  Neural networks offer a computationally efficient approximation of model
predictive control, but they lack guarantees on the resulting controlled
system's properties. Formal certification of neural networks is crucial for
ensuring safety, particularly in safety-critical domains such as autonomous
vehicles. One approach to formally certify properties of neural networks is to
solve a mixed-integer program based on the network. This approach suffers from
scalability issues due to the complexity of solving the resulting mixed-integer
programs. Nevertheless, these issues can be (partially) mitigated via
bound-tightening techniques prior to forming the mixed-integer program, which
results in tighter formulations and faster optimisation. This paper presents
bound-tightening techniques in the context of neural network explicit control
policies. Bound tightening is particularly important when considering problems
spanning multiple time steps of a controlled system, as the bounds must be
propagated through the problem depth. Several strategies for bound tightening
are evaluated in terms of both computational complexity and tightness of the
bounds.
