This plugin gives every widget an extra control field called “Widget logic” that lets you control the pages that the widget will appear on. It provide a text field “Widget logic” you write any WP’s Conditional Tags, or any general PHP code.
In our theme I have created a menu area on header top right side visible one for non logged in user and one for logged in user. Simply I create two menu and using it on Header Top Right widget section by using “Custom Menu” individual widget.
See I am using WordPress conditional tags in widget logic text field.
Click Here for seeing all WordPress conditional tags where you can use them as per your requirements.
This is free plugin and available on WordPress Repository. For downloading this plugin please click on download button.