, will interact with a sufficiently smooth background wave without inducing loss of regularity, which would take the form of a classical dispersive shock for the parent equations. This property is also related to an infinitude of conservation laws, drawing a parallel to the case of completely integrable systems. [ABSTRACT FROM AUTHOR]

In this manuscript, a general class of Jacobian-free iterative schemes for solving systems of nonlinear equations is presented. Once its fourth-order convergence is proven, the most efficient sub-family is selected in order to make a qualitative study. It is proven that the most of elements of this family are very stable, and this is checked by means on numerical tests on several problems of different sizes. Their performance is compared with other known Jacobian-free iterative procedure, being better in the most of results. [ABSTRACT FROM AUTHOR]

Full-waveform inversion (FWI) uses the full information of seismic data to obtain a quantitative estimation of subsurface physical parameters. Anisotropic FWI has the potential to recover high-resolution velocity and anisotropy parameter models, which are critical for imaging the long-offset and wideazimuth data. We develop an acoustic anisotropic FWI method based on a simplified pure quasi Pwave (qP-wave) equation, which can be solved efficiently and is beneficial for the subsequent inversion. Using the inverse Hessian operator to precondition the functional gradients helps to reduce the parameter tradeoff in the multi-parameter inversion. To balance the accuracy and efficiency, we extend the truncated Gauss-Newton (TGN) method into FWI of pure qP-waves in vertical transverse isotropic (VTI) media. The inversion is performed in a nested way: a linear inner loop and a nonlinear outer loop. We derive the formulation of Hessian-vector products for pure qP-waves in VTI media based on the Lagrange multiplier method and compute the model update by solving a Gauss-Newton linear system via a matrix-free conjugate gradient method. A suitable preconditioner and the Eisenstat and Walker stopping criterion for the inner iterations are used to accelerate the convergence and avoid prohibitive computational cost. We test the proposed FWI method on several synthetic data sets. Inversion results reveal that the pure acoustic VTI FWI exhibits greater accuracy than the conventional pseudoacoustic VTI FWI. Additionally, the TGN method proves effective in mitigating the parameter crosstalk and increasing the accuracy of anisotropy parameters. [ABSTRACT FROM AUTHOR]

To address the variable initial state and trail length this paper first presents a robust PD‐type open‐closed‐loop iterative learning control (ILC) law for a multiple‐input‐multiple‐output (MIMO) linear discrete‐time system. It is demonstrated that the convergence condition is dependent on the PD‐type feed‐forward learning gains, while an appropriate feedback learning gain can improve the ILC convergence performance. As a special case of PD‐type open‐closed‐loop ILC law, P‐type and D‐type open‐closed‐loop ILC laws are deduced. The three developed ILC laws ensure that as the number of iterations approaches infinity, the expectation of ILC tracking error will be constrained within a limited range, where the boundary is proportional to the initial state variation. Through a numerical simulation, the effectiveness of the proposed ILC laws is illustrated. [ABSTRACT FROM AUTHOR]

In this paper, we present a generalized adaptive Monte Carlo algorithm using the Diagonal and Off-Diagonal Splitting (DOS) iteration method to solve a system of linear algebraic equations (SLAE). The DOS method is a generalized iterative method with some known iterative methods such as Jacobi, Gauss-Seidel, and Successive Overrelaxation methods as its special cases. Monte Carlo algorithms usually use the Jacobi method to solve SLAE. In this paper, the DOS method is used instead of the Jacobi method which transforms the Monte Carlo algorithm into the generalized Monte Carlo algorithm. we establish theoretical results to justify the convergence of the algorithm. Finally, numerical experiments are discussed to illustrate the accuracy and efficiency of the theoretical results. Furthermore, the generalized algorithm is implemented to price options using the finite difference method. We compare the generalized algorithm with standard numerical and stochastic algorithms to show its efficiency. [ABSTRACT FROM AUTHOR]

