Actuator selection based on singular vector method in linearized Ginzburg-Landau model

In this research based on singular vector method we propose a numerical algorithm to place multiple actuators in a linear system so that the norm of a physical quantity is amplified efficiently. Further, we verify the validity of the proposed method by numerically analyzing the impulse response in a linearized Ginzburg-Landau model, which is known as a simple model of flow fields. Let us briefly introduce the proposed method. We consider a linear model, where the initial physical quantity on some selected points can be set to some values, while that on the other points are set to zero. From the physical point of view, such model corresponds to a model, where impulse input is added from actuators at some selected points. Then, we obtain the state transition matrix associated with the initial and terminal state, and a singular vector decomposition is applied to the matrix to extract the dominant modes. Here, the right singular vectors indicate the sensitivity of the terminal state to the initial state. It is shown that the norm of the terminal state may be maximized when the determinant of the matrices associated with the right singular vectors for the selected points is maximized. Therefore, in this study we select points for actuators by greedy method so that the determinant of such matrices become large as possible, where greedy method is a numerical algorithm that selects each element one by one to obtain the quasi‐optimum solution of combinational problems.