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This paper considers prescribed-time observer (PTO) designs for a class of linear parameter-varying (LPV) systems. Firstly, a full-order prescribed-time observer with time-varying gains is developed. The existence conditions are given in terms of linear matrix inequalities (LMIs). In addition, the reduced-order PTO is also considered in this paper. Moreover, it is shown that the existence conditions under which the full-order PTO exists can also guarantee the existence of a corresponding reduced-order PTO. The advantages of the full-order and the reduced-order PTOs over the existing asymptotic convergence observers are that (1) they can achieve exact estimations in almost any prescribed convergence time regardless of what the system initial values are. (2) the proposed time-varying gain PTOs can avoid the conservatism of the unknown input decoupling conditions brought about by the traditional polytopic LPV observer design methods. Finally, two examples are given to illustrate the effectiveness of the proposed methods.

The coefficient matrices of the linear equation systems arising from the radiation diffusion problems usually have orders of magnitude difference between their off-diagonal entries. While solving these linear equations with a preconditioned iterative method, the entries with small magnitudes may be insignificant to the preconditioner efficiency. In this paper, we use a filter to remove such small entries in the coefficient matrix while constructing the preconditioner. The proposed filter eliminates the small entries first according to a so-called weak dependence matrix, which relies on the conception of the strength of connections in algebraic multigrid. The preconditioner is then built based on the filtered matrix instead of the original one. Four strategies of filtering out entries are designed and investigated. Numerical results for various model-type problems and two real application problems, i.e., the multi-group radiation diffusion equations and the three temperature energy equations, are provided to show the effectiveness of the proposed method. In particular, this paper provides a practical approach to choose a proper parameter in the proposed method, which should help solve linear equation systems of radiation diffusion problems.

Uncertain delay differential equations (UDDEs) involving a current state and a certain past state have been proposed to model an uncertain system with a delay time, such as uncertain delay logistic model. Stability of the UDDEs is a vital problem for its applications. Based on the strong Lipschitz condition, the stability in mean for UDDEs have been investigated. Actually, the strong Lipschitz condition is assumed that it only relates to the current state, it is difficult to be employed to determine the stability in mean for the UDDEs. In this paper, we propose two kinds of new Lipschitz conditions containing the current state and the past state, which are more weaker than the strong Lipschitz condition. Meanwhile, two sufficient theorems based on these new Lipschitz conditions as the tools to judge the stability in mean for the UDDEs are verified. For a special class of the UDDEs, which are proved to be stable in mean without any limited condition. Besides, some examples are discussed in this paper.

In this paper, we study one class of generalized convolution-type singular integral equations in class {0}. Such equations are turned into complete singular integral equations with nodal points and further turned into boundary value problems for analytic function with discontinuous coefficients by Fourier transforms. For such equations, we will propose one method different from classical one and obtain the general solutions and their conditions of solvability in class {0}. Thus, this paper generalizes the theory of classical equations of convolution type.

In this paper, we introduce the bivariate generalization of the Chlodowsky-type q-BernsteinStancuKantorovich operators on an unbounded domain and studied the rate of convergence in terms of the Lipschitz class function and complete modulus of continuity. Further, we establish the weighted approximation properties for these operators. The aim of this paper is to obtain the degree of approximation for these bivariate operators in terms of the partial moduli of continuity and the Peetres K- functional. Then, we give generalization of the operators and investigate their approximations. Furthermore, we show the convergence of the bivariate Chlodowsky-type operators to certain functions by illustrative graphics using Python programming language. Finally, we construct the GBS operators of bivariate Chlodowsky-type q-BernsteinStancuKantorovich and estimate the rate of convergence for these operators with the help of mixed modulus of smoothness.

Survey of fixed point iteration processes.Extension of the pseudo-Newton method idea to other root finding methods.Modifications of the MMP-methods and their convergence visualizations.Non-trivial and intriguing polynomiographs have been obtained. In this paper, an iteration process, referred to in short as MMP, will be considered. This iteration is related to finding the maximum modulus of a complex polynomial over a unit disc on the complex plane creating intriguing images. Kalantari calls these images polynomiographs independently from whether they are generated by the root finding or maximum modulus finding process applied to any polynomial. We show that the images can be easily modified using different MMP methods (pseudo-Newton, MMP-Householder, methods from the MMP-Basic, MMP-Parametric Basic or MMP-EulerSchrder Families of Iterations) with various kinds of non-standard iterations. Such images are interesting from three points of views: scientific, educational and artistic. We present the results of experiments showing automatically generated non-trivial images obtained for different modifications of root finding MMP-methods. The colouring by iteration reveals the dynamic behaviour of the used root finding process and its speed of convergence. The results of the present paper extend Kalantaris recent results in finding the maximum modulus of a complex polynomial based on Newtons process with the Picard iteration to other MMP-processes with various non-standard iterations.

