Showing papers on "Piecewise published in 2021"

$\mathcal {H}_{\infty }$ Synchronization for Fuzzy Markov Jump Chaotic Systems With Piecewise-Constant Transition Probabilities Subject to PDT Switching Rule

Abstract: This article investigates the nonfragile $\mathcal {H}_{\infty }$ synchronization issue for a class of discrete-time Takagi–Sugeno (T–S) fuzzy Markov jump systems. With regard to the T–S fuzzy model, a novel processing method based on the matrix transformation is introduced to deal with the double summation inequality containing fuzzy weighting functions, which may be beneficial to obtain conditions with less conservatism. In view of the fact that the uncertainties may occur randomly in the execution of the actuator, a nonfragile controller design scheme is presented by virtue of the Bernoulli distributed white sequence. The main novelty of this article lies in that the transition probabilities of the Markov chain are considered to be piecewise time-varying, and whose variation characteristics are described by the persistent dwell-time switching regularity. Then, based on the Lyapunov stability theory, it is concluded that the resulting synchronization error system is mean-square exponentially stable with a prescribed $\mathcal {H}_{\infty }$ performance in the presence of actuator gain variations. Finally, an illustrative example about Lorenz chaotic systems is provided to show the effectiveness of the established results.

Finite-Time Event-Triggered Control for Semi-Markovian Switching Cyber-Physical Systems With FDI Attacks and Applications

Abstract: This paper addresses the finite-time event-triggered control problem for nonlinear semi-Markovian switching cyber-physical systems (S-MSCPSs) under false data injection (FDI) attacks. Compared with the traditional time-triggered mechanism, the proposed event-triggered scheme (ETS) can effectively avoid network resource waste. Considering the network-induced delay in the modeling, a closed-loop system model with time delay is established in the unified framework. By the use of a mode-dependent piecewise Lyapunov-Krasovskii functional (LKF), stochastic finite-time stability (SFTS) criteria are established for the resultant closed-loop system. Then, some solvability conditions are established for the desired finite-time controller in light of a linear matrix inequality framework. Finally, an application example of vertical take-off and landing helicopter model (VTOLHM) is provided to demonstrate the effectiveness of the theoretical findings.

New concept in calculus: Piecewise differential and integral operators

Abstract: In the last decades, many methodologies have been suggested to depict behaviors of some complex world’s problems arising in many academic fields. One of these problems is the multi-steps behavior displayed by some problems. A concept of piecewise derivative is introduced in this paper with the aim to model real world problems following multiples processes. We have presented some important properties of these definitions. We considered different scenarios and presented numerical schemes that could be used to solve such problems. Illustrative examples, including chaotic and epidemiological models are presented to see the effectiveness of the suggested concept.

Deep Learning for Channel Estimation: Interpretation, Performance, and Comparison

Abstract: Deep learning (DL) has emerged as an effective tool for channel estimation in wireless communication systems, especially under some imperfect environments. However, even with such unprecedented success, DL methods are often regarded as black boxes and are lack of explanations on their internal mechanisms, which severely limits their further improvement and extension. In this paper, we present preliminary theoretical analysis on DL based channel estimation for single-input multiple-output (SIMO) systems to understand and interpret its internal mechanisms. As deep neural network (DNN) with rectified linear unit (ReLU) activation function is mathematically equivalent to a piecewise linear function, the corresponding DL estimator can achieve universal approximation to a large family of functions by making efficient use of piecewise linearity. We demonstrate that DL based channel estimation does not restrict to any specific signal model and asymptotically approaches to the minimum mean-squared error (MMSE) estimation in various scenarios without requiring any prior knowledge of channel statistics. Therefore, DL based channel estimation outperforms or is at least comparable with traditional channel estimation, depending on the types of channels. Simulation results confirm the accuracy of the proposed interpretation and demonstrate the effectiveness of DL based channel estimation under both linear and nonlinear signal models.

Nonfragile Consensus of Multiagent Systems Based on Memory Sampled-Data Control

Abstract: In this paper, we address the consensus tracking problem for the multiagent system (MAS) based on a nonfragile memory sampled-data controller. Considering the effect of controller gain fluctuation and communication delay, a novel sampled-data control scheme with variable sampling interval is designed for each agent. By developing some new terms, an improved piecewise Lyapunov–Krasovskii functional (LKF) is constructed to take full advantage of characteristic about real sampling pattern. Furthermore, some relaxed matrices constructed in the LKF are not necessarily positive definite. Making full use of the LKF and free-matrix-based integral inequality, some sufficient criteria are developed to ensure the consistency of the MAS. Then, by solving a group of linear matrix inequalities with the maximal sampling interval, the desired sampled-data control gain matrix is obtained. Finally, the numerical example of a 5-agent system is given to illustrate the effectiveness of the proposed approach in this paper.

