Risk-Aware Linear Quadratic Control Using Conditional Value-at-Risk

Stochastic linear quadratic control problems are considered from the viewpoint of risks. In particular, a worst-case conditional value-at-risk (CVaR) objective function is minimized subject to additive disturbances whose first two moments distribution known. The study focuses on three finding optimal feedback gain that minimizes cost of: stationary distribution, one-step, and infinite time horizon. For problem, it proved CVaR equivalent standard (stochastic) regulator. one-step an approach solution as well analytical suboptimal solutions presented. horizon bound for special case discussed. presented theorems illustrated with numerical examples.