{
  "id": "2010.08447",
  "version": "v1",
  "published": "2020-10-16T15:20:43.000Z",
  "updated": "2020-10-16T15:20:43.000Z",
  "title": "Design of periodic scheduling and control for networked systems under random data loss",
  "authors": [
    "Atreyee Kundu",
    "Daniel E. Quevedo"
  ],
  "comment": "Extended version of our manuscript under review",
  "categories": [
    "math.OC",
    "cs.SY",
    "eess.SY"
  ],
  "abstract": "This paper deals with Networked Control Systems (NCSs) whose shared networks have limited communication capacity and are prone to data losses. We assume that among (N) plants, only (M < N) plants can communicate with their controllers at any time instant. In addition, a control input, at any time instant, is lost in a channel with a probability (p). Our contributions are threefold. First, we identify necessary and sufficient conditions on the open-loop and closed-loop dynamics of the plants that ensure existence of purely time-dependent periodic scheduling sequences under which stability of each plant is preserved for all admissible data loss signals. Second, given the open-loop and closed-loop dynamics of the plants, relevant parameters of the shared network and a period for the scheduling sequence, we present an algorithm that verifies our stability conditions and if satisfied, designs stabilizing scheduling sequences. Otherwise, the algorithm reports non-existence of a stabilizing periodic scheduling sequence with the given period and stability margins. Third, given the plant matrices, the parameters of the network and a period for the scheduling sequence, we present an algorithm that designs static state-feedback controllers such that our stability conditions are satisfied. The main apparatus for our analysis is a switched systems representation of the individual plants in an NCS whose switching signals are time-inhomogeneous Markov chains. Our stability conditions rely on the existence of sets of symmetric and positive definite matrices that satisfy certain (in)equalities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-16T15:20:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random data loss",
      "time-dependent periodic scheduling sequences",
      "networked systems",
      "stability conditions",
      "designs static state-feedback controllers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}