Neural-Network-Based Adaptive Singularity-Free Fixed-Time Attitude Tracking Control for Spacecrafts

Abstract: In this article, a neural-network-based adaptive fixed-time control scheme is proposed for the attitude tracking of uncertain rigid spacecrafts. A novel singularity-free fixed-time switching function is presented with the directly nonsingular property, and by introducing an auxiliary function to complete the switching function in the controller design process, the potential singularity problem caused by the inverse of the error-related matrix could be avoided. Then, an adaptive neural controller is developed to guarantee that the attitude tracking error and angular velocity error can both converge into the neighborhood of the equilibrium within a fixed time. With the proposed control scheme, no piecewise continuous functions are required any more in the controller design to avoid the singularity, and the fixed-time stability of the entire closed-loop system in the reaching phase and sliding phase is analyzed with a rigorous theoretical proof. Comparative simulations are given to show the effectiveness and superiority of the proposed scheme.

Asynchronous Event-Triggered Control for Networked Interval Type-2 Fuzzy Systems Against DoS Attacks

Abstract: This article investigates the asynchronous adaptive event-triggered control problem for networked interval type-2 (IT2) fuzzy systems subject to nonperiodic denial-of-service (DoS) attacks. Unlike some existing results, two resilient adaptive event-triggered mechanisms (AETMs) are applied independently to both sensor and controller output while resisting nonperiodic DoS attacks. In particular, the asynchronous resilient AETM thresholds are adaptively varied based on error information between current sampling and latest available packets. Then, a new switched IT2 fuzzy dynamical output feedback system is modeled by discussing the influence of the AETM and nonperiodic DoS attacks simultaneously. Furthermore, mismatched membership functions are considered between dynamic output feedback controller and IT2 fuzzy model, and a slack matrix is introduced to relax stability conditions. Besides, by utilizing the piecewise Lyapunov–Krasovskii function method, sufficient conditions are derived to guarantee that the newly constructed switching system is globally exponentially stable with $H_{\infty }$ performance. Finally, the effectiveness of the developed control approach is illustrated by two examples.

Event-Triggered $H_\infty$ Filtering for Networked Switched Systems With Packet Disorders

Abstract: This paper deals with event-triggered $H_\infty $ filtering problem for switched continuous-time systems with quantization. A multiple periodic sampling-based event-triggering strategy is adopted to select those “necessary” sampled signals to be transmitted. As a result, the amount of communication and the frequency of signal updates can be reduced significantly. Regarding the nonideal communication network, we consider network-induced delays and packet disorders, which are common during packet transmission through networks. In order to cope with packet disorders, an active packet loss approach is introduced. As such, a new time-delay system model is established, by which the filtering error system is modeled as a switched system with an interval time-varying delay. Then, by employing piecewise Lyapunov functional method and average dwell time technique, some criteria are derived to ensure that the filtering error system can achieve a prescribed level of $H_\infty $ performance. Moreover, the relationship between switching instants and the data updating instants in filter is discussed in detail, and the filter gains and event-triggering parameters can be jointly designed in terms of solutions to some linear matrix inequalities. Finally, numerical simulation is provided to verify the effectiveness of the proposed method.

Dissipativity Analysis for T–S Fuzzy System Under Memory Sampled-Data Control

Abstract: The dissipative stability problem for a class of Takagi–Sugeno (T–S) fuzzy systems with variable sampling control is the focus of this paper. The controller signals are assumed to transmit with a constant delay. Our aim is to design the sampled-data controller such that the T–S fuzzy system is globally asymptotically stable with a $(\mathcal {Q},\mathcal {S},\mathcal {R})$ - $\gamma $ -dissipative performance index. The stability is analyzed by using a novel piecewise Lyapunov–Krasovskii functional (LKF) together with a looped-functional and free-matrix-based (FMB) inequality method. First, several useful linear matrix inequality (LMI) conditions are derived to verify the dissipative stability of the T–S fuzzy system and then the controller gains matrices are expressed by resorting the LMI approach with the maximal-allowable upper bound (MAUB) of sampling periods. The proposed LMI conditions can be easily solved by using the MATLAB tool box. Finally, the numerical example of a truck–trailer system is considered and analyzed by the proposed scheme to illustrate the benefit and superiority.

