  Control of complex systems involves both system identification and controller
design. Deep neural networks have proven to be successful in many
identification tasks, however, from model-based control perspective, these
networks are difficult to work with because they are typically nonlinear and
nonconvex. Therefore many systems are still identified and controlled based on
simple linear models despite their poor representation capability. In this
paper we bridge the gap between model accuracy and control tractability faced
by neural networks, by explicitly constructing networks that are convex with
respect to their inputs. We show that these input convex networks can be
trained to obtain accurate models of complex physical systems. In particular,
we design input convex recurrent neural networks to capture temporal behavior
of dynamical systems. Then optimal controllers can be achieved via solving a
convex model predictive control problem. Experiment results demonstrate the
good potential of the proposed input convex neural network based approach in a
variety of control applications. In particular we show that in the MuJoCo
locomotion tasks, we could achieve over 10% higher performance using 5* less
time compared with state-of-the-art model-based reinforcement learning method;
and in the building HVAC control example, our method achieved up to 20% energy
reduction compared with classic linear models.
