Operator Theoretic Methods in the Control of Distributed and Nonlinear Systems.

摘要

In this final technical report, we outline a number of problems in robust and nonlinear control theory which we have studied using an operator theoretic methodology. In particular, we discuss an approach to the structured singular value and mu-synthesis procedure in robust control which is based on a new type of interpolation method. We consider nonlinear extension of H-infinity optimization theory and investigate corresponding question in causality which arise in this area. Moreover, we discuss a saddle-point, game-theoretic approach to such problems. Further. we sketch the application of our skew Toeplitz methods to distributed (infinite dimensional) H-infinity control. We also consider and h-infinity of approach to sampled data systems based on a lifting method, as well as consider problem using h-infinity - H2 combined suboptimal controller. Finally we list some of our results in image processing and computer vision as applied to visual tracking.