Using elements of vector to intersect named list

Question

I have the following vector of elements:

list_alg <- c("rf", "nnet", "knn", "rpart")

and I wish to intersect it with the following named list:

list_tune <- list(
  glmnet = caretModelSpec(method = "glmnet"),
  svm = caretModelSpec(method = "svmRadial"),
  rf = caretModelSpec(method = "rf", importance = TRUE),
  nnet = caretModelSpec(method = "nnet"),
  knn = caretModelSpec(method = "knn"),
  rpart = caretModelSpec(method = "rpart")
)

I've tried variations of intersect(list_alg , list_tune); however this returns an empty list. My goal is to create list that includes elements of list_alg vector; however also keeps the other elements of list_tune (Please see example output below).

The output I am trying to achieve would look like this:

list(rf = list(method = "rf", importance = TRUE), nnet = list(
    method = "nnet"), knn = list(method = "knn"), rpart = list(
    method = "rpart"))

$`rf`
$`rf`$`method`
[1] "rf"

$`rf`$importance
[1] TRUE


$nnet
$nnet$`method`
[1] "nnet"


$knn
$knn$`method`
[1] "knn"


$rpart
$rpart$`method`
[1] "rpart"