Actuator selection focusing on time-series input and output in a linearized Ginzburg-Landau model

We develop a numerical algorithm that optimizes actuator locations in a discrete-time linear time-invariant system by focusing on the time-series input and output so that the system could be controlled efficiently by small inputs. The advantage of our method is that it has a low computational cost and could be applied to a high dimensional system, which is important from the practical point of view. In our method the sensitivity of the time-series output to the time-series input is clarified by applying a singular value decomposition to a matrix that relates them. Then, actuator locations are selected by a determinant-based greedy algorithm so that the determinant of a matrix associated with the sensitivity is maximized, where the greedy algorithm is a numerical method that selects each element one by one to gain the quasi‐optimum solution of combinational problems. Here, the duality between sensor and actuator placement problems is employed. Further, actuator locations in a linearized Ginzburg-Landau model, which is known as a simple model of fluid phenomena, is optimized by the proposed method, and its effectiveness is numerically evaluated by controlling the model by a linear quadratic regulator. We show that the model could be controlled more efficiently with small inputs when actuators are placed by the proposed method based on the determinant than when they are placed at random or based on the trace.