Infinite-horizon Risk-constrained Linear Quadratic Regulator with Average Cost

Feiran Zhao, Keyou You, Tamer Basar

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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.

Original languageEnglish (US)
Title of host publication60th IEEE Conference on Decision and Control, CDC 2021
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781665436595
StatePublished - 2021
Event60th IEEE Conference on Decision and Control, CDC 2021 - Austin, United States
Duration: Dec 13 2021Dec 17 2021

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370


Conference60th IEEE Conference on Decision and Control, CDC 2021
Country/TerritoryUnited States

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization


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