Abstract
This paper studies the relationship between state feedback policies and disturbance response policies for the standard Linear Quadratic Regulator (LQR). For open-loop stable plants, we establish a simple relationship between the optimal state feedback controller ut = K*xt and the optimal disturbance response controller ut = L(H)*;1wt-1 +...+ L(H)*;1wt-H with H-order. Here xt, wt, ut stands for the state, disturbance, control action of the system, respectively. Our result shows that L(H)*,1 is a good approximation of K* and the approximation error ∥K* — L(H)*;1∥ decays exponentially with H. We further extend this result to LQR for open-loop unstable systems, when a pre-stabilizing controller K0 is available.
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