The method of fundamental solutions (MFS) was first proposed by Kupradze in 1963. Since then, the MFS has been extensively applied for solving various kinds of problems in science and engineering. However, few theoretical works have been reported in the literature. In this paper, we devote our work to the error analysis and stability of the MFS for the case of the modified Helmholtz equation. For disk domains, a convergence analysis of the MFS was provided by Li (J. Comput. Appl. Math., 159:113125, 2004) for solving the modified Helmholtz equation. In this paper, the error bounds of the MFS for bounded and simply connected domains are derived for smooth solutions of the modified Helmholtz equation. The exponential convergence rates can be achieved for analytic solutions. The bounds of condition numbers of the MFS are derived for both disk domains and the bounded and simply connected domains, to give the exponential growth via the number of fundamental solutions used. Numerical experiments are carried out to support the theoretical analysis. Moreover, the analysis of this paper is applied to parabolic equations, and some reviews of proof techniques and the analytical characteristics of the MFS are addressed.

In this paper, we consider the eigenvalue bounds for real symmetric matrices whose entries are in a given interval. Based on some matrix computation theories, a new algorithm and some theorems are presented which provide ways for solving the left problems in former papers and obtain satisfying results. Furthermore, the ideas are spread to general symmetric interval matrices. Finally, numerical examples are presented which show the validity of the proposed methods.

This paper research downhole temperature distribution in oil production and water injection using reproducing kernel Hilbert space method (RKHSM) for the first time. The aim of this paper is that using the highly accurate RKHSM can solve downhole temperature problems effectively. According to 2-D mathematical models of downhole temperature distribution, the analytical solution was given in a series expansion form and the approximate solution was expressed by n-term summation of reproducing kernel functions which initial and boundary conditions were selected properly. Numerical results of downhole temperature distribution with multiple pay zones, in which different radial distance and different injection–production conditions (such as injection rate, injection temperature, injection time, oil layer thickness), were carried out by mathematical 7.0, and numerical results correspond to general knowledge and show that use RKHSM to research downhole temperature distribution is feasible and effective.

This paper proposes a H state-feedback control for singular Markovian jump systems with incomplete knowledge of transition probabilities. Different from the previous results where the transition rates are completely known or the bounds of the unknown transition rates are given, a more general situation where the transition rates are partly unknown and the bounds of the unknown transition rates are also unknown is considered. Moreover, in contrast to the singular Markovian jump systems studied recently, the proposed method does not require any tuning parameters that arise when handling non-convex terms related to the mode-dependent Lyapunov matrices and the corresponding self-mode transition rates. Also, this paper uses all possible slack variables related to the transition rates into the relaxation process which contributes to reduce the conservatism. Finally, two numerical examples are provided to demonstrate the performance of H mode-dependent control.

Convergence rate result for a modified steepest descent method and a modified minimal error method for the solution of nonlinear ill-posed operator equation have been proved with noisy data. To our knowledge, convergence rate result for the steepest descent method and minimal error method with noisy data are not known. We provide a convergence rate results for these methods with noisy data. The result in this paper are obtained under less computational cost when compared to the steepest descent method and minimal error method. We present an academic example which satisfies the assumptions of this paper.

In this paper, the Jacobi and Gauss-Seidel-type iteration methods are proposed for solving the matrix equation A X B = C , which are based on the splitting schemes of the matrices A and B. The convergence and computational cost of these iteration methods are discussed. Furthermore, we give the preconditioned Jacobi and Gauss-Seidel-type iteration methods. Numerical examples are given to demonstrate the efficiency of these methods proposed in this paper.

