A Non-Certainty Equivalence Approach to Decentralized Adaptive Control

We approach the decentralized adaptive control problem in a non-certainty equivalence adaptive framework, motivated by the recently proposed immersion and invariance (I&I) methodology. In this paper, we consider continuous large-scale interconnected systems and show that it is theoretically possible to asymptotically track reference signals with zero error in a non-certainty equivalence framework. The controller has a decentralized information structure, in which it is assumed that the each subsystem controller has access to only its corresponding state and reference input. However, we assume implicit cooperation among the controllers by making subsystem objectives common knowledge. We conclude with numerical simulations comparing non-certainty equivalence and certainty equivalence approaches to the decentralized adaptive control problem.