How do I set value of the control that is not mapped to any field?

To do that you need to return the object of the following format from the client action handler function:

return {
    app: {
        form: {
            data: {
                modified: {
                    controlName: value
                }
            }
        }
    }
};

Or you can do that through the DWKit Global API method:

DWKitApp.API.setDataField("controlName", value);

where controlName is the name of the control and value is its value.