An

Introduction: Brain-machine interfaces have reached an unprecedented capacity to measure and drive activity in the brain, allowing restoration of impaired sensory, cognitive or motor function. Classical control theory is pushed to its limit when aiming to design control laws that are suitable for large-scale, complex neural systems. This work proposes a scalable, data-driven, unified approach to study brain-machine-environment interaction using established tools from dynamical systems, optimal control theory, and deep learning. Methods: To unify the methodology, we define the environment, neural system, and prosthesis in terms of differential equations with learnable parameters, which effectively reduce to recurrent neural networks in the discrete-time case. Drawing on tools from optimal control, we describe three ways to train the system: Direct optimization of an objective function, oracle-based learning, and reinforcement learning. These approaches are adapted to different assumptions about knowledge of system equations, linearity, differentiability, and observability. Results: We apply the proposed framework to train an Discussion: We expect that the proposed framework will enable rapid and flexible synthesis of control algorithms for neural prostheses that reduce the need for