Traditionally, 3D modeling of marine controlled-source electromagnetic (CSEM) data (in the frequency domain) involves high-memory demand, requiring solving a large linear system for each frequency. To address this problem, we propose to solve Maxwell's equations in a fictitious dielectric medium with time-domain finite-difference methods, with the support of the correspondence principle. As an advantage of this approach, we highlight the possibility of its implementation for execution with GPU accelerators, in addition to multi-frequency data modeling with a single simulation. Furthermore, we explore using the correspondence principle to the inversion of CSEM data by calculating the gradient of the least-squares objective function employing the adjoint-state method to establish the relationship between adjoint fields in a conductive medium and their counterparts in the fictitious dielectric medium, similar to the approach used in forward modeling. We validate this method through 2D inversions of three synthetic CSEM datasets, computed for a simple model consisting of two resistors in a conductive medium, a model adapted from a CSEM modeling and inversion package, and the last one based on a reference model of turbidite reservoirs on the Brazilian continental margin. We also evaluate the differences between the results of inversions using the steepest descent method and our proposed momentum method, comparing them with the limited-memory BFGS (Broyden–Fletcher–Goldfarb–Shanno) algorithm (L-BFGS-B). In all experiments, we use smoothing by model reparameterization as a strategy for regularizing and stabilizing the iterations throughout the inversions. The results indicate that, although it requires more iterations, our modified momentum method produces the best models, which are consistent with results from the L-BFGS-B algorithm and require less storage per iteration. [ABSTRACT FROM AUTHOR]

We study a type of correlated queue in which its inter-arrival and service times are correlated, with their joint distribution being characterized by a copula function. This characterization allows for very generally correlated inter-arrival and service times. For such a queue, we first derive an infinite system of linear equations for the moments of the waiting time, based on which we design an algorithm to calculate the moments of the waiting time. In contrast with traditional methods, our algorithm incorporates a recursive procedure which is computationally much more efficient. Furthermore, we show how the moments and covariances of the inter-departure times of the queue can be obtained based on the moments of the waiting time. Numerical experiments are provided to validate our method. [ABSTRACT FROM AUTHOR]

Nonlinear state-space models (SSMs) are widely used to model actual industrial processes. System identification is an important method to reduce the uncertainty of the simulation model. In recent years, system identification has been greatly improved with the rise of machine learning. However, there are a few reviews on the latest identification methods based on machine learning. Therefore, this paper focuses on the latest development of identification methods for nonlinear SSM in recent years. In particular, this paper comprehensively compares the identification methods based on traditional methods and machine learning. In addition, according to the type of uncertainty, we divided the paper into the parameter's identification and the identification of unknown parts of the model. Compared with the classification of other reviews, our classification method is clearer. Briefly, this paper organizes the review according to the classification of uncertainty. Each type is extended from offline identification to online identification. Specifically, interval identification and point estimation methods are reviewed for offline parameter identification. For online parameter identification, point estimation methods are reviewed. In the case that the model is partially unknown or black-box, the modeling methods and identification methods are mainly reviewed. In addition to the traditional methods, this paper focuses on the latest progress in the application of machine learning in system recognition. Finally, at the end of the paper, this paper summarizes the existing methods and points out the key problems that still need to be solved. [ABSTRACT FROM AUTHOR]

In this paper, we consider an estimation problem of sideslip angle and cornering stiffness of a vehicle from measurements of yaw rate, lateral acceleration and steering angle. Firstly, a vehicle dynamical model is expressed as a linear parameter‐varying system with cornering stiffness as uncertain parameters. Then, we show a method to estimate the parameters and the state based on moving horizon estimation. We provide a simple algorithm to solve the estimation problem. The effectiveness of the estimation method is evaluated through numerical simulations. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

This paper presents a trajectory-tracking controller of an inverted pendulum system on a self-balancing differential drive platform. First, the system modeling is described by considering approximations of the swing angles. Subsequently, a discrete convex representation of the system via the nonlinear sector technique is obtained, which considers the nonlinearities associated with the nonholonomic constraint. The design of a discrete parallel distributed compensation controller is achieved through an alternative method due to the presence of uncontrollable points that avoid finding a solution for the entire polytope. Finally, simulations and experimental results using a prototype illustrate the effectiveness of the proposal. [ABSTRACT FROM AUTHOR]

In this paper, we apply a two-grid scheme to the DG formulation of the 2D transient Navier–Stokes model. The two-grid algorithm consists of the following steps: Step 1 involves solving the nonlinear system on a coarse mesh with mesh size 퐻, and Step 2 involves linearizing the nonlinear system by using the coarse grid solution on a fine mesh of mesh size ℎ and solving the resulting system to produce an approximate solution with desired accuracy. We establish optimal error estimates of the two-grid DG approximations for the velocity and pressure in energy and L 2 -norms, respectively, for an appropriate choice of coarse and fine mesh parameters. We further discretize the two-grid DG model in time, using the backward Euler method, and derive the fully discrete error estimates. Finally, numerical results are presented to confirm the efficiency of the proposed scheme. [ABSTRACT FROM AUTHOR]

