  In traditional adaptive control, the certainty equivalence principle suggests
a two-step design scheme. A controller is first designed for the ideal
situation assuming the uncertain parameter was known and it renders a Lyapunov
function. Then, the uncertain parameter in the controller is replaced by its
estimation that is updated by an adaptive law along the gradient of Lyapunov
function. This principle does not generally work for a multi-agent system as an
adaptive law based on the gradient of (centrally constructed) Lyapunov function
cannot be implemented in a distributed fashion, except for limited situations.
In this paper, we propose a novel distributed adaptive scheme, not relying on
gradient of Lyapunov function, for general multi-agent systems. In this scheme,
asymptotic consensus of a second-order uncertain multi-agent system is achieved
in a network of directed graph.
