Exact controllability of rational expectations model with multiplicative noise and input delay

This paper considers the rational expectations model with multiplicative noise and input delay,where the system dynamics rely on the conditional expectations of future states.The main contribution is to obtain a sufficient condition for the exact controllability of the rational expectations model.In particular,we derive a sufficient Gramian matrix condition and a rank condition for the delay-free case.The key is the solvability of the backward stochastic difference equations with input delay which is derived from the forward and backward stochastic system.

RANDOM ATTRACTOR FOR A TWO-DIMENSIONAL INCOMPRESSIBLE NON-NEWTONIAN FLUID WITH MULTIPLICATIVE NOISE

This article proves that the random dynamical system generated by a twodimensional incompressible non-Newtonian fluid with multiplicative noise has a global random attractor, which is a random compact set absorbing any bounded nonrandom subset of the phase space.

REGULARITY OF RANDOM ATTRACTORS FOR A STOCHASTIC DEGENERATE PARABOLIC EQUATIONS DRIVEN BY MULTIPLICATIVE NOISE

We study the regularity of random attractors for a class of degenerate parabolic equations with leading term div（o（x）↓△u） and multiplicative noises. Under some mild conditions on the diffusion variable o（x） and without any restriction on the upper growth p of nonlinearity, except that p 〉 2, we show the existences of random attractor in D0^1,2（DN, σ） space, where DN is an arbitrary （bounded or unbounded） domain in R^N N 〉 2. For this purpose, some abstract results based on the omega-limit compactness are established.

Fault detection filter design for linear discrete time-varying systems with multiplicative noise

The problem of fault detection for linear discrete timevarying systems with multiplicative noise is dealt with.By using an observer-based robust fault detection filter（FDF） as a residual generator,the design of the FDF is formulated in the framework of H ∞ filtering for a class of stochastic time-varying systems.A sufficient condition for the existence of the FDF is derived in terms of a Riccati equation.The determination of the parameter matrices of the filter is converted into a quadratic optimization problem,and an analytical solution of the parameter matrices is obtained by solving the Riccati equation.Numerical examples are given to illustrate the effectiveness of the proposed method.

Robust stability analysis for Markovian jumping stochastic neural networks with mode-dependent time-varying interval delay and multiplicative noise

This paper is concerned with the problem of robust stability for a class of Markovian jumping stochastic neural networks （MJSNNs） subject to mode-dependent time-varying interval delay and state-multiplicative noise. Based on the Lyapunov-Krasovskii functional and a stochastic analysis approach, some new delay-dependent sufficient conditions are obtained in the linear matrix inequality （LMI） format such that delayed MJSNNs are globally asymptotically stable in the mean-square sense for all admissible uncertainties. An important feature of the results is that the stability criteria are dependent on not only the lower bound and upper bound of delay for all modes but also the covariance matrix consisting of the correlation coefficient. Numerical examples are given to illustrate the effectiveness.

H^2-regularity random attractors of stochastic non-Newtonian fluids with multiplicative noise

In this paper, the authors study the long time behavior of solutions to stochastic non-Newtonian fluids in a two-dimensional bounded domain, and prove the existence of H2-regularity random attractor.

A Fast Total Variation Algorithm for Multiplicative Noise Removal

In this paper,based on the work in[5],some theoretical analysis on a variational model for multiplicative noise removal is further studied.Moreover,the primal-dual technique is incorporated to design a fast algorithm for the variational model.Some numerical results are presented to illustrate the efficiency of the

GEKF,GUKF and GGPF based prediction of chaotic time-series with additive and multiplicative noises

On the assumption that random interruptions in the observation process are modelled by a sequence of independent Bernoulli random variables, this paper generalize the extended Kalman filtering （EKF）, the unscented Kalman filtering （UKF） and the Gaussian particle filtering （GPF） to the case in which there is a positive probability that the observation in each time consists of noise alone and does not contain the chaotic signal （These generalized novel algorithms are referred to as GEKF, GUKF and GGPF correspondingly in this paper）. Using weights and network output of neural networks to constitute state equation and observation equation for chaotic time-series prediction to obtain the linear system state transition equation with continuous update scheme in an online fashion, and the prediction results of chaotic time series represented by the predicted observation value, these proposed novel algorithms are applied to the prediction of Mackey-Glass time-series with additive and multiplicative noises. Simulation results prove that the GGPF provides a relatively better prediction performance in comparison with GEKF and GUKF.

