Finite-dimensional filter for a class of nonlinear systems with correlated noises

The purpose of this article is to compute an explicit formula for the unnormalized conditional density for the filter associated with a nonlinear filtering problem with correlated noises and a signal process with nonlinear terms in the drift. This article extends the result of Daum to nonlinear filtering systems with correlated noises and incorporates both the Kalman–Bucy and Bene? filters as particular cases.     

Observer-based fault detection for networked discrete-time infinite-distributed delay systems with packet dropouts

This paper addresses the problem of fault detection for networked discrete-time infinite-distributed delay systems with packet dropouts. Both sensor-to-controller and controller-to-actuator packet dropouts are described by two different Bernoulli distributed white sequences, respectively. The problem addressed is to design an observer-based fault detection filter (FDF) such that the error between the residual and the fault is made as small as possible. Unlike most of the existing literature, we have noted that the control input of the observer is different from that of the plant because of packet dropouts in the controller-to-actuator link. Sufficient condition for the existence of the FDF is derived in terms of some linear matrix inequalities (LMIs). When these LMIs are feasible, the explicit expression of the desired FDF can also be characterized. A numerical example is exploited to show the effectiveness of the obtained results.     

Fuzzy speed control and stability analysis of a networked induction motor system with time delays and packet dropouts

Connecting a spatially distributed system with sensors, actuators, and controllers as a networked control system by a shared data network can reduce the wiring and cost remarkably. Networked control strategy has been utilized in remote operation of linear systems. Nonlinearity is the major barrier in implementing a networked control scheme on an induction motor, which is the most widely used motor in industrial applications. In this case, we designed a sliding mode flux observer to linearize the induction motor model, such that the application of the networked control scheme is feasible. Due to the variable QoS, a fuzzy logic speed controller is proposed to adapt various network conditions. As part of the networked controller, a state predictor is designed to compensate the time delay in the feedback channel. In stability analysis, the upper bounds of time delays and packet dropouts are both given in terms of the Lyapunov theorem. Finally, simulations are conducted employing TrueTime toolbox to demonstrate the effectiveness of the control strategy.     

Nonfragile H∞ output tracking control for uncertain singular Markovian jump delay systems with network‐induced delays and data packet dropouts

This article deals with the problem of nonfragile H_∞ output tracking control for a kind of singular Markovian jump systems with time‐varying delays, parameter uncertainties, network‐induced signal transmission delays, and data packet dropouts. The main objective is to design mode‐dependent state‐feedback controller under controller gain perturbations and bounded modes transition rates such that the output of the closed‐loop networked control system tracks the output of a given reference system with the required H_∞ output tracking performance. By constructing a more multiple stochastic Lyapunov–Krasovskii functional, the novel mode‐dependent and delay‐dependent conditions are obtained to guarantee the augmented output tracking closed‐loop system is not only stochastically admissible but also satisfies a prescribed H_∞‐norm level for all signal transmission delays, data packet dropouts, and admissible uncertainties. Then, the desired state‐feedback controller parameters are determined by solving a set of strict linear matrix inequalities. A simple production system example and two numerical examples are used to verify the effectiveness and usefulness of the proposed methods. © 2015 Wiley Periodicals, Inc. Complexity 21: 396–411, 2016     

Estimation of the regression operator from functional fixed-design with correlated errors

We consider the estimation of the regression operator r in the functional model: Y=r(x)+ε, where the explanatory variable x is of functional fixed-design type, the response Y is a real random variable and the error process ε is a second order stationary process. We construct the kernel type estimate of r from functional data curves and correlated errors. Then we study their performances in terms of the mean square convergence and the convergence in probability. In particular, we consider the cases of short and long range error processes. When the errors are negatively correlated or come from a short memory process, the asymptotic normality of this estimate is derived. Finally, some simulation studies are conducted for a fractional autoregressive integrated moving average and for an Ornstein-Uhlenbeck error processes.     

