Start SharePoint User Profile Synchronization using PowerShell

To start user profile Synchronization manually:

• Go to SharePoint Central Administration >> Application Management >> click Manage service applications.
• On the Manage Service Applications >> click in the Name column of the User Profile Service Application
• In Manage Profile Service page >> Under Synchronization section, click Start Profile Synchronization.
• select either Start Incremental Synchronization (To Sync profiles that are changed since the last synchronization), or select Start Full Synchronization to synchronize all profiles

How to change the schedule of incremental sync:
By default, It runs once per day. You can schedule User Profile Incremental Synchronization from:

•  User Profile Service Application 
• Click on "Configure Synchronization Timer Job" under Synchronization 
• Adjust the schedule accordingly
  

Start SharePoint User Profile Synchronization using PowerShell
If you want to do Full import once in a while (say, Weekly!), You can schedule this PowerShell script in Task scheduler. 

Add-PSSnapin Microsoft.SharePoint.PowerShell -ErrorAction SilentlyContinue

#Full Import Flag
$FullImport = $true

#Get User Profile Service Application
$UserProfileService = Get-SPServiceApplication | where { $_.TypeName -eq "User Profile Service Application" }

#Start Importing User Profile Sync
$UserProfileService.StartImport($FullImport)