Actuator placement optimization by determinant-based greedy method in linearized Ginzburg-Landau model*

In this research a numerical algorithm is developed to optimize actuator placement in a linear system with impulsive forcing so that the quantity of state can be varied effectively in various situations. Further, the availability of the proposed method is evaluated by applying it to a linearized Ginzburg-Landau model, which is known as a simple model of fluid phenomena. We consider a multidimensional linear system, where some of the elements in the input is given by a delta function, while the others are set to zero. From the physical point of view this corresponds to a situation where impulsive forcing is added to the system from multiple actuators. We apply singular value decomposition to the matrix which connects the coefficient of input and terminal state. Then, actuator locations are selected by greedy method so that the determinant of a matrix associated with right singular vectors and singular values is maximized, where greedy method is a numerical method which selects elements one by one to gain the quasi‐optimum solution of combinational problems. In the numerical simulation of linearized Ginzburg-Landau model we show that the quantity of state can be varied more effectively by actuators placed by the proposed method than by those placed randomly or according to the trace instead of the determinant of the matrix mentioned above.