## Abstract

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

Original language | English |
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Journal | IEEE Transactions on Automatic Control |

DOIs | |

Publication status | Accepted/In press - 2022 |

Externally published | Yes |

## Keywords

- Costs
- LMIs
- Linear programming
- Optimal control
- Probability distribution
- Regulators
- Uncertainty
- Upper bound
- conditional-value-at-risk
- linear systems
- optimal control
- stochastic optimal control

## ASJC Scopus subject areas

- Control and Systems Engineering
- Computer Science Applications
- Electrical and Electronic Engineering