Characteristics, Nonlinearity of Statistical Control and Relations with Dynamic Game Theory

摘要

The PI was awarded a short-term innovative research grant through the University of North Dakota. The grant period was 15 April 2005 to 14 January 2006. However, during the grant period the PI transferred to Temple University in August 2005. So, the PI is submitting the final progress report with the results that the PI obtained during 15 April 2005 to 31 August 2005. The main objective of this proposal was to develop statistical control theory. Statistical control is a generalization of Kalman's linear-quadratic-Gaussian control, where one optimizes the probability density of the performance index by controlling the cumulants. A statistical controller will have better performance and stability margin than the linear-quadratic-Gaussian controller. In this project, the authors investigated the characteristics of linear statistical controllers, developed nonlinear statistical control theory, and utilized the statistical control paradigm in dynamic game theory.