The network model in this paper involves time delay and partly unknown transition rates, which is more practical than the models in 18,34,35,38.Different from the most existing results with partly unknown transition rates 24-26, the synchronization trajectory in this paper is dynamic, which will be adjusted according to the states of nodes.A randomly occurring event-triggered control strategy is proposed to study the synchronization issue of Markovian jump delayed complex networks with partly unknown transition rates.The positive lower bound of the event intervals is obtained which can exclude undesired accumulation of event instants (Zeno behaviors). In this paper, exponential synchronization problems are investigated for an array of Markovian jump delayed complex networks with partially unknown transition rates and discontinuous diffusions. To impel the array complex networks to achieve exponential synchronization, a new randomly occurring event-triggered control strategy is proposed. The idea of event-triggered control strategy is that the coupling term and controller update data only at the event-triggered instants, which can reduce the communication load and energy consumption. By constructing a novel stochastic Lyapunov-Krasovskii function, some exponential synchronization criteria are obtained in terms of LMIs and famous Halanay inequality. Furthermore, we obtain a positive lower bound of the event intervals which can exclude the Zeno behaviors. Finally, a simulation example is given to illustrate the effectiveness of the theoretical results.

We investigate an impulsive predator prey model with communicable disease.Susceptible pests will perish if impulsive period is smaller than a critical value.The smaller impulsive period is, the faster the susceptible pests go to extinction.Numerical simulations validate the obtained theoretical results. In this paper, we propose an impulsive predator-prey model with communicable disease in the prey species only and investigate its interesting biological dynamics. By the Floquet theory of impulsive differential equation and small amplitude perturbation skills, we have deduced the sufficient conditions for the globally asymptotical stability of the semi-trivial periodic solution and the permanence of the proposed model. We also give the existences of the "infection-free" periodic solution and the "predator-free" solution. Finally, numerical results validate the effectiveness of theoretical analysis for the proposed model in this paper.

In this paper the Hamiltonian approximate analytical approach is extended for solving vibrations of conservative oscillators with the sum of integer and/or non-integer order strong nonlinearities. Solution of the nonlinear differential equation is assumed in the form of a trigonometric function with unknown frequency. The frequency equation is obtained based on the hypothesis that the derivative of the Hamiltonian in amplitude of vibration is zero. The accuracy of the approximate solution is treated with two different approaches: comparing the analytical value for period of vibration with the period obtained numerically and developing an error estimation method based on the ratio between the averaged residual function and the total constant energy of system. The procedures given in the paper are applied for two types of examples: an oscillator with a strong nonlinear term and an oscillator where the nonlinearity is of polynomial type.

The paper is concerned with the hedging of credit derivatives, in particular synthetic collateralized debt obligations (CDOs) tranches and first to default swap (FTD) with respect to actually traded credit default swaps index (CDS index). In the model, we will relax the name homogeneity assumption, that all the names share the same risk-neutral default. We think of two homogeneous groups of names and the default intensities of each group depending both upon the number of survived names in each subgroup. This results a two dimensional Markov chain setting, since the portfolio state is characterized by the number of survived names in each group. Finally, we have achieved the numerical implementation through trinomial trees, by means of Markov chain techniques. The experimental results show that the new extended hedge model in this paper improves the hedge strategies under the name homogeneity case.

The joint distribution of a geometric Brownian motion and its time-integral was derived in a seminal paper by Yor (1992) using Lamperti’s transformation, leading to explicit solutions in terms of modified Bessel functions. In this paper, we revisit this classic result using the simple Laplace transform approach in connection to the Heun differential equation. We extend the methodology to the geometric Brownian motion with affine drift and show that the joint distribution of this process and its time-integral can be determined by a doubly-confluent Heun equation. Furthermore, the joint Laplace transform of the process and its time-integral is derived from the asymptotics of the solutions. In addition, we provide an application by using the results for the asymptotics of the double-confluent Heun equation in pricing Asian options. Numerical results show the accuracy and efficiency of this new method.

This article provides a unified and more direct approach to path-independent Girsanov transformation for (possibly time-inhomogeneous) Markov processes and their corresponding parabolic partial differential equations. The approach is applicable to a large class of Markov processes, including diffusion processes determined by stochastic differential equations, and Markov processes with discontinuous sample paths. In particular, we apply it to reflected diffusions, diffusions with jumps and a class of piecewise deterministic Markov processes that are Markov. The approach of this paper is also applicable to a class of time-inhomogeneous Markov processes that have jumps only at integer times, where the path-independent Girsanov transform have to be given by discontinuous but piecewise differentiable functions. In the last section of this paper, we illustrate this by a simplified stochastic model from insurance mathematics.

