WLS-based partially decentralized adaptive control for coupled ARMAX multi-agent dynamical system

In this paper, partially decentralized adaptive control for a multi-agent dynamic system is studied. There are many agents in the system, and each agent´s state evolves like an ARMAX model with unknown parameters while being intervened by its neighborhood agents, in form of unknown linear interactions. Each agent adopts recursive WLS (weighted least-square) algorithm to estimate its local unknown parameters and designs its local adaptive controller by ldquocertainty equivalencerdquo principle. Generally speaking, it is a question whether such local adaptive controllers can guarantee stability of whole system. In this paper, we not only give the affirmative answer to this question, but also rigorously prove the optimality of decentralized WLS adaptive controller.