In this paper we propose for scalar plants an adaptive LQG controller with adaptive input sensitivity function/loop transfer recovery of an associated adaptive LQ design. The sensitivity recovery can be viewed as a frequency-shaped loop recovery where the weights involve a sensitivity function. The adaptive loop/sensitivity recovery is achieved by feeding back the estimation residuals to the control through a stable bounded input, bounded output (BIBO) adaptive filter Qk. For simplicity we consider fixed but uncertain plants in the model set and identification schemes where there are consistent parameter estimates. For non-minimum phase plants an asymptotic partial recovery is achieved via a recursive least squares update of the BIBO fiIter Qk. The degree of recovery can be prescribed a priori between zero and the maximum possible. For the case of minimum phase plant estimates, full loop recovery may be achieved asymptotically by prescribing a maximum degree of recovery.
The motivation for proposing the new adaptive control algorithm is to enhance robustness of adaptive LQG designs, taking advantage of the robustness enhancement properties of sensitivitylloop recovery for off-line designs. The robustness properties of the new algorithm are demonstrated by simulation results.