{
  "id": "1806.05215",
  "version": "v1",
  "published": "2018-06-13T18:40:14.000Z",
  "updated": "2018-06-13T18:40:14.000Z",
  "title": "Weak Closed-Loop Solvability of Stochastic Linear-Quadratic Optimal Control Problems",
  "authors": [
    "Jingrui Sun",
    "Hanxiao Wang",
    "Jiongmin Yong"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "Recently it has been found that for a stochastic linear-quadratic optimal control problem (LQ problem, for short) in a finite horizon, open-loop solvability is strictly weaker than closed-loop solvability which is equivalent to the regular solvability of the corresponding Riccati equation. Therefore, when an LQ problem is merely open-loop solvable not closed-loop solvable, which is possible, the usual Riccati equation approach will fail to produce a state feedback representation of open-loop optimal controls. The objective of this paper is to introduce and investigate the notion of weak closed-loop optimal strategy for LQ problems so that its existence is equivalent to the open-loop solvability of the LQ problem. Moreover, there is at least one open-loop optimal control admitting a state feedback representation. Finally, we present an example to illustrate the procedure for finding weak closed-loop optimal strategies.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-13T18:40:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic linear-quadratic optimal control problem",
      "weak closed-loop solvability",
      "weak closed-loop optimal strategy",
      "lq problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}