Stabilizing Unknown Nonlinear Systems via Decentralized High-gain Adaptive Control

In this paper, we study decentralized adaptive stabilization for unknown nonlinear systems with square input matrix-valued functions. This problem formulation arises, e.g., in the context of nonlinear networks, where each scalar subsystem can implement its local controller. We show that if the input matrix-valued function possesses a kind of diagonally dominant properties, decentralized stabilization can be achieved by making each local control gain sufficiently large without knowing the exact system dynamics. Furthermore, when each local gain is updated based on the corresponding local information, the boundedness and convergence of both system dynamics and adaptive local gains are guaranteed.