Iterative learning control for a class of nonlinear systems with random packet losses

This paper considers the problem of iterative learning control (ILC) for a class of nonlinear systems with random packet dropouts. It is assumed that an ILC scheme is implemented via a networked control system (NCS), and that during the packet transfer between the remote nonlinear plant and the ILC controller packet dropout occurs. A new formulation is employed to model the packet dropout case, where the random dropout rate is transformed into a stochastic parameter in the system’s representation. Through rigorous analysis, it is shown that under some given conditions, the iterative learning control can guarantee the convergence of the tracking error although some packets are missing. The analysis is also supported by a numerical example.     

Stochastic resonance in a linear static system driven by correlated multiplicative and additive noises

In this work, we investigate the signal transmission in a linear static system driven by correlated multiplicative and additive noises. When the input signal is periodic, we depict the stochastic resonance (SR) phenomenon by employing the signal-to-noise ratio (SNR) theory; while the input signal is aperiodic, we describe the SR phenomenon by using the input–output cross correlation theory. And the exact analytic expressions of the output SNR and the normalized time averaged cross covariance between input and output are obtained. The results show: under the condition of negative correlated noises, SR arises; while with positive correlated or uncorrelated noises, there is no SR. This result may extend the SR theory to a common linear static system.     

Evolution equation for thermodynamic systems with correlated states

We have derived time evolution equations for thermodynamic systems with correlated states, considering the change in a probability density, entropy, and phase space metric at fixed phase‐space locations and obtained simple relations between these quantities for the separate systems. © 2014 Wiley Periodicals, Inc. Complexity 21: 162–165, 2015     

Stochastic stability and state shifts for a time-delayed cancer growth system subjected to correlated multiplicative and additive noises

In the present paper, we investigate the stationary probability distribution(SPD) and the mean treatment time of a time-delayed cancer growth system induced by cross-correlated intrinsic and extrinsic noises. Our main results show that the resonant-like phenomenon of the mean first-passage time (MFPT) appears in the tumor cell growth model due to the interaction of all kinds of noises and time delay. Due to the existence of the resonant-like peak value, by increasing the intensity of multiplicative noise and time delay, it is possible to restrain effectively the development of the cancer cells and enhance the stability of the system. During the process of controlling the diffusion of the tumor cells, it contributes to inhibiting the development of cancer by increasing the cross-correlated noise strength and weakening the additive noise intensity and time delay. Meanwhile, the proper multiplicative noise intensity is conducive to the process of inhibition. Conversely, in the process of exterminating cancer cells of a large density, it can exert positive effects on eliminating the tumor cells by increasing noises intensities and the value of time delay.     

Sharp critical behavior for pinning models in a random correlated environment

This article investigates the effect for random pinning models of long range power-law decaying correlations in the environment. For a particular type of environment based on a renewal construction, we are able to sharply describe the phase transition from the delocalized phase to the localized one, giving the critical exponent for the (quenched) free-energy, and proving that at the critical point the trajectories are fully delocalized. These results contrast with what happens both for the pure model (i.e., without disorder) and for the widely studied case of i.i.d. disorder, where the relevance or irrelevance of disorder on the critical properties is decided via the so-called Harris Criterion (Harris, 1974) [21].     

Deflated GMRES for systems with multiple shifts and multiple right-hand sides

We consider solution of multiply shifted systems of nonsymmetric linear equations, possibly also with multiple right-hand sides. First, for a single right-hand side, the matrix is shifted by several multiples of the identity. Such problems arise in a number of applications, including lattice quantum chromodynamics where the matrices are complex and non-Hermitian. Some Krylov iterative methods such as GMRES and BiCGStab have been used to solve multiply shifted systems for about the cost of solving just one system. Restarted GMRES can be improved by deflating eigenvalues for matrices that have a few small eigenvalues. We show that a particular deflated method, GMRES-DR, can be applied to multiply shifted systems.In quantum chromodynamics, it is common to have multiple right-hand sides with multiple shifts for each right-hand side. We develop a method that efficiently solves the multiple right-hand sides by using a deflated version of GMRES and yet keeps costs for all of the multiply shifted systems close to those for one shift. An example is given showing this can be extremely effective with a quantum chromodynamics matrix.     

