A control loop structure based on semi-nonnegative matrix factorization for input-coupled systems

This paper introduces a control structure based on the semi-nonnegative matrix factorization (SNMF) to simultaneously control multiple subsystems with a reduced number of inputs. The inspiration for this new control construct is a pin array human machine interface, called Digital Clay. Digital Clay uses a row-column method to control many actuators with a few inputs. The singular value decomposition (SVD) was previously studied to simultaneously control all of the actuators when using the row-column method. However, the SVD technique is not physically implantable in the row-column structure of Digital Clay due to the non-negativity constraints of the control signal. This paper proposes a system based on the SNMF, which is a low-rank approximation method with non-negativity constraints. An SNMF algorithm is presented, and its implementation in a feedback control loop, called the SNMF System, is discussed. Simulation results demonstrate the effectiveness of the SNMF System.