TY - GEN
T1 - Infinite-horizon Risk-constrained Linear Quadratic Regulator with Average Cost
AU - Zhao, Feiran
AU - You, Keyou
AU - Basar, Tamer
N1 - 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.
UR - http://www.scopus.com/inward/record.url?scp=85126016490&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85126016490&partnerID=8YFLogxK
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 -