We introduce the notion of porous invariants for multipath affine loops over the integers. These are invariants definable in (fragments of) Presburger arithmetic and, as such, lack certain tame geometrical properties, such a convexity and connectedness. Nevertheless, we show that in many cases such invariants can be automatically synthesised, and moreover can be used to settle reachability questions for various non-trivial classes of affine loops and target sets. For the class of Z -linear invariants (those defined as conjunctions of linear equations with integer coefficients), we show that a strongest such invariant can be computed in polynomial time. For the more general class of N -semi-linear invariants (those defined as Boolean combinations of linear inequalities with integer coefficients), such a strongest invariant need not exist. Here we show that for point targets the existence of a separating invariant is undecidable in general. However we show that such separating invariants can be computed either by restricting the number of program variables or by restricting from multipath to single-path loops. Additionally, we consider porous targets, represented as Z -semi-linear sets (those defined as Boolean combinations of equations with integer coefficients). We show that an invariant can be computed providing the target spans the whole space. We present our tool porous, which computes porous invariants. [ABSTRACT FROM AUTHOR]

This article is focused on the design of an LMI‐based observer for the class of disturbance‐affected nonlinear systems. Two novel LMI conditions are derived by deploying a more general form of the matrix multiplier compared to the one used in the literature. The first method is based on the use of the ℋ∞$$ {\mathscr{H}}_{\infty } $$ criterion, while the second one utilizes an ISS notion. Both LMIs are developed by employing the reformulated Lipschitz property, a well‐known LPV approach and the new variant of Young inequality. The key element of the proposed LMI conditions is the incorporation of the novel matrix multipliers which allow us to include some additional decision variables as compared to the methods proposed in the literature. These additional variables add extra degrees of freedom, thus enhancing the LMI feasibility. Furthermore, the effectiveness of the proposed methodologies is showcased through a numerical example. [ABSTRACT FROM AUTHOR]

This article explores the problem of sampled‐data cooperative robust practical output regulation for nonlinear multi‐agent systems whose leader system is unknown. In this study, the nonlinearities of the follower systems are not constrained by the linear growth condition. Based on the robust control technology and the adaptive control technology, a distributed output‐based sampled‐data control protocol is developed to deal with the uncertainty of the exosystem which can belong to any large known compact set. We first perform the coordinate transformation of closed‐loop system to obtain the so‐called augmented system, and then perform the stability analysis for this system. As a result, it is proven that the steady‐state tracking errors are in any small given neighborhood of the origin. Finally, the performance of the proposed controller is validated by a numerical example. [ABSTRACT FROM AUTHOR]

Quantized signal control has been widely recognized as an effective means for conserving communication resources. However, ensuring stability of quantization‐driven nonlinear systems becomes particularly challenging in the presence of intermittent denial‐of‐service (DoS) attacks and sensor failures. This article explores the stable control problem of quantized nonlinear systems subject to DoS attacks. When an attack exists, all signals are unmeasurable. During the dormant phase of a DoS attack, only the quantized output signal is measurable, while there is a deviation between the received signal and the ideal signal due to sensor failure. To address these challenges, a switch‐type quantized observer is designed in this article to estimate unmeasurable state signals. In addition, we integrate the first‐order dynamic filter into the back‐stepping design process, which not only avoid the obstacles arisen from non‐differentiable output signals, but also simplifies the design process. Furthermore, this article adopts a more flexible sector quantizer and derives a set of adaptive laws to compensate for unknown quantization parameters. It is shown that, by utilizing the estimated signal, the proposed quantized adaptive control is able to effectively fight against DoS attacks and also is fault‐tolerant to sensor failures, guaranteeing semi‐globally uniformly ultimately bounded for all closed‐loop signals. Finally, simulation results validate the effectiveness of the proposed theory. [ABSTRACT FROM AUTHOR]

In this article, a new data‐based iterative learning control (ILC) algorithm is proposed via Gaussian process regression (GPR) to accomplish the trajectory tracking objective of aircraft subject to completely unknown dynamics and strong nonlinearities. The nonlinear system input–output relationship of the unknown aircraft is formulated through GPR by leveraging historical data, based on which an optimal ILC framework is established. The monotonic convergence analysis of the GPR‐based ILC is explored such that high‐precision tracking tasks can be accomplished without prior model knowledge. Simulation tests are further conducted on a commercial aircraft performing a continuous climb operation to illustrate the effectiveness of the GPR‐based ILC approach. [ABSTRACT FROM AUTHOR]

