First of all $('this') should be $(this)
Secondly you're trying to use a read ID from your LI as a variable name. That doesn't work. If you store your plans in an array you can use the ID to search in that array:
var plans=Array();
plans["a1"]=new floorPlan('A1',false,557,1,1);
plans["a2"]=new floorPlan('A2',false,652,1,1);
Then your jQuery code should be altered to this:
$('.sideNav li').click(function() {
// Define the currentPlan
var current = $(this).attr('id');
var currentPlan = plans[current];
alert(currentPlan);
});
I created a JSFiddle for this. Is this what you were looking for?