{
  "id": "2404.02298",
  "version": "v1",
  "published": "2024-04-02T20:49:40.000Z",
  "updated": "2024-04-02T20:49:40.000Z",
  "title": "Output Feedback Periodic Event-triggered Control of Coupled $2\\times 2$ Linear Hyperbolic PDEs",
  "authors": [
    "Eranda Somathilake",
    "Bhathiya Rathnayake",
    "Mamadou Diagne"
  ],
  "comment": "8 pages, 1 figure",
  "categories": [
    "math.OC"
  ],
  "abstract": "This article introduces an observer-based periodic event-triggered control (PETC) strategy for boundary control of a system characterized by $2\\times2$ linear hyperbolic partial differential equations (PDEs). An anti-collocated actuation and sensing configuration is considered, and an exponentially convergent observer for state estimation from boundary data is designed. Initially, a continuous-time dynamic event-triggering mechanism requiring constant monitoring of the triggering function is developed. This mechanism is subsequently adapted into a periodic event-triggering scheme, which necessitates only periodic monitoring to identify when the control input needs updating. The underlying control approach is the PDE backstepping boundary control, implemented in a zero-order hold manner between events. This result marks a substantial improvement over conventional observer-based continuous-time event-triggered control for linear coupled hyperbolic PDEs by removing the requirement for constant monitoring of the triggering function. With the triggering function evaluated periodically, the closed-loop system is inherently free from Zeno behavior. It is demonstrated that under the proposed PETC, the closed-loop system globally exponentially converges to zero in the spatial $L^2$ norm. A simulation study illustrating the theoretical results is presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-02T20:49:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "output feedback periodic event-triggered control",
      "linear hyperbolic pdes",
      "hyperbolic partial differential equations",
      "system globally exponentially converges",
      "event-triggering mechanism requiring constant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}