Based on additive state decomposition technique, this article presents an adaptive dynamic‐surface repetitive control method for a class of uncertain nonlinear systems with mismatched disturbances and input delay. First, the original uncertain nonlinear system is decomposed into a linear time invariant (LTI) primary system responsible for the periodic signal tracing and rejection task, and a nonlinear secondary system with input time delay responsible for the robust stabilization task. A modified repetitive controller with a small correction to the delay constant is then independently designed for the LTI primary system, while an adaptive dynamic surface controller is designed for the nonlinear secondary system. Stability analysis is performed for each subsystem and the design procedure of the whole system is presented in detail. Finally, comparative simulations with other repetitive control and dynamic surface control methods show that the presented method not only relaxes the constraints on the reference inputs and exogenous disturbances, but also ensures that the system has better disturbance rejection and periodic‐signal tracking performance in both transient and steady states. As a result, this method broadens the application of both repetitive control and dynamic surface control. [ABSTRACT FROM AUTHOR]

This article addresses the problem of model predictive control of networked jump systems in the presence of DoS attacks and time delays. In the structural framework of the network predictive control system, we mathematically model the networked jump system by using Markov chains to describe the time delays and a polytope model to describe the jump system phenomenon, considering the properties of DoS attacks and time delays. Based on this, we propose a strategy to lessen the effect of network constraints on the control performance of the system. This strategy involves the corresponding control inputs from the control sequence for real‐time active compensation. It includes adjusting the control sequence application length variation based on the duration of the DoS attacks and time delays at each moment. In addition, we demonstrate the recursive feasibility of the control strategy and the global asymptotic stability of the control system from a theoretical perspective through the Lyapunov stability theory. Finally, the effectiveness of the proposed strategy is verified by simulation arithmetic. [ABSTRACT FROM AUTHOR]

This article addresses the problem of designing an event‐triggered fault detector within a networked nonlinear system described by a Takagi–Sugeno (T–S) fuzzy model, accounting for time‐varying delays and denial‐of‐service (DoS) attacks characterized by a binary Markov chain. Our focus is on constructing an event‐triggered residual system, which aims to detect malfunctions in the original fuzzy system while optimizing communication resource allocation. Specifically, it is tailored to combat DoS attacks in the event generator‐to‐fault detector channel and mitigate network‐induced time‐varying delays. Utilizing the Lyapunov–Krasovskii function approach, we formulate linear matrix inequalities to establish the necessary conditions ensuring the asymptotic mean‐square stability of the residual system, meeting a predefined H∞$$ {H}_{\infty } $$ performance criterion. Finally, the simulation results are presented to validate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This article addresses the identification of unknown nonlinear continuous‐time systems through a linear time‐varying (LTV) approximation as a starting point. The mathematical form of the nonlinear system is unknown and is reconstructed by use of a well‐designed experiment, followed by LTV and linear parameter‐varying (LPV) estimations, and an integration step. The experiment used allows for a linearization of the unknown nonlinear system around a time‐varying operating point (system trajectory), resulting in an LTV approximation. After estimating the LTV model, an LPV model is identified, where the parameter‐varying (PV) coefficients represent partial derivatives of the unknown nonlinear system evaluated at the trajectory. We demonstrate a structural relation in the LPV model structure that ensures that the LPV coefficient vector is the gradient of the unknown nonlinear system. The nonlinear model of the system is then reconstructed through symbolic integration of the PV coefficients. This identification method enables the estimation of the unknown nonlinear system and its mathematical form using input–output measurements. The article concludes by illustrating the method on simulation examples. [ABSTRACT FROM AUTHOR]

In this article, the problem of adaptive finite‐time tracking control for a class of nonlinear systems subject to backlash‐like input hysteresis and multiple objective constraints is investigated. For the purpose of realizing multiple objective constraints, a new time‐varying barrier function (TVBF) is introduced to ensure that all objective constraint functions are always within the defined range. Meanwhile, based on the combination of the command filter approach and adaptive backstepping control, an error compensation system (ECS) is supplied to reduce the impact of filter error on control performance. Additionally, the problem of "singularity" caused by hysteresis is avoided by linearizing the backlash‐like hysteresis model, and Nussbaum‐type function is also applied to reduce the influence of hysteresis on the stability of the system. Then, by combining multi‐dimensional Taylor network (MTN) technology and command filter backstepping approach, an adaptive finite‐time control strategy is designed. The proposed control strategy ensures that all the signals in the closed‐loop system realize finite‐time semi‐globally uniformly ultimately bounded (SGUUB), and the output signal of the system can track the reference signal greatly while adhering to multiple objective constraints. Finally, the effectiveness of the proposed control strategy is verified by a practical simulation example. [ABSTRACT FROM AUTHOR]

