Objective: How much a person should be allowed to interact with a controlled machine? If that machine is safety critical, and if the computer that oversees its operation is essential to its operation and safety, the answer may be that the person should not be allowed to interfere with its operation at all or very little. Moreover, whether the person is a novice or an expert matters. Intellectual Merit: This research algorithmically resolves the tension between the need for safety and the need for performance, something a person may be much more adept at improving than a machine. Using a combination of techniques from numerical methods, systems theory, machine learning, human-machine interfaces, optimal control, and formal verification, this research will develop a computable notion of trust that allows the embedded system to assess the safety of the instruction a person is providing. The interface for interacting with a machine matters as well; designing motions for safety-critical systems using a keyboard may be unintuitive and lead to unsafe commands because of its limitations, while other interfaces may be more intuitive but threaten the stability of a system because the person does not understand the needs of the system. Hence, the person needs to develop trust with the machine over a period of time, and the last part of the research will include evaluating a person's performance by verifying the safety of the instructions the person provides. As the person becomes better at safe operation, she will be given more authority to control the machine while never putting the system in danger. Broader Impacts: The activities will include outreach, development of public-domain software, experimental coursework including two massive online courses, and technology transfer to rehabilitation. Outreach will include exhibits at the Museum of Science and Industry and working with an inner-city high school. The algorithms to be developed will have immediate impact on projects with the Rehabilitation Institute of Chicago, including assistive devices, stroke assessment, and neuromuscular hand control. Providing a foundation for a science of trust has the potential to transform rehabilitation research.