  Designing predictive controllers towards optimal closed-loop performance
while maintaining safety and stability is challenging. This work explores
closed-loop learning for predictive control parameters under imperfect
information while considering closed-loop stability. We employ constrained
Bayesian optimization to learn a model predictive controller's (MPC) cost
function parametrized as a feedforward neural network, optimizing closed-loop
behavior as well as minimizing model-plant mismatch. Doing so offers a high
degree of freedom and, thus, the opportunity for efficient and global
optimization towards the desired and optimal closed-loop behavior. We extend
this framework by stability constraints on the learned controller parameters,
exploiting the optimal value function of the underlying MPC as a Lyapunov
candidate. The effectiveness of the proposed approach is underlined in
simulations, highlighting its performance and safety capabilities.
