How to add predefined places/markers to Leaflet Geocoder

I am using Leaflet Map with geocoder (ESRI) and Routing Machine. I have added two markers, let's say my home and my work

var marker_work = L.marker([50.27, 19.03], { title: 'MyWork'}).addTo(map)
.bindPopup("work").openPopup();

var marker_home = L.marker([50.10, 18.4], { title: 'MyHome'}).addTo(map)
.bindPopup("home").openPopup();

Here is an example fiddle: https://jsfiddle.net/21nmk8so/1/

How can I add this markers/point as a predefined places for ControlGeocoder? I want to use them in search and use as a start point / end point for route calculation.

Another example for the same question: how to add custom-fake city with lat/lon and be able to search (find route) to/from that city.

I don't know if this is the best solution but it is working: Create a custom Geocoder Class which overwrites the geocode function. There you can overwrite the result function and apply suggestions to the result.

L.CustomGeocoder = L.Control.Geocoder.Nominatim.extend({
    suggestions: [],
    setSuggestions(arr){
      this.suggestions = arr;
    },
    createSuggestionFromMarker(marker){
      this.suggestions.push({name: marker.options.title, center: marker.getLatLng()});
    },
    getResultsOfSuggestions(query){
      var results = [];
      this.suggestions.forEach((point)=>{
        if(point.name.indexOf(query) > -1){
          point.center = L.latLng(point.center);
          point.bbox = point.center.toBounds(100);
          results.push(point);
        }
      });
      return results;
    },
    geocode(query, resultFnc, context) {
      var that = this;
      var callback = function(results){
        var sugg = that.getResultsOfSuggestions(query);
        resultFnc.call(this,sugg.concat(results));
      }
      L.Control.Geocoder.Nominatim.prototype.geocode.call(that,query, callback, context);
    }
  })

Then you have to use the new Geocoder Class:

var geocoder = new L.CustomGeocoder({});

var control = L.Routing.control({
  waypoints: [],
  router: new L.Routing.osrmv1({
    language: 'en',
    profile: 'car'
  }),
  geocoder: geocoder
}).addTo(map);

And finally you can add suggestions over markers and theier title option over createSuggestionFromMarker(marker) or setSuggestions(arr):

var suggestions = [
  {
    name: 'Test Car 1',
    center: [50.27, 19.03]
  },
  {
    name: 'Test Car 2',
    center: [50.10, 18.4]
  }
];
geocoder.setSuggestions(suggestions);

var marker_work = L.marker([50.27, 19.03], { title: 'MyWork'}).addTo(map);
var marker_home = L.marker([50.10, 18.4], { title: 'MyHome'}).addTo(map);

geocoder.createSuggestionFromMarker(marker_work);
geocoder.createSuggestionFromMarker(marker_home);

Update, use marker Ref instead of fix latlng

Change this two function, then the marker is referenced and it always searches from the current position of the marker:

    createSuggestionFromMarker(marker){
      this.suggestions.push({name: marker.options.title, marker: marker});
    },
    getResultsOfSuggestions(query){
      var results = [];
      this.suggestions.forEach((point)=>{
        if(point.name.indexOf(query) > -1){
            if(point.marker){
            point.center = point.marker.getLatLng();
          }
          point.center = L.latLng(point.center);
          point.bbox = point.center.toBounds(100);
          results.push(point);
        }
      });
      return results;
    },

You can test this in the demo, when you drag the marker

https://jsfiddle.net/falkedesign/hu25jfd1/