jQuery Validate plugin not validating an element that's not a form input

Question

I need to validate with jQuery Validation Plugin a combobox component: jqxComboBox. This component is applied on a div. So defining

<div id="component_id" />

$( "#component_id" ).jqxComboBox({...});

$("#component_id" ).rules( "add", {
    required: true,                  
    messages:{
        required: "Field is required"
    }
});

throws the following exception: Cannot read property 'nodeType' of undefined. I think it should due to the fact that I'm applying validation rules on a div.

This component generate an input type hidden to hold selected value. I have also tryed to apply validation rules on that hidden component, but this do not works: form is submitted also when hidden has no value.

$('input[type=hidden][name=myName]').rules( "add", {
    required: true,                  
    messages:{
        required: "Field is required"
    }
});

Can someone please give me some hints on how to solve this?