The error is because of you are not submitting any element in the name of
product_id
and you can create the html hidden element
<input type="hidden" name="product_id[]" value="<?php echo $products['product_id']; ?>"></input>
so this will be array so u can access all the values.
and for other elements also create a array like
<input name="product_name" type="text" id="product_name[]" value="<? echo $products['product_name']; ?>"></input>
I think this will solve your problem.