Research Initiation Award: Optimal Stationary Risk Sensitive Log Control

风险敏感线性二次高斯控制（LQG）是对经典LQG控制技术的改进，将噪声引起的系统状态大偏差纳入设计规范。本研究的目的是获得在无限时间区间上定义的系统的风险敏感LQG控制的确定结果，并建立线性系统的结果设计与现有设计之间的关系。研究的主题包括分析风险敏感LQG成本函数的大偏差特性，设计完全和部分观测系统的最优平稳风险敏感LQG控制器，分析评价了风险敏感LQG控制与h∞控制的关系，以及平稳风险敏感LQG控制在望远镜指向等重要物理控制问题中的应用；机器人手臂指向和飞机降落。该研究有望为线性平稳随机系统提供一种新的设计方法，与标准LQG设计相比，该系统具有更好的噪声抑制能力。一个额外的潜在好处是一个新的观点，从重要的h -∞设计方法可以评估。

Risk Sensitive Linear-Quadratic-Gaussian (LQG) control is a modification of the classical LQG control technique that incorporates noise- induced large deviations of the system state into the design specifications. The goal of the research is to obtain definite results for Risk Sensitive LQG control for systems defined on an infinite time interval and to establish the relationship between the resulting design and existing designs for linear systems. The main themes of the research include an analysis of the large deviations properties of the Risk Sensitive LQG cost functional, design of optimal stationary Risk Sensitive LQG controllers for completely and partially observed systems, analytical evaluation of the relationship between Risk Sensitive LQG control and H-infinity control and the application of stationary Risk Sensitive LQG control to important physical control problems such as telescope pointing, robot arm pointing and airplane landing. The research is expected to result in a new design methodology for linear stationary stochastic systems that has improved noise rejection capabilities as compared to the standard LQG design. An additional potential benefit is a new viewpoint from which the important H-infinity design methodology can be evaluated.