My dissertation considers 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 numerous subsystems with a reduced number of 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, which increases the convergence rate by orders of magnitude compared with previous methods. In addition to closed loop control, open loop procedures using the SVD and SNMF are compared with previous scheduling procedures, demonstrating significant performance improvements.
The dissertation presents theoretical results for the controllability of systems using the row-column structure and for the stability and performance of 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.
Winck, R.C. and W.J. Book, “Dimension Reduction for First-Order LTI Subsystems.” IEEE Transactions on Control Systems Technology. (in preparation)
Winck, R.C., and W.J. Book, “Dimension Reduction in a Feedback Loop using the SVD: Results on Controllability and Stability.” Automatica, 2012. (in revision)
Winck, R.C. and W.J. Book, “Methods for Computing the SVD Rank-one Approximation in a Feedback Loop,” ASME Dynamic Systems and Control Conference, October 2012.
Winck, R., J. Kim, W.J. Book, and H. Park, “Command Generation Techniques for a Pin Array using the SVD and SNMF,” International IFAC Symposium on Robot Control, September 2012.
Winck, R., W.J. Book, “A Control Loop Structure Based on Semi-Nonnegative Matrix Factorization for Input-Coupled Systems,” IEEE American Control Conference, June 2012. *Best Session Presentation
Winck, R., W.J. Book, “A Control Loop Structure Based on Singular Value Decomposition for Input-Coupled Systems,” ASME Dynamic Systems and Control Conference, October 2011. *Best Student Paper Finalist