{
  "id": "1610.01892",
  "version": "v1",
  "published": "2016-10-06T14:39:05.000Z",
  "updated": "2016-10-06T14:39:05.000Z",
  "title": "Nonequivalence of Controllability Properties for Piecewise Linear Markov Switch Processes",
  "authors": [
    "Dan Goreac"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1602.00920",
  "categories": [
    "math.OC",
    "math.PR"
  ],
  "abstract": "In this paper we study the exact null-controllability property for a class of controlled PDMP of switch type with switch-dependent, piecewise linear dynamics and multiplicative jumps. First, we show that exact null-controllability induces a con-trollability metric. This metric is linked to a class of backward stochastic Riccati equations. Using arguments similar to the euclidian-valued BSDE in [4], the equation is shown to be equivalent to an iterative family of deterministic Riccati equations that are solvable. Second, we give an example showing that, for switch-dependent coefficients, exact null-controllability is strictly stronger than approximate null-controllability. Finally, we show by convenient examples that no hierarchy holds between approximate (full) controllability and exact null-controllability. The paper is intended as a complement to [15] and [14].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-06T14:39:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "piecewise linear markov switch processes",
      "controllability properties",
      "nonequivalence",
      "exact null-controllability property",
      "deterministic riccati equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}