{
  "id": "1807.03475",
  "version": "v1",
  "published": "2018-07-10T04:18:41.000Z",
  "updated": "2018-07-10T04:18:41.000Z",
  "title": "On Controller Design for Systems on Manifolds in Euclidean Space",
  "authors": [
    "Dong Eui Chang"
  ],
  "comment": "International Journal of Robust and Nonlinear Control (Accepted July 2018",
  "doi": "10.1002/rnc.4294",
  "categories": [
    "math.OC",
    "cs.RO",
    "cs.SY"
  ],
  "abstract": "A new method is developed to design controllers in Euclidean space for systems defined on manifolds. The idea is to embed the state-space manifold $M$ of a given control system into some Euclidean space $\\mathbb R^n$, extend the system from $M$ to the ambient space $\\mathbb R^n$, and modify it outside $M$ to add transversal stability to $M$ in the final dynamics in $\\mathbb R^n$. Controllers are designed for the final system in the ambient space $\\mathbb R^n$. Then, their restriction to $M$ produces controllers for the original system on $M$. This method has the merit that only one single global Cartesian coordinate system in the ambient space $\\mathbb R^n$ is used for controller synthesis, and any controller design method in $\\mathbb R^n$, such as the linearization method, can be globally applied for the controller synthesis. The proposed method is successfully applied to the tracking problem for the following two benchmark systems: the fully actuated rigid body system and the quadcopter drone system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-10T04:18:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "euclidean space",
      "controller design",
      "actuated rigid body system",
      "ambient space",
      "single global cartesian coordinate system"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}