Nonstationary Filtering for Markov Jumping Systems with Fading Channel and Multiplicative Noises

This paper studies the nonstationary filtering problem of Markov jump system under l2 - l∞ performance. Due to the difference in propagation channels, signal strength and phase will inevitably change randomly and cause the waste of signals resources. In response to this problem, a channel fading model with multiplicative noise is introduced. And then a nonstationary filter, which receives signals more efficiently is designed. Meanwhile Lyapunov function is constructed for error analysis. Finally, the gain matrix for filtering is obtained by solving the matrix inequality, and the results showed that the nonstationary filter converges to the stable point more quickly than the traditional asynchronous filter, the stability of the designed filter is verified.

Multiquadric Radial Basis Function Approximation Scheme for Solution of Total Variation Based Multiplicative Noise Removal Model

This article introduces a fastmeshless algorithm for the numerical solution nonlinear partial differential equations(PDE)by Radial Basis Functions(RBFs)approximation connected with the Total Variation(TV)-basedminimization functional and to show its application to image denoising containing multiplicative noise.These capabilities used within the proposed algorithm have not only the quality of image denoising,edge preservation but also the property of minimization of staircase effect which results in blocky effects in the images.It is worth mentioning that the recommended method can be easily employed for nonlinear problems due to the lack of dependence on a mesh or integration procedure.The numerical investigations and corresponding examples prove the effectiveness of the recommended algorithm regarding the robustness and visual improvement as well as peak-signal-to-noise ratio(PSNR),signal-to-noise ratio(SNR),and structural similarity index(SSIM)corresponded to the current conventional TV-based schemes.

Mean-Square Output Consensus of Heterogeneous Multi-Agent Systems with Multiplicative Noises in Dynamics and Measurements

This paper studies the output consensus problem of heterogeneous linear stochastic multiagent systems with multiplicative noises in system parameters and measurements,where the system noise in each agent is allowed to be different.By employing stochastic output regulation theory and the stochastic Lyapunov function approach,a composite controller embedded with stochastic output regulator equations(SOREs)and a stochastic dynamic compensator is designed to achieve the meansquare output consensus of the multi-agent systems.To implement the consensus algorithm,a sufficient condition for feasible solutions of the SOREs is first established in terms of Lyapunov and Selvester equations.Then the time-varying SOREs are approximated by the Euler-Maruyama method combined with an a-posteriori partial estimation of the increments of the Brownian motion.A numerical example illustrates the theoretical results.

Adaptive cubature Kalman filter with the estimation of correlation between multiplicative noise and additive measurement noise

Mobile robots are often subject to multiplicative noise in the target tracking tasks,where the multiplicative measurement noise is correlated with additive measurement noise.In this paper,first,a correlation multiplicative measurement noise model is established.It is able to more accurately represent the measurement error caused by the distance sensor dependence state.Then,the estimated performance mismatch problem of Cubature Kalman Filter(CKF)under multiplicative noise is analyzed.An improved Gaussian filter algorithm is introduced to help obtain the CKF algorithm with correlated multiplicative noise.In practice,the model parameters are unknown or inaccurate,especially the correlation of noise is difficult to obtain,which can lead to a decrease in filtering accuracy or even divergence.To address this,an adaptive CKF algorithm is further provided to achieve reliable state estimation for the unknown noise correlation coefficient and thus the application of the CKF algorithm is extended.Finally,the estimated performance is analyzed theoretically,and the simulation study is conducted to validate the effectiveness of the proposed algorithm.

Containment Control of Multi-Agent Systems with Stochastic Multiplicative Noises

This paper investigates the containment problem of continuous-time multi-agent systems with multiplicative noises,where the first-order and second-order multi-agent systems are studied respectively.Based on stochastic analysis tools,algebraic graph theory,and Lyapunov function method,the containment protocols based the relative states measurement with multiplicative noises are developed to guarantee the mean square and almost sure containment.Moreover,the sufficient conditions and necessary conditions related to the control gains are derived for achieving mean square and almost sure containment.It is also shown that multiplicative noises may works positively for the almost sure containment of the first-order multi-agent systems.Simulation examples are also introduced to illustrate the effectiveness of the theoretical results.