Fuzzy-Affine-Model-Based Output Feedback Dynamic Sliding Mode Controller Design of Nonlinear Systems

Abstract: This paper investigates the problem of output feedback sliding mode control (SMC) for a class of uncertain nonlinear systems through Takagi–Sugeno fuzzy affine models. By adopting a state-input augmentation method, a descriptor system is first constructed to characterize the dynamical properties of the sliding motion. Based on a common quadratic Lyapunov function and piecewise quadratic Lyapunov functions, sufficient conditions for asymptotic stability analysis of the sliding motion are obtained with some convexification techniques. An output feedback dynamic SMC design scheme is proposed to force the states of the resulting closed-loop system onto the sliding surface locally in finite time. Two simulation examples are finally shown to illustrate the effectiveness of the proposed approaches.

The piecewise reproducing kernel method for the time variable fractional order advection-reaction-diffusion equations

Abstract: This paper structures some new reproductive kernel spaces based on Legendre polynomials to solve time variable order fractional advection-reaction-diffusion equations. Some examples are given to show the effectiveness and reliability of the method.

Resilient Static Output Feedback Control of Linear Semi-Markov Jump Systems With Incomplete Semi-Markov Kernel

Abstract: This article is concerned with the problem of the static output-feedback control for a class of discrete-time linear semi-Markov jump systems (SMJSs). Through a mode-dependent resilient control scheme and an invertible linear transformation, a resulting equivalent closed-loop system can be obtained. The embedded Markov chain (EMC) is piecewise homogeneous, which leads to incomplete semi-Markov kernel is variable in the finite interval. A novel class of multivariate dependent Lyapunov function is constructed, which is mode-dependent, elapsed-time-dependent, and variation-dependent. Numerically testable stabilization criteria are established for discrete-time linear SMJSs via abovementioned Lyapunov function. Under bound sojourn time, a desired stabilizing controller is designed such that the closed-loop system is mean-square stable. Finally, the theoretical results are applied to a practical RLC circuit system to show the effectiveness and applicability of the proposed control strategy.

A level set method based on additive bias correction for image segmentation

Abstract: Intensity inhomogeneity brings great difficulties to image segmentation. This problem is partly solved by the multiplicative bias field correction model. However, some other problems still exist, such as slow segmentation speed and narrow application field. In this paper, an additive bias correction (ABC) model based on intensity inhomogeneity is proposed. The model divides the observed image into three parts: additive bias function, reflection edge structure function and Gaussian noise. Firstly, the local area and local clustering criterion of intensity inhomogeneity are defined. Secondly, by introducing the level set function, the local clustering criterion is transformed into an energy function based on the level set model. Finally, the structure of the estimated bias field and the reflection edge is computed through the process of minimizing the energy function while the image is segmented. In order to improve the stability of the system, a de-parameterized regularization function and an adaptive data-driven term function are designed. Compared with the traditional multiplicative model, the addition model has faster calculation speed. The proposed model can obtain ideal segmentation effect for images with intensity inhomogeneity. Experiment results show that the proposed method is more robust, faster and more accurate than traditional piecewise and multiplicative models.

Threshold-Function-Dependent Quasi-Synchronization of Delayed Memristive Neural Networks via Hybrid Event-Triggered Control

Abstract: This article addresses the quasi-synchronization problem of delayed memristive neural networks (MNNs) via hybrid event-triggered control. First, a hybrid event-triggering mechanism with a novel threshold function is devised. Therein, an exponential decay term and a non-negative constant term are additionally introduced. It can further extend the time span between two successively triggered events and therefore can reduce the amount of triggering times in comparison with some existing event-triggering mechanisms. Then, by constructing a time-dependent and piecewise Lyapunov functional, a less conservative criterion for quasi-synchronization of drive-response delayed MNNs is formulated in terms of linear matrix inequalities. In addition, an explicit expression of the error bound is provided and the design of the feedback gain is presented for a predetermined error bound. Finally, a numerical example is given to demonstrate the effectiveness of the theoretical analysis and the advantages of the proposed event-triggering scheme.

Exponentially Stable Periodic Oscillation and Mittag-Leffler Stabilization for Fractional-Order Impulsive Control Neural Networks With Piecewise Caputo Derivatives.

