SUMMARY

The thesis focuses on the application of singular value decomposition (SVD) and semi-nonnegative matrix factorization (SNMF) within feedback control systems, called the SVD System and SNMF System, to control many subsystems with reduced control inputs. The subsystems are coupled using a row-column structure that constrains the inputs to be rank-one when properly ordered in a matrix form. Past techniques for controlling systems in this row-column structure have focused on scheduling procedures that offer limited performance. The SVD and SNMF Systems permit simultaneous control of every subsystem, offering orders of magnitude improvement in the convergence rate over previous methods. In addition to these closed loop techniques, open loop and command generation procedures are presented and compared with previous scheduling procedures, demonstrating significant performance improvements. This thesis presents theoretical results for the controllability of systems using the row-column structure and for the stability and performance for the SVD and SNMF Systems. In addition to theoretical analysis, practical challenges to the implementation of the SVD and SNMF Systems are examined, such as the need for physical multiplication of the row and column inputs and the need to compute the SVD and SNMF online, in real-time. Numerous simulation examples are provided that demonstrate the theoretical concepts, compare the performance of the various techniques, and raise new questions. In particular a dynamic simulation of a pin array device, called Digital Clay, and two physical demonstrations are used to assess the feasibility of the SVD and SNMF Systems for specific applications.