The paper aims to investigate the H ∞ control problem for systems perturbed by jump random noise, i.e., Poisson-driven stochastic systems (SSs). Firstly, this paper uses the Doob-Meyer decomposition and measure theory to give a model transformation method, and Poisson-driven SSs, which are SSs driven by semi-martingale, are transformed into SSs driven by compensated Poisson process. Since SSs driven by compensated Poisson process are SSs driven by martingale, we can use effective properties and tools in martingale theory to investigate the H ∞ control problem. Secondly, this paper utilizes martingale theory to deal with the jump item and the sum of stochastic integrals (SIs) with respect to (w.r.t.) the continuous part of states in Ito formula, and then gives an equivalent Ito formula for SDEs driven by compensated Poisson process. Thirdly, on the basis of these, this paper presents a simple H ∞ controller design method. Furthermore, the design criterion contains information about the average number of jump random events in a unit time, and one can utilize convex optimization algorithm to estimate the maximum average number of jump random events in a unit time, which the closed-loop system can tolerate to achieve the stability and H ∞ performance. Finally, the usefulness of the design result is verified by two numerical examples.

For nonlinear Kalman filtering, process noise and observation noise affect the accuracy of system filtering, and filtering accuracy is related to observable degree. That is, the calculation of observable degree will be affected by process noise and observation noise. Traditional solutions for observable degree of nonlinear systems do not take noise into account. In this paper, the observable degree theory is solved by using the Cramer-Rao Lower Bound and the Lie derivative in differential geometry theory. The process noise and the observation noise are taken into account in the calculation matrix of the nonlinear observable degree. The paper proposes a new method based on condition number fusion. The iterative algorithm is used to make the condition number of the fused matrix reach the minimum value. In the result, the error of observable degree calculation can be reduced. The validity of the proposed method is verified by simulation, and the calculation theory of nonlinear observable degree is improved.

Many papers have applied the meshless method to approximate a function by using a set of scattered data. To use a meshless method, we need to predefine a positive real number as a radius of the local sphere or a positive integer as the number of interior points. This is while the effect of a fixed number as the radius of a local sphere or as the number of interior points could be different for different parts of a complex domain. This paper contains the construction of ellipsoidal neighborhoods for the meshless interpolation and approximation methods with local support functions and local behavior. By using these new neighborhoods, the trend of local data could be found easily. The advantage of this method over the current methods is the use of ellipsoidal local neighborhoods which include points with the most impact on the approximation of the function. We applied these methods to the data of the daily temperature and humidity of Alberta, Canada.

Strain modal parameters are more sensitive to the local structural damage than displacement modal parameters. Therefore, it will be more effective to locate damage based on the change of strain modes. In this paper, the sensitivity matrix between strain mode and elemental stiffness parameter is deduced. Further more, the relationship of strain modal information and damage parameter of beam-like structures is established. In order to quantify the influence of the uncertainty in the strain modal information on the identification results, this paper treats measurement noise as probabilistic and interval variable and deduces the corresponding formula of structural elemental stiffness parameters. Due to the definition of uncertainties, different damage indexes including deterministic index, uncertainty index and combination index are established or introduced to quantify the damage extent and damage possibility. The validity of the proposed method is verified by a numerical example and an experimental work. The effectiveness and robustness of the displacement modal information based method is compared with the proposed method. The characteristics of different damage indexes are discussed by statistical means in the numerical example. The results indicates that the combination index has more advantages in identifying the damage under uncertainties.

The arithmetic–geometric index (AG(G)) was recently introduced as a modification of the well-known geometric–arithmetic index (GA(G)). This paper reports results on searching for extremal AG-graphs for various classes of simple graphs. Additionally, relations between these two indices are elaborated. Results on combinations A G + G A , A G − G A , AG · GA, and AG/GA are given. The paper is concluded with four conjectures that have been derived based on computer investigations.

