One way to get enzymatic degradability of PEG gels is by crosslinking with thiol-flanked peptide sequences degradable by MMPs or other enzymes, as in the attached paper. If you use PEG DA, however, the beta-thio-esters formed by the nucleophilic conjugate addition will also be hydrolytically degradable. To prevent the latter you can use PEG VS in stead of PEG DA. For more information/methods see papers by Jeff Hubbell and Matthias Lutolf.
In addition to Hubbell's and Lutolf's great work on enzyme-cleavable gels, recommended in the previous reply, there's been an approach to forming pH-degradable hydrogels by Haag and co-workers. Here's the reference: