Inverse Problem of LQ-PID Control for TCP/AQM Routers

Abstract

In this paper, we take into considerations of the inverse problem for LQ-PID control. Solving the inverse problem, explicit formulas are developed such that the closed loop system is optimal by an LQ-PID controller. The inverse problem of LQ-PID control is analytically formulated via the frequency-domain and algebraic characterizations of LQR with respect to special forms of the state weighting matrix Q. We apply the LQ-PID control to AQM(Active Queue Management) routers from the viewpoint of the inverse problem. In the controller design procedure, the practical effectiveness of the proposed analysis is demonstrated by the numerical simulation of AQM routers.