A necessary and sufficient stabilization condition for discrete time-varying stochastic systems with multiplicative noise

This paper investigates a fundamental problem of stabilization for time-varying multiplicative noise stochastic systems. A necessary and sufficient stabilization condition is presented based on the receding horizon approach. The explicit time-varying controller is designed if the condition is satisfied. The presented results are new to the best of our knowledge.

Optimal LQG control for discrete time-varying system with multiplicative noise and multiple state delays

This paper is concerned with the optimal linear quadratic Gaussian(LQG)control problem for discrete time-varying system with multiplicative noise and multiple state delays.The main contributions are twofolds.First,in virtue of Pontryagin’s maximum principle,we solve the forward and backward stochastic difference equations(FBSDEs)and show the relationship between the state and the costate.Second,based on the solution to the FBSDEs and the coupled difference Riccati equations,the necessary and sufficient condition for the optimal problem is obtained.Meanwhile,an explicit analytical expression is given for the optimal LQG controller.Numerical examples are shown to illustrate the effectiveness of the proposed algorithm.

An LDG Method for Stochastic Cahn-Hilliard Type Equation Driven by General Multiplicative Noise Involving Second-Order Derivative

In this paper,we propose a local discontinuous Galerkin(LDG)method for themulti-dimensional stochastic Cahn-Hilliard type equation in a general form,which involves second-order derivative Du in the multiplicative noise.The stability of our scheme is proved for arbitrary polygonal domain with triangular meshes.We get the sub-optimal error estimate O(h^(k))if the Cartesian meshes with Q^(k) elements are used.Numerical examples are given to display the performance of the LDG method.

New Splitting Algorithms for Multiplicative Noise Removal Based on Aubert-Aujol Model

In this paper,we propose new algorithms for multiplicative noise removal based on the Aubert-Aujol(AA)model.By introducing a constraint from the forward model with an auxiliary variable for the noise,the NEMA(short for Noise Estimate based Multiplicative noise removal by alternating direction method of multipliers(ADMM))is firstly given.To further reduce the computational cost,an additional proximal term is considered for the subproblem with regard to the original variable,the NEMA_(f)(short for a variant of NEMA with fully splitting form)is further proposed.We conduct numerous experiments to show the convergence and performance of the proposed algorithms.Namely,the restoration results by the proposed algorithms are better in terms of SNRs for image deblurring than other compared methods including two popular algorithms for AA model and three algorithms of its convex variants.

An Efficient Variational Model for Multiplicative Noise Removal

In this paper,an efficient variational model for multiplicative noise removal is proposed.By using a MAP estimator,Aubert and Aujol[SIAM J.Appl.Math.,68(2008),pp.925-946]derived a nonconvex cost functional.With logarithmic transformation,we transform the image into a logarithmic domain which makes the fidelity convex in the transform domain.Considering the TV regularization term in logarithmic domain may cause oversmoothness numerically,we propose the TV regularization directly in the original image domain,which preserves more details of images.An alternative minimization algorithm is applied to solve the optimization problem.The z-subproblem can be solved by a closed formula,which makes the method very efficient.The convergence of the algorithm is discussed.The numerical experiments show the efficiency of the proposed model and algorithm.

Global Well-posedness of the Stochastic Generalized Kuramoto-Sivashinsky Equation with Multiplicative Noise

Global well-posedness of the initial-boundary value problem for the stochastic generalized KuramotoSivashinsky equation in a bounded domain D with a multiplicative noise is studied. It is shown that under suitable sufficient conditions, for any initial data u0 ∈L2（D×Ω）, this problem has a unique global solution u in the space L2（Ω, C（[0, T ], L2（D））） for any T 〉 0, and the solution map u0 →u is Lipschitz continuous.

The Convex Relaxation Method on Deconvolution Model with Multiplicative Noise

In this paper,we consider variational approaches to handle the multiplicative noise removal and deblurring problem.Based on rather reasonable physical blurring-noisy assumptions,we derive a new variational model for this issue.After the study of the basic properties,we propose to approximate it by a convex relaxation model which is a balance between the previous non-convex model and a convex model.The relaxed model is solved by an alternating minimization approach.Numerical examples are presented to illustrate the effectiveness and efficiency of the proposed method.