Estimation of elastic coefficients for a multiple beam structure

In this paper, we consider the estimation of spatially dependent elastic parameters in a static distributed model of a simple structure composed of two beams at a fixed angle to one another. We formulate the potential energy functional of the system and obtain existence of optimal estimators to a regularized-output least-squares estimation problem. We discuss regularity and approximation results for the basic problem and penalized problem in which nonconforming elements are used to model the junction of the beams. Numerical examples are presented and generalizations to multiple-beam systems are discussed.This work was supported in part by AFOSR Grant 91-0017.     

Wavelet optimal estimations for a density with some additive noises

Using wavelet methods, Fan and Koo study optimal estimations for a density with some additive noises over a Besov ball $B_{r,q}^s(L)(r,q⩾1)$ and over $L^2$ risk (Fan and Koo, 2002 [13]). The $L^{\infty }$ risk estimations are investigated by Lounici and Nickl (2011) [19]. This paper deals with optimal estimations over $L^p(1⩽p⩽\infty )$ risk for moderately ill-posed noises. A lower bound of $L^p$ risk is firstly provided, which generalizes Fan–Koo and Lounici–Nickl's theorems; then we define a linear and non-linear wavelet estimators, motivated by Fan–Koo and Pensky–Vidakovic's work. The linear one is rate optimal for $r⩾p$, and the non-linear estimator attains suboptimal (optimal up to a logarithmic factor). These results can be considered as an extension of some theorems of Donoho et al. (1996) [10]. In addition, our non-linear wavelet estimator is adaptive to the indices s, r, q and L.     

Production and marketing decisions with multiple objectives in a competitive environment

This paper presents an application of the mathematical program which has been called the Fritz John problem to a situation in applied economics. A model is presented which enables a firm to maximize profit, subject to constraints on maintenance of market share in the face of collusive action by competitors and subject to resource constraints. An example problem is formulated and solved.The authors wish to acknowledge comments and suggestions offered by J. W. Blankenship and R. E. Kuenne.     

A mathematical model for discrete-time buffer systems with correlated output process

This article considers an infinite buffer system with one or more input channels and multiple output channels. Transmission of messages from the buffer is synchronous and the arrival process of messages to the buffer is general. Each of the output channels is subjected to a random interruption process, i.e., the number of available output channels varies in time and is stochastic. The analysis of this system is carried out under the assumption that the output process can be described as a first order Markov process, i.e., the probability distribution of the number of available output channels during some clock time interval depends only on the number of available output channels during the previous clock time interval.A set of equations describing the behavior of this buffer system is derived. For a number of interesting special cases this set is solved and explicit expressions are obtained for the probability generating function of the number of messages in the buffer. Several prior studies are found as special cases of the present one. An illustrative example is treated and the results are compared to the ones obtained for an uncorrelated output process with the same equilibrium distribution. Some considerable deviations from these results are found.     

Dynamic programming for fuzzy systems with fuzzy environment

A dynamic programming functional equation for a multi-stage decision problem with fuzzy dynamics and environment is formulated and solved by a process of fuzzy interpolation. This is an extension of the Bellman-Zadeh model.     

Mixed model identification for linear time‐invariant systems with mixed noises in frequency domain

In this paper, we present a new method for frequency domain identification of discrete linear time‐invariant systems. We take consideration of the case where the output noises are mixed or unknown. In order to deal with this problem, a new mixed model structure is used correspondingly. The augmented Lagrangian method (ALM) is combined in selection of poles for the shifted Cauchy kernels to get solutions to the optimal problem. Simulations show the proposed method can get efficient approximation to the original systems.