Powered exoskeletons have the potential to revolutionize the labor workplace across many disciplines, from manufacturing to agriculture. However, there are still many barriers to adoption and widespread implementation of exoskeletons. One major research gap of powered exoskeletons currently is the development of a control framework to best cooperate with the user. This limitation is first in understanding the physical and cognitive interaction between the user and exoskeleton, and then in designing a controller that addresses this interaction in a way that provides both physical assistance towards completing a task, and a decrease in the cognitive demand of operating the device. This work demonstrates that multi-objective, optimization-based control can be used to provide a coincident implementation of autonomous robot control, and human-input driven control. A parameter called 'acceptance' can be added to the weights of the cost functions to allow for an automatic trade-off in control priority between the user and robot objectives. This is paired with an update function that allows for the exoskeleton control objectives to track the user objectives over time. This results in a cooperative, powered exoskeleton controller that is responsive to user input, dynamically adjusting control autonomy to allow the user to act to complete a task, learn the control objective, and then offload all effort required to complete the task to the autonomous controller. This reduction in effort is physical assistance directly towards completing the task, and should reduce the cognitive load the user experiences when completing the task. To test the hypothesis of whether high task assistance lowers the cognitive load of the user, a study is designed and conducted to test the effect of the shared autonomy controller on the user's experience operating the robot. The user operates the robot under zero-, full-, and shared-autonomy control cases. Physical workload, measured through the force they exert to complete the task, and cognitive workload, measured through pupil dilation, are evaluated to significantly show that high-assistance operation can lower the cognitive load experienced by a user alongside the physical assistance provided. Automatic adjustment in autonomy works to allow this assistance while allowing the user to be responsive to changing objectives and disturbances. The controller does not remove all mental effort from operation, but shows that high acceptance does lead to less mental effort. When implementing this control beyond the simple reaching task used in the study, however, the controller must be able to both track to the user's desired objective and converge to a high-assistance state to lead to the reduction in cognitive load. To achieve this behavior, first is presented a method to design and enforce Lyapunov stability conditions of individual tasks within a multi-objective controller. Then, with an assumption on the form of the input the user will provide to accomplish their intended task, it is shown that the exoskeleton can stably track an acceptance-weighted combination of the user and robot desired objectives. This guarantee of following the proper trajectory at corresponding autonomy levels results in comparable accuracy in tracking a simulated objective as the base shared autonomy approach, but with a much higher acceptance level, indicating a better match between the user and exoskeleton control objectives, as well as a greater decrease in cognitive load. This process of enforcing stability conditions to shape human-exoskeleton system behavior is shown to be applicable to more tasks, and is in preparation for validation with further user studies. / Doctor of Philosophy / Powered exoskeletons are robots that can be worn by users to physically aid them in accomplishing tasks. These robots differ in scale, from single-joint devices like powered ankle supports or lower-back braces for lifting, to large, multi-joint devices with a broad range of capabilities and potential applications. These multi-joint exoskeletons have been used in many applications such as medical rehabilitation robots, and labor-assisting devices for enhancing strength and avoiding injury. Broader use and adoption in industry could have a great positive impact on the experience of workers performing any heavy-labor tasks. There are still barriers to widespread adoption, however. When closely interacting with machinery like a powered exoskeleton, workers want guarantees of saftey, trust, and cooperation that current exoskeletons have not been able to provide. In fact, studies have shown that industrial devices capable of providing significant assistive force when accomplishing a task, also tend to impart additional, uncomfortable disturbance forces on the user. For example, a lower-body exoskeleton meant to help in lifting tasks might make the simple act of walking more difficult, both physically and mentally. There is a need for exoskeletons that are intuitively cooperative, and can provide both physical assistance towards completing a task and cognitive assistance that makes coordinating with the human user easier. In this dissertation we examine the control problem of powered exoskeletons. In the past, many powered exoskeleton controllers are direct, scripted controllers with exact objectives, or actions tied only to human input. To go beyond this, we leverage "multi-objective-control", originally designed for humanoid robots, which is capable of controlling the robot to accomplish multiple goals at the same time. This approach is the base on which a more complex controller can be created. We show first that the multi-objective control can be used to achieve human desired actions and robot autonomous control tasks at the same time, with a parameter to trade-off which actor, the human or the robot, has the priority control at that time. This framework has the capacity to allow the human to instruct the robot in tasks to accomplish, and then robot can fully mimic the user, offloading the physical effort required to accomplish the task. It is proposed that this offloading of effort from the user will also lower the cognitive load the user is under when actively commanding the exoskeleton. To test this hypothesis, a user study is conducted where human operators work with an upper-body powered exoskeleton to complete a simple reaching task. This study shows that on average, the more assistance the exoskeleton provides to the user, the lower their mental demand is. Additionally, when responding to new challenges or sudden disturbances, the robot can easily cooperate, balancing its own autonomy with the user's to allow the user to respond as they need to their changing environment, then resume active assistance when the change is resolved. Finally, to guarantee that the exoskeleton responds quickly and accurately to the user's intentions, a new strategy is derived to update the robot's internal objectives to match the users' goals. This strategy is based on the assumption that the exoskeleton knows what type of task the user is trying to complete. If this is true, then the exoskeleton can estimate the users objectives from the actions they task, and ensure assistance towards completing the task. This control design is proven in simulation, and in preparation for followup studies to evaluate the user experience of this improved strategy.