{
  "aliases": null,
  "backlinks": [
    {
      "field": "uses",
      "target": "7RPV2T29CF"
    },
    {
      "field": "uses",
      "target": "9NSCZ2KBEB"
    },
    {
      "field": "uses",
      "target": "CP25WM5537"
    },
    {
      "field": "uses",
      "target": "D3FHYZ4P1R"
    },
    {
      "field": "uses",
      "target": "RQBNA1ZRJW"
    },
    {
      "field": "uses",
      "target": "YQYJTKD0W2"
    },
    {
      "field": "uses",
      "target": "YR43719RWE"
    },
    {
      "field": "defines",
      "target": "SBQVGQPXT1"
    }
  ],
  "body": "\n## Summary\n\nA control system is a dynamical system whose evolution depends on an input that can be chosen, the control.\nFor systems governed by [[ordinary differential equations|0NT64JV96A]] it has the form $x' = f(x, u)$, where $x$ is the state and $u$ is the control.\nIt is the basic object of control theory.\nThat theory asks which states can be reached, how to steer the system, and how to do so in the best way.\n\n## Explanations\n\n### L1 human\n\nA car is a control system: its position and speed are the state, and the driver chooses the pedals and the steering wheel.\nThe laws of motion say how the state changes for each choice of the inputs.\nThe driver wants to reach a goal, such as parking, by choosing the inputs well over time.\nA simple mathematical example is $x_1' = x_2$, $x_2' = u$: a point on a line whose acceleration $u$ can be chosen.\n",
  "commit": "547b6eddb8f2feb8d579f2d633d22a27b7e132fc",
  "front": {
    "kind": "concept",
    "msc": [
      "93C15",
      "34H05",
      "93C10"
    ],
    "name": "Control system",
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Control_theory"
      }
    ],
    "tag": "ZPDTVZQN5K"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/ZPDTVZQN5K/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/ZPDTVZQN5K.md",
  "msc": [
    "93C15",
    "34H05",
    "93C10"
  ],
  "name": "Control system",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/ZPD/ZPDTVZQN5K.md",
  "status": null,
  "tag": "ZPDTVZQN5K",
  "uri": "m2://ZPDTVZQN5K",
  "url": "https://math2.tamnd.com/wiki/control-system/",
  "writing": {
    "tag": "ZPDTVZQN5K",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}