Inversion sequences are finite sequences of non-negative integers, where the value of each entry is bounded from above by its position. Patterns in inversion sequences have been studied by Corteel-Martinez-Savage-Weselcouch and Mansour-Shattuck in the classical case, where patterns can occur in any positions, and by Auli-Elizalde in the consecutive case, where only adjacent entries can form an occurrence of a pattern. These papers classify classical and consecutive patterns of length 3 into Wilf equivalence classes according to the number of inversion sequences avoiding them. In this paper we consider vincular patterns in inversion sequences, which, in analogy to Babson-Steingr\'{\i}msson patterns in permutations, require only certain entries of an occurrence to be adjacent, and thus generalize both classical and consecutive patterns. Solving a conjecture of Lin and Yan, we provide a complete classification of vincular patterns of length 3 in inversion sequences into Wilf equivalence classes, and into more restrictive classes that consider the number of occurrences of the pattern and the positions of such occurrences. We find the first known instance of patterns in inversion sequences where these two more restrictive classes do not coincide., Comment: 18 pages, 9 figures

Due to instability being induced easily by parameter disturbances of network systems, this paper investigates the multistability of memristive Cohen-Grossberg neural networks (MCGNNs) under stochastic parameter perturbations. It is demonstrated that stable equilibrium points of MCGNNs can be flexibly located in the odd-sequence or even-sequence regions. Some sufficient conditions are derived to ensure the exponential multistability of MCGNNs under parameter perturbations. It is found that there exist at least ( w + 2 ) l (or ( w + 1 ) l ) exponentially stable equilibrium points in the odd-sequence (or the even-sequence) regions. In the paper, two numerical examples are given to verify the correctness and effectiveness of the obtained results.

In the analysis of the economic growth factors, people often use the CES (constant elasticity of substitution) production function model to calculate the contribution rate of influencing factors to economic growth. However, the traditional CES production function model does not consider the period characteristic of technological progress on economic growth, so this paper puts forward a modified CES production function model. On the parameter estimation of the model, this paper presents an improved PSO (particle swarm optimization) algorithm with high precision and fast convergence. Using the modified CES production function model, this paper provides a scientific method to calculate the contribution rates of all factors influencing the economic growth. Finally, this paper performs the empirical analysis of the contribution rates of all factors influencing China’s economic growth.

A new viscosity method of split variational inclusion problem is proposed.The method is based on conjugate gradient method and averaged mapping approach.The strong convergence of the sequences generated by the method is proved.The results are the generalization of the previously known results in this area. In this paper, we introduce and study a new viscosity approximation method based on the conjugate gradient method and an averaged mapping approach for finding a common element of the set of solutions of a constrained convex minimization problem and the set of solutions of a split variational inclusion problem. Under suitable conditions, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of the split variational inclusion problem and the set of solutions of the constrained convex minimization problem. The results presented in this paper are the supplement, extension and generalization of the previously known results in this area. Finally, preliminary numerical results indicate the feasibility and efficiency of the proposed methods.

This paper investigates the problem of feedback fuzzy control design for networked systems involving both random measurement and actuation delays and subject to quantization and random packet dropout. It is assumed that system state or output signal is quantized before being communicated. The paper focuses initially on an observer-based output feedback fuzzy controller design and then derives a state feedback controller as special case. Sufficient conditions for the existence of an admissible fuzzy controller are established to ensure the exponential stability of the resulting closed-loop fuzzy system. Simulation experiments on a lab-scale four-tank system to demonstrate the applicability of the designed fuzzy control algorithm.

The stochastic direct simulation method is a numerical scheme for approximating the solutions of ordinary differential equations by path simulations of certain associated Markov jump processes. Its particular features make it suitable especially when applied to ODE systems originating from the spatial discretization of PDEs. The present paper provides further improvements to this basic method, which are based on the predictor-corrector principle. They are made possible by the fact that in its context a full path of the jump process is computed. With this full set of data one can perform either Picard iterations, Runge-Kutta steps, or a combination, with the goal of increasing the order of convergence. The improved method is applied to standard test problems such as a reaction-diffusion equation modeling a combustion process in 1D and 2D as well as to the radiation-diffusion equations, a system of two partial differential equations in two space dimensions which is very demanding from the computational point of view. Further optimization aspects which are also discussed in this paper are related to the efficient implementation of sampling algorithms based on Huffman trees.

