The following worked for me inside the function for the form

public function form( $instance ) {
    $my_widget = $this;
    $widget_identifier = "{$this->id_base}-{$this->number}";
}

The following worked for me inside the function for the form

public function form( $instance ) {
    $my_widget = $this;
    $widget_identifier = "{$this->id_base}-{$this->number}";
}

Edit: the following also works

public function form( $instance ) {
    $widget_identifier = $this->id;
}