Abstract: It is well known that the conventional fractional-order neural networks (FONNs) cannot generate nonconstant periodic oscillation. For this point, this article discusses a class of impulsive FONNs with piecewise Caputo derivatives (IPFONNs). By using the differential inclusion theory, the existence of the Filippov solutions for a discontinuous IPFONNs is investigated. Furthermore, some decision theorems are established for the existence and uniqueness of the (periodic) solution, global exponential stability, and impulsive control global stabilization to IPFONNs. This article achieves four key issues that were not solved in the previously existing literature: 1) the existence of at least one Filippov solution in a discontinuous IPFONN; 2) the existence and uniqueness of periodic oscillation in a nonautonomous IPFONN; 3) global exponential stability of IPFONNs; and 4) impulsive control global Mittag-Leffler stabilization for FONNs.

Abrupt transitions in variational quantum circuit training

Abstract: Variational quantum algorithms dominate gate-based applications of modern quantum processors. The so-called layerwise trainability conjecture appears in various works throughout the variational quantum computing literature. The conjecture asserts that a quantum circuit can be trained piecewise, e.g., that a few layers can be trained in sequence to minimize an objective function. Here, we prove this conjecture false. Counterexamples are found by considering objective functions that are exponentially close (in the number of qubits) to the identity matrix. In the finite setting, we found abrupt transitions in the ability of quantum circuits to be trained to minimize these objective functions. Specifically, we found that below a critical (target-gate-dependent) threshold, circuit training terminates close to the identity and remains near to the identity for subsequently added blocks trained piecewise. A critical layer depth will abruptly train arbitrarily close to the target, thereby minimizing the objective function. These findings shed light on the divide-and-conquer trainability of variational quantum circuits and apply to a wide collection of contemporary literature.

Asynchronous Sampled-Data Filtering Design for Fuzzy-Affine-Model-Based Stochastic Nonlinear Systems

Abstract: This article studies the asynchronous sampled-data filtering design problem for Ito stochastic nonlinear systems via Takagi–Sugeno fuzzy-affine models. The sample-and-hold behavior of the measurement output is described by an input delay method. Based on a novel piecewise quadratic Lyapunov–Krasovskii functional, some new results on the asynchronous sampled-data filtering design are proposed through a linearization procedure by using some convexification techniques. Simulation studies are given to illustrate the effectiveness of the proposed method.

Locally Aware Piecewise Transformation Fields for 3D Human Mesh Registration

Abstract: Registering point clouds of dressed humans to parametric human models is a challenging task in computer vision. Traditional approaches often rely on heavily engineered pipelines that require accurate manual initialization of human poses and tedious post-processing. More recently, learning-based methods are proposed in hope to automate this process. We observe that pose initialization is key to accurate registration but existing methods often fail to provide accurate pose initialization. One major obstacle is that, despite recent effort on rotation representation learning in neural networks, regressing joint rotations from point clouds or images of humans is still very challenging. To this end, we propose novel piecewise trans-formation fields (PTF), a set of functions that learn 3D translation vectors to map any query point in posed space to its correspond position in rest-pose space. We com-bine PTF with multi-class occupancy networks, obtaining a novel learning-based framework that learns to simultaneously predict shape and per-point correspondences between the posed space and the canonical space for clothed human. Our key insight is that the translation vector for each query point can be effectively estimated using the point-aligned local features; consequently, rigid per bone trans-formations and joint rotations can be obtained efficiently via a least-square fitting given the estimated point correspondences, circumventing the challenging task of directly regressing joint rotations from neural networks. Further-more, the proposed PTF facilitate canonicalized occupancy estimation, which greatly improves generalization capability and results in more accurate surface reconstruction with only half of the parameters compared with the state-of-the-art. Both qualitative and quantitative studies show that fit-ting parametric models with poses initialized by our net-work results in much better registration quality, especially for extreme poses.

Event-based secure control of T-S fuzzy based 5-DOF active semi-vehicle suspension systems subject to DoS attacks

Abstract: This paper investigates the problem of resilient secure control of cloud-aided 5-DOF active semi-vehicle suspension systems (SVSSs). A novel joint model considering both the event-triggered mechanism (ETM) and DoS attacks is established. Under such a model, during the active period of DoS attacks, periodic transmission attempt is made to ensure the control system can receive the control information at the earliest time; the ETM turns to be a conventional one when the DoS attack is in sleeping period. Meanwhile, the valid attack period is proposed to address the problem of the DoS attack ending within a sampling period, which is a challenging problem in modeling DoS attacks. Takagi-Sugeno (T--S) fuzzy model is used to characterize the uncertainties of sprung and unsprung mass of SVSSs. By converting the cloud-aided active SVSS into a fuzzy-based switched time-delay system, and using the method of piecewise Lyapunov function, sufficient conditions are derived to ensure the performances of active SVSSs subject to DoS attacks. Finally, the effectiveness of the proposed method is validated by a numerical example of active SVSSs subject to DoS attacks.