This paper deals with the dissipativity and passivity analysis for discrete-time stochastic neural networks with probabilistic time-varying delays. The main contribution of this paper is to reduce the conservatism of the dissipativity conditions for the considered neural networks by utilizing the reciprocally convex combination approach. This approach is proposed to bound the forward differences of the double and triple summable terms taken in the Lyapunov functional. By introducing a stochastic variable with a Bernoulli distribution, the information of probability distribution of the time-varying delays are considered and transformed into one with deterministic time-varying delays. By employing Lyapunov functional approach, sufficient conditions are derived in terms of linear matrix inequalities to guarantee that the considered neural networks to be strictly ( Q , S , R ) - γ -dissipative and passive. Finally, numerical examples are given to demonstrate the effectiveness of the obtained results.

The main aim of the paper is to prove that the implicit numerical approximation can converge to the true solution to highly nonlinear hybrid stochastic pantograph differential equation. After providing the boundedness of the exact solution, the paper proves that the backward Euler-Maruyama numerical method can preserve boundedness of moments, and the numerical approximation converges strongly to the true solution. Finally, the exponential stability criterion on the backward Euler-Maruyama scheme is given, and a high order example is provided to illustrate the main result.

In this paper, we address the problem of unknown input observer design, which simultaneously estimates state and unknown input, of a class of nonlinear discrete-time systems with time-delay. A novel approach to the state estimation problem of nonlinear systems where the nonlinearities satisfy the one-sided Lipschitz and quadratically inner-bounded conditions is proposed. This approach also allows us to reconstruct the unknown inputs of the systems. The nonlinear system is first transformed to a new system which can be decomposed into unknown-input-free and unknown-input-dependent subsystems. The estimation problem is then reduced to designing observer for the unknown-input-free subsystem. Rather than full-order observer design, in this paper, we propose observer design of reduced-order which is more practical and cost effective. By utilizing several mathematical techniques, the time-delay issue as well as the bilinear terms, which often emerge when designing observers for nonlinear discrete-time systems, are handled and less conservative observer synthesis conditions are derived in the linear matrix inequalities form. Two numerical examples are given to show the efficiency and high performance of our results.

The paper proposes a new approach for function approximation by 'estimating' the second derivative, using Taylor series, where the samples of the function and its first derivatives at the sample points are known. Without such 'estimation', these initial data, can approximate the function traditionally using the first order Taylor approximation, but with more error. If we desire to improve the approximation via second order Taylor series, then we can estimate the 'pseudo' second derivatives of the function in three different ways. All these three ways are investigated in this paper. The pseudo second derivatives help in computing many more sample points of the function within each sampling interval. Thus, the approach acts like a mathematical 'magnifying glass'. Two examples are treated to compare the efficiencies of the methods. Also, a qualitative study for upper bound of error of the approximations is studied in detail.

In this paper, we are concerned with the open problem of the global boundedness of the Lu system based on Lyapunov stability theory, which was proposed by Zhang and Mu (2012). The innovation of the paper is that this paper not only proves the Lu system is global bounded according to dynamical systems theory but also gives the bounds of the Lu system.

Let D = ( P , B ) be any nontrivial nonsymmetric 2-(v, k, λ) design. In this paper we construct a connected, regular and bipartite graph, say IG v , b ( D ) , from D . Some graphic properties of IG v , b ( D ) are investigated. In particular, the results in the paper bridges the equivalency between edge-transitivity of IG v , b ( D ) and flag-transitivity of D . With the equivalency, it is obtained that IG v , b ( D ) is a semisymmetric graph as long as D is a nonsymmetric flag-transitive 2-(v, k, λ) design.

In this paper, we study four classes of discrete type equations with harmonic singular operator and convolution. Such equations are turned into boundary value problems for analytic function with discontinuous coefficients by discrete Fourier transform. The general solutions and the conditions of solvability are obtained in class h by our method. Thus, this paper generalizes the theory of classical equations of convolution type.

This paper investigates absolute exponential stability and stabilization with L1-gain performance of switched nonlinear positive systems with time-varying delay. Nonlinear functions considered in the paper are located in a sector field and the time-varying delay is unknown but bounded. The notion of absolute exponential L1 stability of switched nonlinear positive systems is first introduced. A nonlinear Lyapunov-Krasovskii functional is constructed for the underlying systems. By using the Lyapunov-Krasovskii functional, a sufficient condition for absolute exponential L1 stability of the systems is established in terms of linear programming. Then, absolute exponential L1 control synthesis of the systems is addressed. A feedback control law containing nonlinear functions and a state-feedback control law are designed, respectively. By comparing with existing results, it is shown that the present design is less conservative. Finally, an illustrative example is provided to illustrate the effectiveness of the results.

