Research Initiation Award: Optimal Stationary Risk Sensitive Log Control

风险敏感型线性二次型高斯(LQG)控制是对经典LQG控制技术的一种改进，它将噪声引起的系统状态的大偏差引入到设计指标中。研究的目的是对定义在无限时间区间上的系统得到明确的风险敏感LQG控制结果，并建立所得到的线性系统设计与已有设计之间的关系。研究的主要内容包括风险敏感LQG代价泛函的大偏差性质的分析，完全观测系统和部分观测系统的最优平稳风险敏感LQG控制器的设计，风险敏感LQG控制与H_无穷控制关系的分析评价以及静态风险敏感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着陆。这项研究有望为线性平稳随机系统带来一种新的设计方法，与标准的LQG设计相比，该方法具有更好的噪声抑制能力。另一个潜在的好处是一个新的观点，从这个角度可以评估重要的H-无穷大设计方法。

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.