A controlled Markov process in a Hilbert space and an ergodic cost functional are given for a control problem that is solved where the process is a solution of a parameter-dependent semilinear stochastic differential equation and the control can occur only on the boundary or at discrete points in the domain. The linear term of the semilinear differential equation is the infinitesimal generator ...

For the detection of contaminations in urban water supply networks we introduce a continuous optimal control model governed by partial differential equations. We derive a linear mixedinteger model by discretization of the dynamics of the partial differential equations and by approximations to the cost functional. Finally, we present numerical results for artificial and real-world networks.

An optimal control problem is studied for a linear mean-field stochastic differential equation with a quadratic cost functional. The coefficients and the weighting matrices in the cost functional are all assumed to be deterministic. Closed-loop strategies are introduced, which require to be independent of initial states; and such a nature makes it very useful and convenient in applications. In ...

One of the most efficient methods for determining the equilibria of a continuous parameterized family of differential equations is to use predictor-corrector continuation techniques. In the case of partial differential equations this procedure must be applied to some finite dimensional approximation which of course raises the question of the validity of the output. We introduce a new technique ...

Differential equations are extensively used for modeling dynamics of physical processes in many scientific fields such as engineering, physics, and biomedical sciences. Parameter estimation of differential equation models is a challenging problem because of high computational cost and high-dimensional parameter space. In this article, we propose a novel class of methods for estimating parameter...

Abstract The fractional differential equation is used to quantify the cost management system of Chinese cross-border e-commerce enterprises. At same time, influence mechanism this preliminarily explored in paper. Then paper makes quantitative and simulation tests on balance stability control e-commerce. end report, impact new laws regulations international China analyzed. results show that mult...