In this paper, we present a new iterative method based on the hybrid viscosity approximation method and the hybrid steepest-descent method for finding a common element of the set of solutions of generalized mixed equilibrium problems and the set of common fixed points of a finite family of nonexpansive mappings in Hilbert spaces. Furthermore, we prove that the proposed iterative method has strong convergence under some mild conditions imposed on algorithm parameters. The results presented in this paper improve and extend the corresponding results reported by some authors recently.

The purpose of this paper is to introduce a new iterative method that is the combination of the proximal point algorithm, viscosity approximation method and alternating resolvent method for finding the common zeros of two accretive operators in Banach spaces. And we will prove the strong convergence theorems for the iterative algorithms and give the example of the main theorems. The results of this paper are improvements and extensions of the corresponding ones announced by many others.

In this paper, we provide a novel fractional particle swarm optimization (FPSO) algorithm. The traditional PSO is one of the most well-known bio-inspired algorithms used in optimization problems, which basically consists of a number of particles that collectively move in search of the global optimum. Nevertheless, despite its success over the past 20 years, the PSO is also known to be unable to converge, and even stagnate, in many complex problems with multiple local optima. In order to overcome this drawback, this paper proposes a modified version of the PSO algorithm, considering a fractional calculus approach. Stability results evaluation is carried out to analytically prove the convergence of the fractional extensions. This is naturally followed by simulation results to test the fractional-based PSOs under several well-known objective functions, thus highlighting the relationship between the fractional order velocity and position of particles with the convergence of the algorithm. Experimental results show that the FPSO and its variants significantly outperform the traditional PSO.

In this paper, we study a class of approximation problems appearing in data approximation and signal processing. The approximations are constructed as combinations of polynomial splines (piecewise polynomials) whose parameters are subject to optimisation and so called prototype functions whose choice is based on the application rather than optimisation. We investigate two types of models, namely Model 1 and Model 2 in order to analyse the singularity of their system matrices. The main difference between these two models is that in Model 2, the signal is shifted vertically (signal biasing) by a polynomial spline function. The corresponding optimisation problems can be formulated as Linear Least Squares Problems (LLSPs). If the system matrix is non-singular, then, the corresponding problem can be solved inexpensively and efficiently, while for singular cases, slower (but more robust) methods have to be used. To choose a better suited method for solving the corresponding LLSPs we have developed a singularity verification rule. In this paper, we develop necessary and sufficient conditions for non-singularity of Model 1 and sufficient conditions for non-singularity of Model 2. These conditions can be verified much faster than the direct singularity verification of the system matrices. Therefore, the algorithm efficiency can be improved by choosing a suitable method for solving the corresponding LLSPs.

A class of two-point quartic-order simple-zero finders and their dynamics are investigated in this paper by extending King's fourth-order family of methods. With the introduction of an error corrector having a weight function dependent on a function-to-function ratio, higher-order convergence is obtained. Through a variety of test equations, numerical experiments strongly support the theory developed in this paper. In addition, relevant dynamics of the proposed methods is successfully explored for a prototype quadratic polynomial as well as parameter spaces and dynamical planes.

This paper investigates the L2-L∞ filtering problem for stochastic systems driven by Poisson processes and Wiener processes. Firstly, this paper presents an approach to transform the expectation of stochastic integral with respect to Poisson process into the expectation of Lebesgue integral by the martingale theory. Then, based on this, a filter is designed to guarantee that the filtering error system is mean-square asymptotically stable and its L2-L∞ performance satisfies a prescribed level. Finally, a simulation example is given to illustrate the effectiveness of the proposed filtering scheme.

This paper studies a class of global fractional-order projective dynamical systems involving set-valued perturbations in real separable Hilbert spaces. We prove that the set of solutions for this type of systems is nonempty and closed under some suitable conditions. Furthermore, we show that the set of solutions is continuous with respect to initial value in the sense of Hausdorff metric. Finally, an interesting numerical example is given to illustrate the validity of the main theorem presented in this paper.

