Fluid flow control applications of ℋ2 optimal actuator and sensor placement

In the control of distributed parameter systems, the problem of effective actuator and sensor placement is not well understood, and the use of suboptimal placement methodology is common. We discuss a technique we recently proposed that iterates toward the optimal actuator and sensor placement for ℋ
2
synthesis, minimizing the closed-loop ℋ
2
norm from exogenous inputs to exogenous outputs. The iteration is based on an efficient computation of the ℋ
2
norm's gradient with respect to actuator and sensor placements.We demonstrate the technique on the Orr-Sommerfeld/Squire model of fluid flow, and review previous results from the linearized Ginzburg-Landau model. Finally, we use these results to analyze the validity of previous placement approaches.