  We present a heuristic policy and performance bound for risk-sensitive convex
stochastic control that generalizes linear-exponential-quadratic regulator
(LEQR) theory. Our heuristic policy extends standard, risk-neutral model
predictive control (MPC); however, instead of ignoring uncertain noise terms,
our policy assumes these noise terms turns out either favorably or unfavorably,
depending on a risk aversion parameter. In the risk-seeking case, this modified
planning problem is convex. In the risk-averse case, it requires minimizing a
difference of convex functions, which is done (approximately) using the
convex-concave procedure. In both cases, we obtain a lower bound on the optimal
cost as a by-product of solving the planning problem. We give a numerical
example of controlling a battery to power an uncertain load, and show that our
policy reduces the risk of a very bad outcome (as compared with standard
certainty equivalent control) with negligible impact on the the average
performance.
