  This work investigates a reduced-complexity adaptive methodology to consensus
tracking for a team of uncertain high-order nonlinear systems with switched
(possibly asynchronous) dynamics. It is well known that high-order nonlinear
systems are intrinsically challenging as feedback linearization and
backstepping methods successfully developed for low-order systems fail to work.
At the same time, even the adding-one power-integrator methodology, well
explored for the single-agent high-order case, presents some complexity issues
and is unsuited for distributed control. At the core of the proposed
distributed methodology is a newly proposed definition for separable functions:
this definition allows the formulation of a separation-based lemma to handle
the high-order terms with reduced complexity in the control design. Complexity
is reduced in a twofold sense: the control gain of each virtual control law
does not have to be incorporated in the next virtual control law iteratively,
thus leading to a simpler expression of the control laws; the order of the
virtual control gains increases only proportionally (rather than exponentially)
with the order of the systems, dramatically reducing high-gain issues.
