How to execute an ansible playbook using a jenkins pipeline script?
If you have Jenkins user public key, on your target hosts authorized keys file, for the user you want to login as, ssh connection authorization should work. 

This is an example of Jenkinsfile step. 

ansiblePlaybook colorized: true, installation: 'Ansible', inventory: 'inventory', playbook: 'playbook.yml',tags: "" , skippedTags: "", extras: "--extra-vars ' hst=targetHost "



This is Ansible Inventory example. You can define the args at the host level as well.

[targetHost]
17.14.69.21 ansible_ssh_user=sshuser

[all:vars]
ansible_connection=ssh
ansible_ssh_common_args='-o StrictHostKeyChecking=no -oHostKeyAlgorithms=+ssh-dss'