Mathematical Sciences: Risk Sensitive Stochastic Control

9531276 Fleming风险敏感随机控制研究期望指数代价准则的优化问题。 它提供了随机和确定性（鲁棒控制）方法之间的联系。 风险敏感控制与随机过程的大偏差理论有关。 动态的两个玩家游戏也自然出现在分析中。 对于由受控随机微分方程描述的连续时间模型，利用非线性偏微分方程粘性解方法分析了这些博弈（称为微分博弈）。 这项研究的一部分涉及风险 灵敏控制，具有完整的状态信息（状态反馈）。 将考虑现有理论的扩展以及在工程控制和金融经济学中的应用。 本项目的第二部分涉及部分状态信息（输出反馈）风险敏感控制，其中的理论是欠发达。 分析中的一个关键思想是信息状态。 控制理论中的干扰抑制问题是设计反馈控制律，使系统在存在干扰的情况下保持稳定和满意的性能。 不可预测的系统输入（或干扰）。 在风险敏感随机控制中，扰动被建模为随机事件，并被描述为系统的指数判据 性能已被使用。 优化这种风险敏感标准的反馈控制提供了更好的保护，以防止可能导致非常差的系统性能的罕见干扰。 例如，在数据通信系统中的路由流中，控制设计试图避免由于罕见的重业务突发而导致的长延迟和缓冲器溢出。 风险敏感控制理论还提供了随机控制理论和另一种广泛使用的方法（鲁棒控制）之间的自然联系，其中干扰以确定性（非随机）方式建模。 ***

9531276 Fleming Risk sensitive stochastic control is concerned with the optimization of expected exponential cost criteria. It provides a link between stochastic and deterministic (robust control) approaches. Risk sensitive control is related to large deviations theory for stochastic processes. Dynamic two player games also arise naturally in the analysis. For continuous time models described by controlled stochastic differential equations, these games (called differential games) are analyzed using viscosity solution methods for nonlinear partial differential equations. One part of this research concerns risk sensitive control, with complete state information (state feedback). Extensions of existing theory, and applications to engineering control and financial economics will be considered. A second part of this project concerns partial state information (output feedback) risk sensitive control, where the theory is less well developed. A key idea in the analysis is that of information state. The disturbance attenuation problem in control theory is to design feedback control laws which give system stability and satisfactory performance in the presence of unpredictable system inputs (or disturbances). In risk sensitive stochastic control, disturbances are modeled as random events and an exponential criterion of system performance is used. Feedback controls which optimize such risk sensitive criteria provide better protection against rare disturbances which may cause very poor system performance. For example, in routing flows in data communication systems, the control design seeks to avoid long delays and buffer overflows due to rare bursts of heavy traffic. Risk sensitive control theory also provides a natural link between stochastic control theory and another widely used approach (robust control) in which disturbances are modeled in a deterministic (non-random) manner. ***