TY - GEN
T1 - Infinite-horizon Risk-constrained Linear Quadratic Regulator with Average Cost
AU - Zhao, Feiran
AU - You, Keyou
AU - Basar, Tamer
N1 - Funding Information:
This research was supported by National Natural Science Foundation of China under Grant no. 62033006. F. Zhao and K. You are with the Department of Automation and BNRist, Tsinghua University, Beijing 100084, China. e-mail: zhaofr18@mails.tsinghua.edu.cn, youky@tsinghua.edu.cn. T. Bas¸ar is with the Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801 USA. e-mail:basar1@illinois.edu.
Publisher Copyright:
© 2021 IEEE.
PY - 2021
Y1 - 2021
N2 - The behaviour of a stochastic dynamical system may be largely influenced by those low-probability, yet extreme events. To address such occurrences, this paper proposes an infinite-horizon risk-constrained Linear Quadratic Regulator (LQR) framework with time-average cost. In addition to the standard LQR objective, the average one-stage predictive variance of the state penalty is constrained to lie within a user-specified level. By leveraging the duality, its optimal solution is first shown to be stationary and affine in the state, i.e., u(x,λz.ast;)=-K(λz.ast;)x+l(λz.ast;), where λz.ast; is an optimal multiplier, used to address the risk constraint. Then, we establish the stability of the resulting closed-loop system. Furthermore, we propose a primal-dual method with a sublinear convergence rate to find an optimal policy u(x,λz.ast;). Finally, a numerical example is provided to demonstrate the effectiveness of the proposed framework and the primal-dual method.
AB - The behaviour of a stochastic dynamical system may be largely influenced by those low-probability, yet extreme events. To address such occurrences, this paper proposes an infinite-horizon risk-constrained Linear Quadratic Regulator (LQR) framework with time-average cost. In addition to the standard LQR objective, the average one-stage predictive variance of the state penalty is constrained to lie within a user-specified level. By leveraging the duality, its optimal solution is first shown to be stationary and affine in the state, i.e., u(x,λz.ast;)=-K(λz.ast;)x+l(λz.ast;), where λz.ast; is an optimal multiplier, used to address the risk constraint. Then, we establish the stability of the resulting closed-loop system. Furthermore, we propose a primal-dual method with a sublinear convergence rate to find an optimal policy u(x,λz.ast;). Finally, a numerical example is provided to demonstrate the effectiveness of the proposed framework and the primal-dual method.
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U2 - 10.1109/CDC45484.2021.9683474
DO - 10.1109/CDC45484.2021.9683474
M3 - Conference contribution
AN - SCOPUS:85126016490
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 390
EP - 395
BT - 60th IEEE Conference on Decision and Control, CDC 2021
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 60th IEEE Conference on Decision and Control, CDC 2021
Y2 - 13 December 2021 through 17 December 2021
ER -