Currently, Jira (7.13 / 8.8) doesn't offer a safe & supported mechanism for programmatically installing or upgrading Atlassian Apps (JSW, JSD, Portfolio) or 3rd party Apps that could be used in an automation of some sort.

Alternatives vary from copying the installed-plugins folder from a temp instance that's been manually installed/upgraded or unpacking jar/OBRs into that folder — yet each App has it's own particularities (like not all jars from within obr/dependencies should be copied, etc).