  We propose a methodology for performing risk-averse quadratic regulation of
partially observed Linear Time-Invariant (LTI) systems disturbed by process and
output noise. To compensate against the induced variability due to both types
of noises, state regulation is subject to two risk constraints. The latter
renders the resulting controller cautious of stochastic disturbances, by
restricting the statistical variability, namely, a simplified version of the
cumulative expected predictive variance of both the state and the output. Our
proposed formulation results in an optimal risk-averse policy that preserves
favorable characteristics of the classical Linear Quadratic (LQ) control. In
particular, the optimal policy has an affine structure with respect to the
minimum mean square error (mmse) estimates. The linear component of the policy
regulates the state more strictly in riskier directions, where the process and
output noise covariance, cross-covariance, and the corresponding penalties are
simultaneously large. This is achieved by "inflating" the state penalty in a
systematic way. The additional affine terms force the state against pure and
cross third-order statistics of the process and output disturbances. Another
favorable characteristic of our optimal policy is that it can be pre-computed
off-line, thus, avoiding limitations of prior work. Stability analysis shows
that the derived controller is always internally stable regardless of parameter
tuning. The functionality of the proposed risk-averse policy is illustrated
through a working example via extensive numerical simulations.
