An uncertain random variable is a measurable function from a probability space to the set of uncertain variables. In this paper, subadditivity property of chance measure and some inequalities on expected value for uncertain random variables including Jensen’s Inequality, Liapunov Inequality and cp Inequality are proved. Based on these inequalities, linear property and other properties of conver...

Abstract This article researches the interval‐driven variable convergence rate robust stability/stabilization of uncertain impulsive stochastic systems. First, a new conception stability for systems is presented in conjunction with idea generalized pole configurations. Also, criterion given, which can reflect and regulate system state. In addition, algorithm designed by means an stabilization m...

Entropy is a measure of the uncertainty associated with an uncertain variable. So far, entropy, quadratic entropy and sine entropy have been proposed for uncertain variables. This paper will propose a triangular entropy for uncertain variables, and verify its properties such as translation invariance and positive linearity.

On the quadratic stabilization of uncertain linear time varying systems by means of linear state variable feedback, Wei introduced the concept of antisymmetric stepwise configuration (ASC) and proved that having this configuration is a necessary and sufficient condition for uncertain linear systems to be quadratically stabilizable by means of a linear state variable feedback. However, because h...

In this paper, we extend the sliding mode idea to a class of unmatched uncertain variable structure systems. This method is achieved with introducing a new terminal sliding variable and the finite time stability of proposed method is proved using a new particular finite time condition in both reaching and sliding phases. In reaching phase new sliding mode controller is derived to guarantee the ...

Shortest path problem is a fundamental problem in network optimization and combinational optimization. The existing literature mainly concerned with the problem in deterministic, stochastic or fuzzy environments by using different tools. Different from the existing works, we investigate shortest path problem by regarding arc lengths as uncertain variables which are employed to describe the beha...

The classic newsboy problem assumes the market demand to be a random variable. However, when the decision maker wants to expand the market share, he has to provide a subjective estimate of new market demand distribution due to the lack of historical data. Thus, randomness and uncertainty simultaneously appear in a newsboy problem. The aim of this work is to extend the analysis of the classic ne...

wind power generation is variable and uncertain. in the power systems with high penetration of wind power, determination of equivalent operating reserve is the main concern of systems operator. in this paper, a model is proposed to determine operating reserves in simultaneous market clearing of energy and reserve by stochastic programming based on scenarios generated via monte carlo simulation ...

1 School of Electrical and Information Engineering, Xihua University, Chengdu 610096, China 2 School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu 610054, China 3 School of Electrical and Electronic Engineering, The University of Adelaide, Adelaide SA 5005, Australia 4 School of Engineering and Science, Victoria University, Melbourne, VIC 8001, Austra...