In this paper, the stability problem is investigated for a class of reaction-diffusion uncertain memristive neural networks with time-varying delays and leakage term. To investigate the dynamic behavior of the memristive system, we turn to the qualitative analysis of a relevant differential inclusion under the framework of Filippov's solution, which is easier to handle. By using Lyapunov stability theory, Jensen integral inequality, Schur complement Lemma, free-weighting matrix approach together with the linear matrix inequality (LMI) approach, the sufficient conditions are derived to ensure the stability of the considered systems. The easy-to-test stability criteria established in this paper depend on the leakage delay as well as the reaction-diffusion terms, which is more reasonable. Moreover, the existing stability criteria can be treated as a special case of this paper. Finally, two numerical examples are exploited to show the effectiveness of the derived LMI-based stability conditions.

In this paper, based on block style spectral decomposition of the block skew circulant with circulant blocks (BSCCB) matrix, the structure perturbation is discussed, which includes the condition number and relative error of the BSCCB linear system. Then the optimal backward perturbation bound of the BSCCB linear system is analyzed. Simultaneously, the algorithm for the optimal backward perturbation bound is presented. At the end of the paper, a numerical example is provided to verify the effectiveness of the algorithm.

This paper is concerned with the approximate controllability of the semilinear fractional evolution equations with nonlocal and impulsive conditions. Our main results are obtained by utilizing the technique of approximate solution and the theory of fixed point. In addition, the impulsive functions in this paper are supposed to be continuous and the nonlocal item is divided into two cases: Lipschitz continuous and only continuous, which generalizes the previous contributions. Finally two examples are worked out to illustrate our obtained results.

In this paper we study and obtain the existence of a positive almost periodic solution to the nonlinear differential equation with delays that describes the so-called hematopoiesis model. The main tool utilized to establish our existence result consists of the fixed-point theorem in a cone. Two examples are given at the end of the paper to illustrate our main result.

This paper considers the three-dimensional path planning problem for horizontal oil wells. The decision variables in this problem are the curvature, tool-face angle and switching points for each turn segment in the path, and the optimization objective is to minimize the path length and target error. The optimal curvatures, tool-face angles and switching points can be readily determined using existing gradient-based dynamic optimization techniques. However, in a real drilling process, the actual curvatures and tool-face angles will inevitably deviate from the planned optimal values, thus causing an unexpected increase in the target error. This is a critical challenge that must be overcome for successful practical implementation. Accordingly, this paper introduces a sensitivity function that measures the rate of change in the target error with respect to the curvature and tool-face angle of each turn segment. Based on the sensitivity function, we propose a new optimization problem in which the switching points are adjusted to minimize target error sensitivity subject to continuous state inequality constraints arising from engineering specifications, and an additional constraint specifying the maximum allowable increase in the path length from the optimal value. Our main result shows that the sensitivity function can be evaluated by solving a set of auxiliary dynamic systems. By combining this result with the well-known time-scaling transformation, we obtain an equivalent transformed problem that can be solved using standard nonlinear programming algorithms. Finally, the paper concludes with a numerical example involving a practical path planning problem for a Ci-16-Cp146 well.

We compute a smooth meta-model of a given set of data points based on local-support free-form parametric curves.Our method applies a particle-based metaheuristic approach to determine optimal values of unknowns of the fitting curve.The method does not assume any knowledge about the underlying function of data beyond the data points.Our approach performs well and in a fully automatic way even for underlying functions exhibiting challenging features.Our experiments show that our approach outperforms previous approaches in terms of generality and fitting error accuracy. This paper concerns the process of computing the underlying function of a given set of data points. In many cases, it is not possible to obtain an analytical solution for this problem so the goal is transformed into that of computing a meta-model instead. In this paper we seek to compute a smooth meta-model of such points based on local-support free-form parametric curves. Given an initial parameterization, our method applies a particle-based metaheuristic approach to determine optimal values for the breakpoints and poles of the fitting curve, which is well-known to be a continuous nonlinear optimization problem. The performance of our approach is evaluated by its application to two illustrative examples: a synthetic academic shape and a real-world shape. Our experimental results show that the proposed scheme performs very well, even for shapes with underlying functions exhibiting challenging features, such as self-intersections and sharp changes of curvature. Comparative results show that our approach outperforms previous approaches in terms of generality and fitting error accuracy.