  Learning-based predictive control is a promising alternative to
optimization-based MPC. However, efficiently learning the optimal control
policy, the optimal value function, or the Q-function requires suitable
function approximators. Often, artificial neural networks (ANN) are considered
but choosing a suitable topology is also non-trivial. Against this background,
it has recently been shown that tailored ANN allow, in principle, to exactly
describe the optimal control policy in linear MPC by exploiting its piecewise
affine structure. In this paper, we provide a similar result for representing
the optimal value function and the Q-function that are both known to be
piecewise quadratic for linear MPC.
