A multi-enzyme complex that catalyzes the oxidative decarboxylation of 2-oxoadipate to glutaryl-CoA, thereby acting in the final step of lysine and tryptophan catabolism within mitochondria. The complex comprises multiple copies of three enzymes referred to as E1, E2 and E3: 2-oxoadipate dehydrogenase (E1), dihydrolipoamide S-succinyltransferase (E2) and dihydrolipoamide dehydrogenase (E3). The 2-oxoadipate dehydrogenase (E1) component is analogous to the oxoglutarate dehydrogenase (E1) component of the OGDH complex, while the E2 and E3 components of the two complexes are identical. (Adapted from PMID:29191460, PMID:32695416, PMID:33045952.]