Lower bounds on the cost functional for systems governed by partial differential equations

Given two systems, one governed by a partial differential equation of a parabolic type and the other governed by a partial differential equation of a hyperbolic type, a cost functional is defined. For each system, an inequality is derived. From these inequalities, lower bounds on the cost functional can be estimated.     

椭圆-抛物系统的近似能控性

设计了两类控制器同时作用于椭圆-抛物系统:一类是传统的内部控制(分布控制器);另一类是以一个时变系数形式描述的内部控制(块控制器,κ(t)只是和时间有关,而与空间位置x没有关系,所以称块控制器,是相对于分布控制而言的).由于这里讨论的系统是非线性的,也只能得到全局近似能控性,不能得到精确零能控性.设计这样的控制器的目的...     

Monte-Carlo estimation of time-dependent statistical characteristics of random dynamical systems

The problem of estimating the time-dependent statistical characteristics of a random dynamical system is studied under two different settings. In the first, the system dynamics is governed by a differential equation parameterized by a random parameter, while in the second, this is governed by a differential equation with an underlying parameter sequence characterized by a continuous time Markov chain. We propose, for the first time in the literature, stochastic approximation algorithms for estimating various time-dependent process characteristics of the system. In particular, we provide efficient estimators for quantities such as the mean, variance and distribution of the process at any given time as well as the joint distribution and the autocorrelation coefficient at different times.     

Boundary Controllability and Observability of a One-Dimensional Nonuniform SCOLE System

A hybrid system, composed of an elastic beam governed by an Euler-Bernoulli beam equation with variable coefficients and a linked rigid body governed by an ordinary differential equation, is considered. Various controllability/observability properties of the system under bounday control/observation are studied. It is shown that an open-loop smooth/singular controller of either torque control or force control is sufficient to make the system exactly controllable in arbitrarily short time duration. The work was carried out with the support of the National Natural Science Foundation of China and the Russian Foundation for Fundamental Researches, Grant 02-01-00554.     

Uniform stability properties of switched systems with switchings governed by digraphs

Characterizations of various uniform stability properties of switched systems described by differential inclusions, and whose switchings are governed by a digraph, are developed. These characterizations are given in terms of stability properties of the system with restricted switchings and also in terms of Lyapunov functions.     

Direct solution of a riccati equation arising in stochastic control theory

We study a regulator problem for a system governed by a linear stochastic differential equation with unbounded coefficients in Hilbert spaces.     

Implications of vector attachment and host grooming behaviour for vector population dynamics and distribution of vectors on their hosts

Towards gaining a mechanistic understanding of the co-feeding transmission dynamics of tick-borne diseases, we develop a delay differential equation model for vector-host population dynamics. In addition to the intrinsic demographic dynamics of both vector and host populations, the model has the distribution dynamics of vector individuals on hosts governed by vector attachment and host grooming behaviour. We introduce the concept of basic infestation number, derive analytic formulae for calculating it and use these formulae to characterize the distribution patterns. We also show how some of these patterns naturally lead to bi-stability and nonlinear oscillations in the vector and host populations.     

Systems governed by ordinary differential equations with continuous,switching and impulse controls

Optimal control problem for systems governed by ordinary differential equations with continuous, switching and impulse controls are studied. It is proved that the value function of the problem is the unique viscosity solution of the corresponding Hamilton-Jacobi-Bellman system.     

On the differential variational inequalities of parabolic‐elliptic type

We consider a model of infinite dimensional differential variational inequalities formulated by a parabolic differential inclusion and an elliptic variational inequality. The existence of global solution and global attractor for the semiflow governed by our system is proved by using measure of noncompactness. Copyright © 2017 John Wiley & Sons, Ltd.     

A FINITE ELEMENT COLLOCATION METHOD FOR TWO-PHASE INCOMPRESSIBLE IMMISCIBLE PROBLEMS

Two-phase,incompressible,immiscible flow in porous media is governed by a coupled system of nonlinear partial differential equations.The pressure equation is elliptic, whereas the concentration equation is parabolic,and both are treated by the collocation scheme.Existence and uniqueness of solutions of the algorithm are proved.A optimal convergence analysis is given for the method.