This article studies decentralized adaptive asymptotic tracking control of time‐varying interconnected nonlinear systems. To address the obstacles caused by interactions and these unknown time‐varying parameters, a smooth function and a bound estimation approach are introduced. Additionally, by means of a class of funnel functions and barrier Lyapunov function approach, a prescribed performance control strategy is constructed, allowing tracking accuracy and the settling time to be predetermined in accordance with control requirements, without relying on initial conditions or design parameters. Particularly, reasoned proofs have been given to confirm that the presented control method not only guarantees the prescribed transient performance, but also achieves the asymptotic tracking without requiring knowledge of high‐order derivatives of the reference signal. Ultimately, the efficiency of our approach is verified by simulation results. [ABSTRACT FROM AUTHOR]

This article proposes a novel event‐triggered economic model predictive control (EMPC) scheme with shrinking prediction horizon of nonlinear systems subject to the constraints on the state and control. Some auxiliary positive‐definite functions at economic optimal equilibrium points are defined for economic performance functions. The optimal value function of the auxiliary function is used to design an adjustable stability constraint, which is imposed on the original EMPC optimization problem. The stability constraint is relaxed to design the triggered scheme avoiding Zeno behavior, while the prediction horizon is shrinked in different degrees by judging whether the last state within the triggered interval is in the terminal region. The involved parameter can be used to achieve a sensible compromise between system performance and computational complexity. The sufficient conditions guaranteeing the recursive feasibility and stability of the EMPC are derived. Finally, the effectiveness of the algorithm is illustrated by a continuously stirred tank reactor example. [ABSTRACT FROM AUTHOR]

In this paper, we proposed several disturbance observer‐based matrix‐weighted consensus algorithms. A new disturbance observer is firstly designed for linear systems with unknown matched or mismatched disturbances representable as the multiplication of a known time‐varying matrix with a unknown constant vector. Under some assumptions on the boundedness and persistent excitation of the regression matrix, the disturbances can be estimated at an exponential rate. Then, a suitable compensation input is provided to compensate the unknown disturbances. Second, disturbance‐observer based consensus algorithms are proposed for matrix‐weighted networks of single‐ and double‐integrators with matched or mismatched disturbances. We show that both matched and mismatched disturbances can be estimated and actively compensated, and the consensus system uniformly globally asymptotically converges to a fixed point in the kernel of the matrix‐weighted Laplacian. Depending on the network connectivity, the system can asymptotically achieve a consensus or a cluster configuration. The disturbance‐observer based consensus design is further extended for a network of higher‐order integrators subjected to disturbances. Finally, simulation results are provided to support the mathematical analysis. [ABSTRACT FROM AUTHOR]

The output consensus problem for heterogeneous linear multi‐agent systems (MASs) without strongly connected communication graphs is investigated via quantization communication. In this work, we propose an efficient distributed control law composed of distributed quantized observers and compensators to accomplish this task. Particularly, we first employ a dynamic encoding–decoding scheme to design the distributed quantized observer, which is able to accurately estimate the state of the leader for MASs. Then, an appropriate compensator is constructed to show that asymptotic output consensus can be achieved with 5‐level quantizer, even if neither global knowledge of communication graphs nor the information about initial states of all agents is required. Finally, a numerical example is used to validate the effectiveness of our distributed control law for MASs. [ABSTRACT FROM AUTHOR]

The focus of this article lies in the adaptive command filter tracking control problems for a class of switched time‐delay systems with an asymmetric dead‐zone and external disturbance under arbitrary switching. First, the external disturbance is estimated via an exact disturbance observer. Then, an echo state network (ESN) was adopted to approximate unknown function in system without tuning the weights between a reservoir and an input layer. Second, the time‐varying input of the dead‐zone model is considered as uncertain physical quantity of the system based on the dead‐zone slope boundary information. Third, an adaptive command filtered controller is employed to conquer the matter of "explosion of complexity" encountered in the traditional backstepping method. The filtering errors present in a dynamic surface control (DSC) approach are effectively eliminated by means of error compensation signals. A prescribed performance control (PPC) is resorted to confine the system output to meet prescribed steady‐state and transient tracking performances. The time delay terms are compensated by a Lyapunov–Krasovskii functional. The semi‐globally ultimately uniformly boundedness of all states in the closed‐loop system is ensured by the Liapunov's stability criterion. Finally, the validity of the developed control scheme is further verified through a simulation example. [ABSTRACT FROM AUTHOR]

