Linear Matrix Inequality-Based Design of Structured Sparse Feedback Controllers for Sensor and Actuator Networks

A sensor and actuator network (SAN) is a control system where many sensors and actuators are connected through a communication network. In a SAN with redundant sensors and actuators, it is important to consider choosing sensors and actuators used in control design. Depending on applications, it is also important to consider not only the choice of sensors/actuators but also that of communication channels in which some sensors/actuators are connected. In this paper, based on a linear matrix inequality (LMI) technique, we propose a design method for structured sparse feedback controllers. An LMI technique is one of the fundamental tools in systems and control theory. First, the sparse reconstruction problems for vectors and matrices are summarized. Next, two design problems are formulated, and an LMI-based solution method is proposed. Finally, two numerical examples are presented to show the effectiveness of the proposed method.