In this paper, an uncertain version of Borel-Cantelli lemma is proved. Besides, some convergence theorems of continuous uncertain measure are proposed. Using these theorems, it is proved that the uncertainty distribution function of the uncertain integral on a real function is a normal one.

A method is proposed to compute robust inner-approximations the backward reachable set of nonlinear systems and generate a control law that drives trajectories starting in these target set. The merges dissipation inequalities integral quadratic constraints (IQCs) with both hard soft IQC factorizations, allowing for variety perturbations including parametric uncertainty, unmodeled dynamics, unce...

Uncertainty theory is a branch of mathematics based on normality, monotonicity, self-duality, countable subadditivity, and product measure axioms. Different from randomness and fuzziness, uncertainty theory provides a new mathematical model for uncertain phenomena. A key concept to describe uncertain quantity is uncertain variable, and expected value operator provides an average value of uncert...

For uncertain differential equations, we cannot always obtain their analytic solutions. Early researchers have described the Euler method and Runge–Kutta method for solving uncertain differential equations. This paper proposes a new numerical method—Adams method to solve uncertain differential equations. Some numerical experiments are given to illustrate the efficiency of our numerical method. ...

Uncertain process is an important tool tomodel dynamic uncertain systems. This paper proposes a special type of uncertain processes, named contour processes, whose sample paths can be classified by their inverse uncertainty distributions. It is shown that the set of contour processes is closed under the extreme value operator and the time integral operator as well as the monotone function. As a...

*Correspondence: [email protected] Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China Abstract Uncertain differential equations have been widely applied to many fields especially to uncertain finance. Unfortunately, we cannot always get the analytic solution of uncertain differential equations. Early researchers have put up a numerical method based on t...

In this work, we propose a tube-based model predictive control (MPC) scheme for state- and input-constrained linear systems subject to dynamic uncertainties characterized by integral quadratic constraints (IQCs). particular, extend the framework of $\rho$</tex-mat...