  In this paper, a distributed average tracking problem is studied for
Lipschitz-type nonlinear dynamical systems. The objective is to design
distributed average tracking algorithms for locally interactive agents to track
the average of multiple reference signals. Here, in both the agents' and the
reference signals' dynamics, there is a nonlinear term satisfying the
Lipschitz-type condition. Three types of distributed average tracking
algorithms are designed. First, based on state-dependent-gain designing
approaches, a robust distributed average tracking algorithm is developed to
solve distributed average tracking problems without requiring the same initial
condition. Second, by using a gain adaption scheme, an adaptive distributed
average tracking algorithm is proposed in this paper to remove the requirement
that the Lipschitz constant is known for agents. Third, to reduce chattering
and make the algorithms easier to implement, a continuous distributed average
tracking algorithm based on a time-varying boundary layer is further designed
as a continuous approximation of the previous discontinuous distributed average
tracking algorithms.
