SUMMARY

The proposed research 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 multiple subsystems with reduced control inputs. The motivation for this work is a pin array human machine interface, called Digital Clay. Digital Clay uses a technique to control the pins, called the row-column method, which reduces the number of control valves from nxm to n+m. The SVD and SNMF Systems permit simultaneous, dependent control of sets of subsystems that are coupled by the row-column method. The use of the SVD differs from previous control applications because it reduces the dimension of the control inputs. The application of the SNMF in control systems is new in itself. The proposed research will include theoretical analysis of the SVD and SNMF Systems as well as the physical implementation of both. Additionally, an open loop procedure will be developed that uses the SVD and the SNMF to improve on the line scanning procedure currently used with Digital Clay. These open loop methods will also be applied as command generators for the SVD and SNMF Systems.