Adaptive LQG Control with Loop Transfer Recovery

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 Q~. 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 filter 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 sensitivity/loop recovery for off-line designs. The robustness properties of the new algorithm are demonstrated by simulation results.