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 userspecified level. By leveraging the duality, its optimal solution is first shown to be stationary and affine in the state, i.e., u(x, λ * ) = −K(λ * )x + l(λ * ), where λ * 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 sublinear convergence rate to find an optimal policy u(x, λ * ). Finally, a numerical example is provided to demonstrate the effectiveness of the proposed framework and the primal-dual method.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.