Actuator constraints, particularly saturation limits, are an intrinsic and long‐standing problem in the implementation of most control systems. Model reference adaptive control (MRAC) is no exception and it may suffer considerably when actuator saturation is encountered. With this in mind, this paper proposes an anti‐windup strategy for model reference adaptive control schemes subject to actuator saturation. A prominent feature of the proposed compensator is that it has the same architecture as well‐known nonadaptive schemes, namely model recovery anti‐windup, which rely on the assumption that the system model is known accurately. Since, in the adaptive case, the model is largely unknown, the proposed approach uses an "estimate" of the system matrices for the anti‐windup formulation and modifies the adaptation laws that update the controller gains; if the (unknown) ideal control gains are reached, the model recovery anti‐windup formulation is recovered. The main results provide conditions under which, if the ideal control signal eventually lies within the control constraints, then the system states will converge to those of the reference model, that is, the tracking error will converge to zero asymptotically. The article deals with open‐loop stable linear systems and highlights the main challenges involved in the design of anti‐windup compensators for model‐reference adaptive control systems, demonstrating its success via a flight control application. [ABSTRACT FROM AUTHOR]

This paper investigates the state and actuator fault reconstruction problem in a class of switched linear systems subjected to unknown external disturbances according to average dwell time (ADT) technique. First, a robust switched sliding mode observer (SMO) is developed to simultaneously reconstruct the states of the switched system and the actuator faults. A novel and less conservative sufficient stability conditions are then established using the multiple quadratic Lyapunov function technique and the ADT approach. These conditions are formulated as linear matrix inequalities (LMI) to facilitate the design of the SMO. The observer gains matrices are obtained throughout the resolution of LMI using convex optimization techniques. Next, actuator faults are estimated by utilizing the concept of equivalent output injection, achieved through an analysis of the state error dynamics during the sliding motion. Finally, simulation results are considered to illustrate the applicability and efficiency of the developed method. It showcases the rapid and accurate convergence of the estimated system states and actuator fault to the real variables. [ABSTRACT FROM AUTHOR]

In this paper, the control problem of prescribed-time adaptive neural stabilization for a class of non-strict feedback stochastic high-order nonlinear systems with dynamic uncertainty and unknown time-varying powers is discussed. The parameter separation technique, dynamic surface control technique, and dynamic signals were used to eradicate the influences of unknown time-varying powers together with state and input unmodeled dynamics, and to mitigate the computational intricacy of the backstepping. In a non-strict feedback framework, the radial basis function neural networks (RBFNNs) and Young's inequality were deployed to reconstruct the continuous unknown nonlinear functions. Finally, by establishing a new criterion of stochastic prescribed-time stability and introducing a proper bounded control gain function, an adaptive neural prescribed-time state-feedback controller was designed, ensuring that all signals of the closed-loop system were semi-global practical prescribed-time stable in probability. A numerical example and a practical example successfully validated the productivity and superiority of the control scheme. [ABSTRACT FROM AUTHOR]

This work studies a coupled non-linear Schrödinger system with a singular source term. First, we investigate the question of the local existence of solutions. Second, one proves the existence of global solutions which scatter in some Sobolev spaces. Finally, one establishes the existence of non-global solutions. The main difficulty here is to overcome the regularity problem in the non-linearity. Indeed, because of the singularity of the source term, the classical contraction method in the energy space fails in such a regime. So, this paper is to fill such a gap in the literature. The argument follows ideas in T. Cazenave and I. Naumkin (Comm. Contemp. Math. , 19 (2017), 1650038). This consists to remark that the singularity problem is only near the origin. So, one needs to impose that the solution stays away from zero. This is not trivial, since there is no maximum principle for the Schrödinger equation. The existence of global solutions which scatter follows with the pseudo-conformal transformation via the existence of local solutions. Finally, the existence of non-global solutions follows with the classical variance method. [ABSTRACT FROM AUTHOR]