can a 4th generation Ipad support ios 11?

Sorry, no, not possible.

If your iPad is currently running, or cannot be updated beyond iOS 10.3.3/4, then have an iPad4.

Update support for iPad4 ended September 2017. The final iOS releases for this model were iOS 10.3.3 (WiFi Only models) and iOS 10.3.4 (WiFi & Cellular). iPad4 cannot be updated to any later major version of iOS as it lacks the minimum hardware requirements needed to run more recent versions. The 32-bit platform upon which this iPad is based is effectively obsolete. Later versions of iOS are designed for 64-bit hardware.

Many App Developers have also dropped support for older devices and iOS versions preceding iOS11/12/13 - and have withdrawn older versions of their Apps from the Apple App Store. Withdrawal of Apps supporting older models of iPad is making their utility and usefulness significantly more limited. Once compatible versions Apps are withdrawn, you’ll not be able (re)download or (re)install them.

If Apps that you need to use now have higher minimum iOS-version requirements, your only option is to replace your iPad with newer model. Even the basic current iPad7 supports current iPadOS 13.x and forthcoming iPadOS14 - and has hardware specifications and capabilities that will vastly outperform your old iPad4.

I hope this information is helpful - if only in clearly stating the limitations of your iPad4 and available options.

You are very welcome. I’m sorry it wasn’t the news you were hoping to learn.