Research on Stochastic Systems and Filtering Theory and Applications

该提案涵盖了随机控制的四个主要领域。第一类是关于Ito和宽带噪声驱动系统的奇异摄动随机系统，有限和无限时间问题，参数奇异性和非线性滤波问题的逼近。第二个涉及繁忙交通中的排队和生产系统的控制、逼近和极限问题，以及相关的数值方法。特殊情况包括路径选择和奇异控制，无限时间间隔的控制，优先级调度的数值方法，以及在具有多条线路的虚拟电路系统中出现的问题的类型。第三个领域是有效的数值算法，其中将强调反射、奇异、遍历、约束和繁忙的交通问题，因为可用于这些问题的相对较少。最后一类涉及基于实际观测数据的高维随机系统的参数控制的有效和鲁棒蒙特卡罗优化的一些新方法。

The proposal covers four major areas in Stochastic Control. The first concerns singularly perturbed stochastic systems for both Ito and wide bandwidth noise driven systems, finite and infinite time problems, parametric singularities and approximations to the nonlinear filtering problems. The second concerns control, approximation and limit problems for queues and production systems in heavy traffic, and associated numerical methods. Special cases includes routing and singular control, control over an infinite time interval, numerical methods for scheduling under priorities, and the types of problems which occur in virtual circuit systems with many lines. The third area is that of efficient numerical algorithms, where reflected, singular, ergodic, constrained and heavy traffic problems will be emphasized, since there is relatively little available for these problems. The last class concerns some promising new approaches to the efficient and robust monte carlo optimization of parametrized controls of stochastic systems of high dimension, where the control is based on the actual observed data.