The route you are showing there would be to edit an arbitrary user. If you plan to edit the signed in user, you can instead make your own routes that does not require an ID in the url
Route::get('profile', 'ProfileController@show');
Route::get('profile/edit', 'edit');
Route::put('profile', 'ProfileController@update');
Route::delete('profile', 'ProfileController@destroy');
Each of these would then just get the correct user using Auth::getUser()