Adaptive decentralized control with nonminimum-phase closed-loop channel zeros

We apply retrospective cost adaptive control (RCAC) to a two-channel decentralized disturbance rejection problem. It is shown that the closed-loop channel zeros for each subcontroller consist of the plant zeros and poles of the remaining subcontroller. The nonminimum-phase (NMP) closed-loop channel zeros are included in the modeling information required by RCAC. Two adaptation schemes are presented. In one-controller-at-a-time adaptation, one subcontroller is adapted with the other subcontroller fixed at zero. The first subcontroller is then fixed while the second subcontroller is adapted taking into account the NMP closed-loop channel zeros. We also consider concurrent adaptation, where both controllers are updated at the same time. Finally, we apply this technique to decentralized control of the position and shape of a 2DOF lumped flexible body.