Hypocoercivity of piecewise deterministic Markov process-Monte Carlo

Abstract: In this paper we derive spectral gap estimates for several Piecewise Deterministic Markov Processes, namely the Randomized Hamiltonian Monte Carlo, the Zig-Zag process and the Bouncy Particle Sampler. The hypocoercivity technique we use, presented in (Dolbeault et al., 2015), produces estimates with explicit dependence on the parameters of the dynamics. Moreover the general framework we consider allows to compare quantitatively the bounds found for the different methods.

Adaptive nonsingular predefined-time control for attitude stabilization of rigid spacecrafts

Abstract: This article proposes a novel adaptive nonsingular predefined-time control strategy for rigid spacecrafts with inertia uncertainties. Following the backstepping recursive design procedures, an adaptive attitude controller is systematically presented to ensure that the spacecraft attitude can converge into a small region around the origin within a predefined time, which can be explicitly determined in advance by assigning a simple parameter. Moreover, by designing quadratic functions in the controllers, the singularity can be avoided directly without using any filters or piecewise continuous functions, such that the stability analysis becomes more concise and straightforward. Simulations are conducted to show the effectiveness of the presented method.

Fuzzy-Affine-Model-Based Sampled-Data Filtering Design for Stochastic Nonlinear Systems

Abstract: This article addresses the sampled-data piecewise affine (PWA) filter design problem for Ito stochastic nonlinear systems represented by Takagi–Sugeno fuzzy affine models. An input delay method is used to describe the sample-and-hold behavior of the measurement output. Based on a novel piecewise quadratic Lyapunov–Krasovskii functional, some new results on the robust sampled-data PWA filtering design are proposed through a linearization procedure by using some convexification techniques. Simulation studies on a tunnel diode circuit system, and an inverted pendulum system are given to illustrate the effectiveness of the proposed method.

Synchronization Control for Discrete-Time-Delayed Dynamical Networks With Switching Topology Under Actuator Saturations

Abstract: This article is concerned with the synchronization control problem for a class of discrete-time dynamical networks with mixed delays and switching topology. The saturation phenomenon of physical actuators is specifically considered in designing feedback controllers. By exploring the mixed-delay-dependent sector conditions in combination with the piecewise Lyapunov-like functional and the average-dwell-time switching, a sufficient condition is first established under which all trajectories of the error dynamics are bounded for admissible initial conditions and nonzero external disturbances, while the $l_{2}$ – $l_\infty $ performance constraint is satisfied. Furthermore, the exponential stability of the error dynamics is ensured for admissible initial conditions in the absence of disturbances. Second, by using some congruence transformations, the explicit condition guaranteeing the existence of desired controller gains is obtained in terms of the feasibility of a set of linear matrix inequalities. Then, three convex optimization problems are formulated regarding the disturbance tolerance, the $l_{2}$ – $l_\infty $ performance, and the initial condition set, respectively. Finally, two simulation examples are given to show the effectiveness and merits of the proposed results.

Modeling third waves of Covid-19 spread with piecewise differential and integral operators: Turkey, Spain and Czechia

Abstract: Several collected data representing the spread of some infectious diseases have demonstrated that the spread does not really exhibit homogeneous spread. Clear examples can include the spread of Spanish flu and Covid-19. Collected data depicting numbers of daily new infections in the case of Covid-19 from countries like Turkey, Spain show three waves with different spread patterns, a clear indication of crossover behaviors. While modelers have suggested many mathematical models to depicting these behaviors, it becomes clear that their mathematical models cannot really capture the crossover behaviors, especially passage from deterministic resetting to stochastics. Very recently Atangana and Seda have suggested a concept of piecewise modeling consisting in defining a differential operator piece-wisely. The idea was first applied in chaos and outstanding patterns were captured. In this paper, we extend this concept to the field of epidemiology with the aim to depict waves with different patterns. Due to the novelty of this concept, a different approach to insure the existence and uniqueness of system solutions are presented. A piecewise numerical approach is presented to derive numerical solutions of such models. An illustrative example is presented and compared with collected data from 3 different countries including Turkey, Spain and Czechia. The obtained results let no doubt for us to conclude that this concept is a new window that will help mankind to better understand nature.