Is there an http-API for Siemens Logo
Look up "Application examples for LOGO!", download, read the source.
also random googling gets you "I have found a useful tool for studying communication protocols of LOGO under setup directory Program Files\Siemens\LOGOComfort_V5\lib\classes.jar..." doesn't look like HTTP at first glance, not even clear if it is based on tcp and not, say, udp, yet it does appear to be a good start, try to recreate that chap's dev environment and I think you're solid.
also below, assuming you have same generation controller:
http://wiki.ibhsoftec.com/en/OPCServer:Variables_from_LOGO!_RCE
and here's a library, supposedly supports C#:
http://www.adontec.com/index.htm?GO=/s7-library.htm
On the newest Logo 8 with the built-in web server, it is possible, and not even that difficult.
I'm documenting my findings here: https://github.com/jankeymeulen/siemens-logo-rest, maybe one day I will write a wrapper, but it's pretty straightforward to use it e.g. with Node-RED.
E.g. to read the status from I1:
curl 'http://192.168.1.100/AJAX' -H 'Security-Hint: ABCDEFGHIJKLMNOPQRSTUVWXYZ123456' --data-binary 'GETVARS:v1,129,0,0,1,1'
Security hint you'll need to sniff once, but it can be reused indefinitely (from the same IP address).
I know this question is now over 2 years old, but just for the sake of completeness and if somebody stumbles over this question while looking for an Siemens Logo HTTP-API:
The newer modules (0ba7 and 0ba8) are equipped with an ethernet port and therefore capable of speaking the S7 protocol. There are free libs out in the net implementing this protocol like libnodave or snap7.
I implemented some sort of a "middleware" with C#/WCF which is communicating trough libnodave with the Logo and exposing a simple REST/JSON API for controlling. Thanks to MONO this also runs on the good old Raspberry Pi 24/7 with low power consumption. You can find it here, unfortunately my site is in german language only.
I am new to the Siemens Logo automation system.
If it supports HTTP (not HTTPS), and you want to reverse-engineer the API, then you might be able to sniff the messages sent to the Ethernet interface.
However this task is brutal, at least you have enough time/patience, I wouldn't recommend it.
You have more options in the market. Anything that supports X10 (ancient), Insteon or Z-Wave might get you in the right direction.
I have experience with Insteon.They charge $200 for the SDK, and rumors say that the SDK is not well documented and developing can be a pain, but there's a free library that you can get here.
http://soapboxautomation.com/support-2/fluentdwelling-support/
You only need the modem COM / USB and you're ready to control X10 and Insteon devices.