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arXiv · 1610.05021

Stochastic Linear Quadratic Optimal Control Problems in Infinite Horizon

Jingrui Sun·Jiongmin Yong
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Abstract

This paper is concerned with stochastic linear quadratic (LQ, for short) optimal control problems in an infinite horizon with constant coefficients. It is proved that the non-emptiness of the admissible control set for all initial state is equivalent to the $L^2$-stabilizability of the control system, which in turn is equivalent to the existence of a positive solution to an algebraic Riccati equation (ARE, for short). Different from the finite horizon case, it is shown that both the open-loop and closed-loop solvabilities of the LQ problem are equivalent to the existence of a static stabilizing solution to the associated generalized ARE. Moreover, any open-loop optimal control admits a closed-loop representation. Finally, the one-dimensional case is worked out completely to illustrate the developed theory.

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Jingrui Sun, Jiongmin Yong. 2016-10-17. Stochastic Linear Quadratic Optimal Control Problems in Infinite Horizon. https://arxiv.org/abs/1610.05021

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