A <Emphasis Type="Italic">d</Emphasis>-person Differential Game with State Space Constraints

We consider a network of d companies (insurance companies, for example) operating under a treaty to diversify risk. Internal and external borrowing are allowed to avert ruin of any member of the network. The amount borrowed to prevent ruin is viewed upon as control. Repayment of these loans entails a control cost in addition to the usual costs. Each company tries to minimize its repayment liability. This leads to a d -person differential game with state space constraints. If the companies are also in possible competition a Nash equilibrium is sought. Otherwise a utopian equilibrium is more appropriate. The corresponding systems of HJB equations and boundary conditions are derived. In the case of Nash equilibrium, the Hamiltonian can be discontinuous; there are d interlinked control problems with state constraints; each value function is a constrained viscosity solution to the appropriate discontinuous HJB equation. Uniqueness does not hold in general in this case. In the case of utopian equilibrium, each value function turns out to be the unique constrained viscosity solution to the appropriate HJB equation. Connection with Skorokhod problem is briefly discussed.     

Asymptotic Analysis of State Constrained Semilinear Optimal Control Problems

The asymptotic behavior of state-constrained semilinear optimal control problems for distributed-parameter systems with variable compact control zones is investigated. We derive conditions under which the limiting problems can be made explicit. We gratefully acknowledge the support of the DAAD. The paper was prepared during the visit of the first author at the Institute of Applied Mathematics II, University Erlangen-Nuremberg in 2003.     

Field-based hypotheses on advancing standards for mathematical practice

The Common Core State Standards in Mathematics (CCSSM, 2010) are organized around two types of standards: the standards for mathematical content and standards for mathematical practice. The central goal of this paper is to present cognitive and instructional analyses of standards for mathematical practice through a discussion of field-based activities with inservice secondary mathematics teachers and students. A potential value of the study is that it provides researchers with specific field-based hypotheses on advancing standards for mathematical practice.     

一类半线性双曲系统的状态观测问题

本文考虑一类半线性双曲系统的状态观测问题,给出了一个(求解)算法并证明了其在某种相当强的意义上的有效性.     

Carleman estimates for stochastic parabolic equations with Neumann boundary conditions and applications

By a dual method, two Carleman estimates for forward and backward stochastic parabolic equations with Neumann boundary conditions are established. Then they are used to study a null controllability problem and a state observation problem for some stochastic forward parabolic equations with Neumann boundary conditions.     

SEQUENTIAL QUADRATIC PROGRAMMING METHODS FOR OPTIMAL CONTROL PROBLEMS WITH STATE CONSTRAINTS

A Kind of direct methods is presented for the solution of optimal control problems with state constraints.These methods are sequential quadratic programming methods.At every iteration a quadratic programming which is obtained by quadratic approximation to Lagrangian function and Linear approximations to constraints is solved to get a search direction for a merit function.The merit function is formulated by augmenting the Lagrangian funetion with a penalty term.A line search is carried out along the search direction to determine a step length such that the merit function is decreased.The methods presented in this paper include continuous sequential quadratic programming methods and discreate sequential quadrade programming methods.     

基于MATLAB的异步电动机线性化控制系统的仿真

从异步电动机在同步旋转坐标系下的状态方程出发，在一定的条件下，对其系数矩阵简化．推出异步电动机的线性化控制模型．并基于该模型得出异步电动机的线性化控制系统．以给定电机为例，对该模型的有效性、响应用MATLAB进行仿真分析．验证的结果说明上述模型具有实用价值．