Your system has nvida chips. So please install driver from
Addtional Drivers (press Super / Win, and search for it). Reboot and see if it solves the problem.
If above not working try following (but don't uninstall the driver)
sudo gedit /etc/default/grub
Change this line
to something like below
GRUB_CMDLINE_LINUX_DEFAULT="quiet splash acpi_osi=Linux acpi_backlight=vendor"
sudo update-grub and reboot . See if brightness keys are working.
It is still possible ubuntu won't remember your brightness settings. So you have to change brightness each time.
Please let us know the result as many sony users are facing this problem.
Update: This is for setting brightness manually.
Try following for path shown by
ls /sys/class/backlight/*/brightness and replace accordingly.
Get the maximum brightness:
Try a lower value to set the brightness, say output is 2048 so I will try with half of it
echo 1024| sudo tee /sys/class/backlight/intel_backlight/brightness
If this works, make this happen in each login automatically by doing the following
sudo gedit /etc/rc.local
Enter this line just before
exit 0. It should look like
echo YOUR_VALUE_HERE > /sys/class/backlight/intel_backlight/brightness
Also you can try with xdotool