Structured Model Reference Adaptive Control in the presence of bounded disturbances

We present a novel method to carry out Structured Model Reference Adaptive Control (MRAC) of poorly determined systems (for example, imprecise knowledge of the plant matrices) that are subject to bounded unknown disturbances. In the case of most mechanical systems, a sub-set of the governing differential equations are perfectly known, for example, the description of the kinematic relations. It is recognized that these equations are free of disturbance forces/torques as well. Hence all the learning and adaptation for MRAC should be confined to the momentum level equations (acceleration differential equations) governing the system: dynamics. For the large class of systems considered, only the momentum equations are perturbed by unknown disturbances. While taking into account this special structure for mechanical systems, robust adaptive feedback control laws are derived that ensure stability and bounded tracking errors even in the presence of disturbance. We demonstrate our results through numerical simulation of example problems.