Yes the open chain is in equilibrium with the cyclic succinimide product and this is "well established". It can be controlled with pH but more than likely, I would suggest simply purchasing a commercially available orthogonally protected amino acid to avoid this altogether.

E.g., see "Spontaneous cyclization of the aspartic acid side chain to the succinimide derivative" Chem Comm, 1992, issue 12.

Yes, reaction conditions including temperature, pH, solvation and coupling reagents help to control!

Aspartimide formation is especially prevalent in peptides containing Asp-Gly or Asp-Ser sequences. I think the most effective way to minimize aspartimide formation would be during the synthesis stages by using one of the strategies below:

1. A widely established approach is the use of optimized side-chain protecting group on Asp. Many Asp derivatives are commercially available such as Fmoc-Asp(OMpe)-OH. Some new ones such as Fmoc-Asp(OEpe)-OH, Fmoc-Asp(OPhp)-OH and others were recently reported. (J. Pept Sci. 2015 Aug;21(8):680-687)

2. If you must use Asp(t-Bu) for whatever reason, then another strategy would be to play with the deprotection conditions, such as addition of organic acids (5% formic acid) to the piperidine cleavage solution.

3. Replacement of piperidine with a much milder base (piperazine) is also known to reduce aspartimide formation.

4. Adding HOBt to the piperidine deprotecting solution is also known to reduce aspartimide formation.

5. Another strategy would be to replace the residue adjacent to the Asp carboxyl with a bulky residue (if permissible) to completely block aspartimide formation, although not an option in this case.

6. There are other less popular strategies also such as use of pseudoproline or Dmb protected peptides to reduce aspartimide but they have their own issues.

This is a highly sequence dependent phenomenon - I suggest to try a standard protocol first (with Fmoc-Asp(OtBu)-OH), using brief base treatments (e.g. 30% piperidine/DMF, 1 min then 3 min). Depending on the length and sequence of your particular peptide, it may not be as big a problem as it is made out to be.