State estimation for Markov-type genetic regulatory networks with delays and uncertain mode transition rates

This Letter is concerned with the robust state estimation problem for uncertain time-delay Markovian jumping genetic regulatory networks (GRNs) with SUM logic, where the uncertainties enter into both the network parameters and the mode transition rate. The nonlinear functions describing the feedback regulation are assumed to satisfy the sector-like conditions. The main purpose of the problem addressed is to design a linear estimator to approximate the true concentrations of the mRNA and protein through available measurement outputs. By resorting to the Lyapunov functional method and some stochastic analysis tools, it is shown that if a set of linear matrix inequalities (LMIs) is feasible, the desired state estimator, that can ensure the estimation error dynamics to be globally robustly asymptotically stable in the mean square, exists. The obtained LMI conditions are dependent on both the lower and the upper bounds of the delays. An illustrative example is presented to demonstrate the feasibility of the proposed estimation schemes.     

不确定离散时间输入饱和系统的鲁棒预见控制

本文研究一类具有输入饱和的不确定离散时间系统的鲁棒预见控制问题.与以往对误差信号和系统方程取差分不同,本文引入状态辅助变量,利用系统状态向量与辅助变量之差代替通常的状态差分,使得输入饱和不确定离散系统的扩大误差系统的构造成为可能.另外,本文推导的扩大误差系统不再包含误差向量,这不仅降低系统的阶数而且允许输出矩阵带有不确...     

Non-intrusive hybrid interval method for uncertain nonlinear systems using derivative information

This paper proposes a new non-intrusive hybrid interval method using derivative information for the dynamic response analysis of nonlinear systems with uncertain-butbounded parameters and/or initial conditions. This method provides tighter solution ranges compared to the existing polynomial approximation interval methods. Interval arithmetic using the Chebyshev basis and interval arithmetic using the general form modified affine basis for polynomials are developed to obtain tighter bounds for interval computation.To further reduce the overestimation caused by the "wrapping effect" of interval arithmetic, the derivative information of dynamic responses is used to achieve exact solutions when the dynamic responses are monotonic with respect to all the uncertain variables. Finally, two typical numerical examples with nonlinearity are applied to demonstrate the effectiveness of the proposed hybrid interval method, in particular, its ability to effectively control the overestimation for specific timepoints.     

Uncertain models for single facility location problems on networks

In practical location problems on networks, the vertex demand is usually non-deterministic. This paper employs uncertainty theory to deal with this non-deterministic factor in single facility location problems. We first propose the concepts of satisfaction degree for both vertices and the whole network, which are used to evaluate products assignment. Based on different network satisfaction degree, two models are constructed. The solution to these models is based on Hakimi’s results, and some examples are given to illustrate these models.     

Design,modelling and simulation of a new nonlinear and full adaptive backstepping speed tracking controller for uncertain PMSM

In this study, a new nonlinear and full adaptive backstepping speed tracking control scheme is developed for an uncertain permanent magnet synchronous motor (PMSM). Except for the number of pole pairs, all the other parameters in both PMSM and load dynamics are assumed unknown. Three phase currents and rotor speed are supposed to be measurable and available for feedback in the controller design. By designing virtual control inputs and choosing appropriate Lyapunov functions, the final control and parameter estimation laws are derived. The overall control system possesses global asymptotic stability; all the signals in the closed loop system remain bounded, according to stability analysis results based on Lyapunov stability theory. Further, the proposed controller does not require computation of regression matrices, with the result that take the nonlinearities in quite general. Simulation results clearly exhibit that the controller guarantees tracking of a time varying desired reference speed trajectory under all the uncertainties in both PMSM and load dynamics without singularity and overparameterization. The results also show that all the parameter estimates converge to their true values on account of the fact that reference speed signal chosen to be sufficiently rich ensures persistency of excitation condition. Consequently, the proposed controller ensures strong robustness against all the parameter uncertainties and unknown bounded load torque disturbance in the PMSM drive system. Numerical simulations demonstrate the performance and feasibility of the proposed controller.     

Linguistic power aggregation operators and their application to multiple attribute group decision making

The aim of this study is to develop new linguistic aggregation operators based on the power-average (PA) operator, such as the linguistic power average (LPA) operator, the linguistic weighted PA operator, and the LPOWA operator. We studied some desired properties of the developed operators, such as idempotency and commutativity. Moreover, we developed two approaches to deal with group decision-making problems under linguistic environments. If the weighting vector of the decision makers was known, we developed an approach based on the linguistic weighted PA operator. On the other hand, if the weighting vector of the decision maker was unknown, we developed a different approach based on the LPOWA operator. We also developed new uncertain linguistic operators under uncertain linguistic environments, such as the ULPA operator, the uncertain linguistic weighted PA operator, and the ULPOWA operator. We extended these approaches, which are based on ULWPA and ULPOWA operators, respectively, to solve group decision-making problems under an uncertain linguistic environment. Finally, a practical example is provided to illustrate the multiple-attribute group decision-making process.     

Nonparametric predictive utility inference

We consider the natural combination of two strands of recent statistical research, i.e., that of decision making with uncertain utility and that of Nonparametric Predictive Inference (NPI). In doing so we present the idea of Nonparametric Predictive Utility Inference (NPUI), which is suggested as a possible strategy for the problem of utility induction in cases of extremely vague prior information. An example of the use of NPUI within a motivating sequential decision problem is also considered for two extreme selection criteria, i.e., a rule that is based on an attitude of extreme pessimism and a rule that is based on an attitude of extreme optimism.     

Modified projective synchronization of uncertain fractional order hyperchaotic systems

Base on the stability theory of fractional order system, this work mainly investigates modified projective synchronization of two fractional order hyperchaotic systems with unknown parameters. A controller is designed for synchronization of two different fractional order hyperchaotic systems. The method is successfully applied to modified projective synchronization between fractional order Rössler hyperchaotic system and fractional order Chen hyperchaotic system, and numerical simulations illustrate the effectiveness of the obtained results.     

Fuzzy linear regression and its applications to forecasting in uncertain environment

Linear regression has been used for many years in developing mathematical models for application in marketing, management, and sales forecasting. In this paper, two different sales forecasting techniques are discussed. The first technique involves non-fuzzy abstract methods of linear regression and econometrics. A study of the international market sales of cameras, done in 1968 by John Scott Armstrong, utilized these non-fuzzy forecasting techniques. The second sales forecasting technique uses fuzzy linear regression introduced by H. Tanaka, S. Uejima, and K. Asai, in 1980. In this paper, a study of the computer and peripheral equipment sales in the United States is discussed using fuzzy linear regression. Moreover, fuzzy linear regression is applied to forecasting in an uncertain environment. Finally, some possible improvements and suggestions for further study are mentioned.     

LMI-Based Robust <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> Control of Uncertain Neutral Systems with State and Input Delays

Robust stabilization and robust H_∞ control problems for a class of uncertain neutral system with state and input delays are considered. By choosing a Lyapunov-Krasovskii functional, an alternative delay-dependent sufficient condition for the existence of a controller is derived in terms of linear matrix inequalities. Furthermore, a convex optimization problem can be formulated to obtain an H_∞ controller which minimizes an upper H_∞ norm bound of the closed-loop state-input delayed system.