Abstract. This dissertation considers the general problem of controlling dynamic systems subject to large-scale sensor and actuator uncertainties.  The assumption is made that the uncertainty is limited to either pure rotation or that each axis is rotated independently. Although uncertainty can appear in more general forms, this representation describes a ``net-effect'' when the ideal axes have become misaligned that is of fundamental importance to the control of numerous systems.  Adaptive observers and controllers are introduced that guarantee perfect reference trajectory tracking even with the appearance of these large-scale uncertainties.  The following problems are considered: (I) the problem of rigid-body attitude tracking with vector measurements, unknown gyro bias, and unknown body inertia matrix is addressed for the first time.   (II) An adaptive observer is developed for the scenario where the control is pre-multiplied by an unknown constant scaling and rotation matrix which gives a non-affine representation of the uncertainty.  An observer and control are shown through a stability analysis to guarantee perfect tracking and to establish a separation like property for this problem.  (III)  The class of uncertainties where each axis of the control is independently misaligned is examined.  The problem is split into studies of in-plane and out-of-plane misalignment angles given that they exhibit fundamental technical differences in establishing convergence.  Where possible, rigorous stability proofs are given for a series of adaptive observers.  The structure of the observers assure that the estimates do not introduce any singularities into the control problem other than those inherent from the misalignment geometry.  The inherent singularities are avoided through the use of projection schemes which allow for extension to the control problem.  This work represents the first significant effort to develop observers and controllers for this class of misalignments.