I noticed that there is a value PeoplePicker which may control this. But I dont know how to do it.
You can migrate existing web application from classic-mode to claims-based authentication and hence allow the FBA there, using PowerShell. Follow this TechNet article for details:
I don't see any reasons why you can't try this approach with the Central Administration application.
P.S. If something went wrong, I believe SharePoint Configuration Wizard could recover the CA web application.
I would not advise this unless there was no windows authentication.
You risk locking yourself out and not being able to alter configuration to fix access problems.
If you need to provide external access to central admin, I advise using a secure Citrix server or VPN to expose central admin to users who are not directly connected to the domain.