{
  "id": "1812.07534",
  "version": "v1",
  "published": "2018-12-18T18:01:11.000Z",
  "updated": "2018-12-18T18:01:11.000Z",
  "title": "Value of Information in Feedback Control",
  "authors": [
    "Touraj Soleymani",
    "John S. Baras",
    "Sandra Hirche"
  ],
  "categories": [
    "math.OC",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "In this article, we investigate the impact of information on networked control systems, and illustrate how to quantify a fundamental property of stochastic processes that can enrich our understanding about such systems. To that end, we develop a theoretical framework for the joint design of an event trigger and a controller in optimal event-triggered control. We cover two distinct information patterns: perfect information and imperfect information. In both cases, observations are available at the event trigger instantly, but are transmitted to the controller sporadically with one-step delay. For each information pattern, we characterize the optimal triggering policy and optimal control policy such that the corresponding policy profile represents a Nash equilibrium. Accordingly, we quantify the value of information $\\operatorname{VoI}_k$ as the variation in the cost-to-go of the system given an observation at time $k$. Finally, we provide an algorithm for approximation of the value of information, and synthesize a closed-form suboptimal triggering policy with a performance guarantee that can readily be implemented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-18T18:01:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "feedback control",
      "event trigger",
      "distinct information patterns",
      "closed-form suboptimal triggering policy",
      "optimal control policy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}