Mathematical Sciences: Risk Sensitive Stochastic Control

点击翻译按钮获取中文摘要

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. ***