Brain-computer interfaces (BCI) can assist paralyzed individuals and amputees by translating their neural activity into movements of a BCI plant, such as a computer cursor or prosthetic limb. For many years, the field sought offline decoders that could best map neural activity to arm movements. It has become increasingly recognized that designing an effective online, closed-loop decoder is quite a different challenge. A key difference is that, in a closed-loop setting, the subject receives sensory feedback about the state of the BCI plant and can compensate for errors by generating new neural activity patterns. To engineer clinically-viable, closed-loop BCI systems, many fundamental questions about the neural underpinnings of their performance must be answered. Can subjects generate arbitrary neural activity patterns to compensate for errors? Do subjects form an internal model of the BCI plant to achieve proficient control in the presence of noisy, delayed feedback? Do subjects exploit the redundancy inherent in the mapping from neural activity to BCI plant kinematics to maximize control accuracy? A critical roadblock for answering these questions is the lack of an appropriate statistical framework to rigorously analyze closed-loop BCI data on a timestep-by-timestep basis. We propose to develop such a framework inspired by control theory, in close conjunction with novel closed-loop BCI experiments. We will train non-human primates to perform dextrous control of a BCI cursor using neural activity recorded in primary motor cortex with chronic, multi-electrode arrays. We will test the hypothesis that BCI learning depends on constraints imposed by the underlying neural circuitry. In parallel, we will develop and validate algorithms to explain the observed, high-dimensional neural activity at each timestep by accounting for the sensory feedback, subject's internal model of the BCI cursor, and behavioral task goals. We will then leverage the developed algorithms to investigate whether subjects can exploit neural redundancy during BCI control. Broader Impact: We envision five areas of broader impact. First, BCI systems promise to dramatically improve the quality of life for disabled patients. Clinical trials are ongoing, so opportunities exist to translate our research directly and in the near term into clinical practice. Second, our understanding of the neural basis for arm movement control is still incomplete, in large part because the system is so complex. BCIs provide a simplified motor control system, where a well-defined relationship exists between neural activity and movement. As such, BCIs provide a novel experimental testbed to investigate the neural mechanisms of motor control and learning. Third, the statistical framework we develop may be applicable to the study of feedback control systems in other domains. Fourth, with the advent of large-scale neural recordings, systems neuroscience is becoming a far more quantitative field. The next generation of researchers must be well-versed in computational and biological principles. We believe that our collaboration provides an excellent dual-training environment for our students and postdocs. Fifth, our research discoveries can directly feed into our classroom teaching. Yu teaches Neural Signal Processing at CMU and Batista teaches Control Theory in Neuroscience at Pitt;both are annual, graduate-level courses. Intellectual Merit: In the last decade, several groups have demonstrated compelling proof-of- concept laboratory demonstrations of closed-loop BCI control. For clinical translation, one of the major challenges is to improve the performance and robustness of BCI systems. To make this leap, we believe that it is critical to rigorously study existing systems to understand i) why some BCI decoders work better than others, ii) to what extent we can depend on the subjects'ability to learn, and iii) the neural strategies adopted by the subjects for proficient control. There is a long-overdue need for a general statistical framework for dissecting closed-loop BCI data, which we propose to develop. Discoveries enabled by the developed methods will help us and others in the field to design high-performance, clinically-viable BCI systems that allow the subject to quickly reach and maintain a high level of proficiency.