Is it impossible to set Avast! AV Free up so that when it has completed its scan it logs a report, exits, logs out and shuts the PC down? If not each time then on demand.
Have a rummage through the avastUI to get familiar with the things that avast can do and this is one of them (see image), also check the avast Help Center which has a wealth of information.
However, even with the option set to shut down the system, there may be other things running that may block that.