TY - JOUR

T1 - Risk-Aware Linear Quadratic Control Using Conditional Value-at-Risk

AU - Kishida, Masako

AU - Cetinkaya, Ahmet

N1 - Funding Information:
The work of Ahmet Cetinkaya was supported by JST ERATO HASUO Metamathematics for Systems Design Project under Grant JPMJER1603.
Publisher Copyright:
© 1963-2012 IEEE.

PY - 2023/1/1

Y1 - 2023/1/1

N2 - 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.

AB - 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.

KW - Conditional-value-at-risk (CVaR)

KW - linear systems

KW - optimal control

KW - stochastic optimal control

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U2 - 10.1109/TAC.2022.3142131

DO - 10.1109/TAC.2022.3142131

M3 - Article

AN - SCOPUS:85123318182

SN - 0018-9286

VL - 68

SP - 416

EP - 423

JO - IRE Transactions on Automatic Control

JF - IRE Transactions on Automatic Control

IS - 1

ER -