Consensus for the fractional‐order double‐integrator multi‐agent systems based on the sliding mode estimator

Abstract

Consensus for the fractional-order double-integrator multi-agent systems is mainly studied in this study. First, a control law based on the sliding mode estimator is proposed to achieve consensus for the multi-agent systems, where the linear systems and the non-linear systems are discussed, respectively. Second, a distributed control law based on the sliding mode estimator is given to accomplish distributed consensus for the multi-agent systems, the linear systems and the non-linear systems are also considered, respectively. The validity of the designed control laws is proved by choosing the adaptive Lyapunov candidate functions. Finally, several examples are presented to demonstrate the obtained results and show the advantage of the proposed control laws in the convergence speed.