  In this paper, both the fixed-time distributed consensus tracking and the
fixed-time distributed average tracking problems for double-integrator-type
multi-agent systems with bounded input disturbances are studied, respectively.
Firstly, a new practical robust fixed-time sliding mode control method based on
the time-based generator is proposed. Secondly, a fixed-time distributed
consensus tracking observer for double-integrator-type multi-agent systems is
designed to estimate the state disagreements between the leader and the
followers under undirected and directed communication, respectively. Thirdly, a
fixed-time distributed average tracking observer for double-integrator-type
multi-agent systems is designed to measure the average value of reference
signals under undirected communication. Note that both the observers for the
distributed consensus tracking and the distributed average tracking are devised
based on time-based generators and can be extended to that of high-order
multi-agent systems trivially. Furthermore, by combing the fixed-time sliding
mode control with the fixed-time observers, the fixed-time controllers are
designed to solve the distributed consensus tracking and the distributed
average tracking problems. Finally, a few numerical simulations are shown to
verify the results.
