  We present heuristic policies and performance bounds for risk-sensitive
convex stochastic control that generalize linear-exponential-quadratic
regulator (LEQR) theory. Our heuristic policy extends standard, risk-neutral
model predictive control (MPC): instead of ignoring uncertain noise terms, as
in MPC, our heuristic 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 risk-averse MPC reduces the risk of a very bad
outcome (as compared with standard, risk-neutral MPC) with negligible impact on
the the average performance.
