Share your experience!
First of all.Switch ON your phone in Safe Mode(to clear out any apps that might bug the Update Center's App).
How to activate Safe Mode:
1.Switch OFF your phone.
2.Wait until the XPERIA logo fades out.
3.Quickly press and hold Volume Down button.
4.You have now open your phone in safe mode.
After that,try open Update Center.
5.If you want to get out from Safe Mode,just switch OFF your phone and restart it back again.
If that does not work,check whether Update Center App is enable or not.
Go to Settings->Apps->Swipe to the most right to "All Apps" section->Search for Update Center and enable it(if you found it disable,if it is already enable,just leave it).
And if that does not solve it.fix it using Sony Update Service(SUS).Download it and fix it(tutorials are inside the application) link: