Model predictive control (MPC) achieves stability and constraint satisfaction
for general nonlinear systems, but requires computationally expensive online
optimization. This paper studies approximations of such MPC controllers via
neural networks (NNs) to achieve fast online evaluation. We propose safety
augmentation that yields deterministic guarantees for convergence and
constraint satisfaction despite approximation inaccuracies. We approximate the
entire input sequence of the MPC with NNs, which allows us to verify online if
it is a feasible solution to the MPC problem. We replace the NN solution by a
safe candidate based on standard MPC techniques whenever it is infeasible or
has worse cost. Our method requires a single evaluation of the NN and forward
integration of the input sequence online, which is fast to compute on
resource-constrained systems. The proposed control framework is illustrated on
three non-linear MPC benchmarks of different complexity, demonstrating
computational speedups orders of magnitudes higher than online optimization. In
the examples, we achieve deterministic safety through the safety-augmented NNs,
where naive NN implementation fails