Q:

How to run docker-compose up -d at system start up?

To let the containers autostart at startup point, I tried to add the command:  
cd directory_has_docker-compose.yml && docker-compose up -d  in /etc/rc.local.    
but then after I reboot the machine, the containers not work.
How run docker-compose up -d at system start up?

A:

When we use crontab or the deprecated /etc/rc.local file, we need a delay (e.g. sleep 10, depending on the machine) to make sure that system services are available. Usually, systemd (or upstart) is used to manage which services start when the system boots. You can try use the similar configuration for this:
# /etc/systemd/system/docker-compose-app.service

[Unit]
Description=Docker Compose Application Service
Requires=docker.service
After=docker.service

[Service]
Type=oneshot
RemainAfterExit=yes
WorkingDirectory=/srv/docker
ExecStart=/usr/local/bin/docker-compose up -d
ExecStop=/usr/local/bin/docker-compose down
TimeoutStartSec=0

[Install]
WantedBy=multi-user.target

Or, if you want run without the -d flag:
# /etc/systemd/system/docker-compose-app.service

[Unit]
Description=Docker Compose Application Service
Requires=docker.service
After=docker.service

[Service]
WorkingDirectory=/srv/docker
ExecStart=/usr/local/bin/docker-compose up
ExecStop=/usr/local/bin/docker-compose down
TimeoutStartSec=0
Restart=on-failure
StartLimitIntervalSec=60
StartLimitBurst=3

[Install]
WantedBy=multi-user.target

Change the WorkingDirectory parameter with your dockerized project path. And enable the service to start automatically:
systemctl enable docker-compose-app

A:

You should be able to add: 
restart: always 

to every service you want to restart in the docker-compose.yml file

A:

If your docker.service enabled on system startup 
$ sudo systemctl enable docker

and your services in your docker-compose.yml has 
restart: always

all of the services run when you reboot your system if you run below command only once
docker-compose up -d

