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In this paper, both the fixed-time distributed consensus tracking and thefixed-time distributed average tracking problems for double-integrator-typemulti-agent systems with bounded input disturbances are studied, respectively.Firstly, a new practical robust fixed-time sliding mode control method based onthe time-based generator is proposed. Secondly, a fixed-time distributedconsensus tracking observer for double-integrator-type multi-agent systems isdesigned to estimate the state disagreements between the leader and thefollowers under undirected and directed communication, respectively. Thirdly, afixed-time distributed average tracking observer for double-integrator-typemulti-agent systems is designed to measure the average value of referencesignals under undirected communication. Note that both the observers for thedistributed consensus tracking and the distributed average tracking are devisedbased on time-based generators and can be extended to that of high-ordermulti-agent systems trivially. Furthermore, by combing the fixed-time slidingmode control with the fixed-time observers, the fixed-time controllers aredesigned to solve the distributed consensus tracking and the distributedaverage tracking problems. Finally, a few numerical simulations are shown toverify the results.

Fixed-Time Cooperative Tracking Control for Double-Integrator Multi-Agent Systems: A Time-Based Generator Approach