RESOLUTION
Plesk checks status of uploaded web application using tomcat manager with the URL http://DOMAIN_NAME:9080/manager/list. If Plesk cannot login to Tomcat manager for some reasons it shows 'unknown' status for an application.
- Make sure that the domain you are trying to manage is resolved to the Plesk server
- Check that Tomcat server is configured properly and listens on the 9080 port, 1569.
- Verify that manager login/password for the domain in Plesk database correspond to the values in appropriate memory database file as described in the article 758.
- Examine the article 829.