Does postgres have any configuration similar to mysql innodb_thread_concurrency? InnoDB provides an innodb_thread_concurrency option  to limit the number of concurrent storage engine operations MySQL can perform at a time. Seems like InnoDB controls (schedules) execution of its thread.

Does PostgreSQL provide any configuration that allow us to limit the number of concurrent operations performed at a time? 
Does postgresql controls execution of its child processes or does it delegate this task to the OS?
PostgreSQL doesn't control execution of its child processes explicitly. If I borrow your words, PostgreSQL delegates that task to the OS.

PostgreSQL allows multiple clients to connect simultaneously. Each client connects a child process (referred to as a backend process), and each running backend  process handles all queries issued by the connected client. It is a very simple and classical server-client type multi-process architecture.

(I add more information.)

PostgreSQL can control the maximum number of connected clients by the configuration parameter max_connections (in the same way as MySQL),
but does not control the activities of the running backend processes depending on the server activity.

In addition, some helper processes, such as autovacuum related processes and checkpointer,  can be controlled their activities by themselves depending on the server activity.