  The growing scale and complexity of safety-critical control systems
underscore the need to evolve current control architectures aiming for the
unparalleled performances achievable through state-of-the-art optimization and
machine learning algorithms. However, maintaining closed-loop stability while
boosting the performance of nonlinear control systems using data-driven and
deep-learning approaches stands as an important unsolved challenge. In this
paper, we tackle the performance-boosting problem with closed-loop stability
guarantees. Specifically, we establish a synergy between the Internal Model
Control (IMC) principle for nonlinear systems and state-of-the-art
unconstrained optimization approaches for learning stable dynamics. Our methods
enable learning over arbitrarily deep neural network classes of
performance-boosting controllers for stable nonlinear systems; crucially, we
guarantee Lp closed-loop stability even if optimization is halted prematurely,
and even when the ground-truth dynamics are unknown, with vanishing
conservatism in the class of stabilizing policies as the model uncertainty is
reduced to zero. We discuss the implementation details of the proposed control
schemes, including distributed ones, along with the corresponding optimization
procedures, demonstrating the potential of freely shaping the cost functions
through several numerical experiments.
