Smooth Model Predictive Control with Applications to Statistical
  Learning
Kwangjun Ahn Daniel Pfrommer Jack Umenberger Tobia Marcucci Zak Mhammedi Ali Jadbabaie
Statistical learning theory and high dimensional statistics have had a
tremendous impact on Machine Learning theory and have impacted a variety of
domains including systems and control theory. Over the past few years we have
witnessed a variety of applications of such theoretical tools to help answer
questions such as: how many state-action pairs are needed to learn a static
control policy to a given accuracy? Recent results have shown that continuously
differentiable and stabilizing control policies can be well-approximated using
neural networks with hard guarantees on performance, yet often even the
simplest constrained control problems are not smooth. To address this void, in
this paper we study smooth approximations of linear Model Predictive Control
(MPC) policies, in which hard constraints are replaced by barrier functions,
a.k.a. barrier MPC. In particular, we show that barrier MPC inherits the
exponential stability properties of the original non-smooth MPC policy. Using a
careful analysis of the proposed barrier MPC, we show that its smoothness
constant can be carefully controlled, thereby paving the way for new sample
complexity results for approximating MPC policies from sampled state-action
pairs.