$$ \varvec{H}_{\infty } $$ H ∞ Optimal Actuator and Sensor Placement for Linear Systems

Abstract

Optimizing the placement of actuators and sensors for the control and monitoring tasks is one of the most important and challenging research topics in the comprehensive aircraft control systems. This paper proposes a new way to address this issue, in which Heat and Wave Equation discretized by the Finite Differential Method (FDM) were used to describe the inputs/outputs propagation mode for control systems. By utilizing a robust controller design to the models, the complicated optimal actuator and sensor placement problem can be transformed to a judgement on specific characteristics. The feedback controller was designed based on the \( H_{\infty } \) Optimal Control Principles, where the external input \( w \) is considered to be the perturbation. The optimal placement is able to be obtained at the place with the best performed controller. The simulation results show that it is reasonable to solve the actuator and sensor placement optimization problem using the proposed method and the results for the two models shared an agreeable trend. Therefore, the process of optimizing the placement of sensors and actuators for control and monitoring system could serve as a natural extension to other structures.