Fixed-time consensus for multi-agent systems under directed and switching interaction topology

A class of robust consensus algorithms with predefined‐time convergence under switching topologies

“…However, such works do not consider disturbances affecting the agents and, more importantly, they do not guarantee that consensus is reached before a finite time, which could be easily arbitrarily preassigned. Notice also that the Lyapunov functions in our proofs are different than in previous methods, such as in other works . Consequently, the proposed predefined‐time consensus results do not follow trivially from the existing literature.…”

“…An essential part of our approach is the convexity result provided in Lemma . Finally, one can see that existing consensus protocols such as in other works are subsumed in our approach. In fact, the consensus protocols in the works of Zuo and Tie, Ning et al, and Wang et al are derived from and by taking k =1, p =1− s and q =1+ s , s ∈(0,1).…”

“…For solving this problem, the work of Ning et al presents robust fixed‐time consensus protocols that can be designed to satisfy time constraints, being this, in our opinion, the closest approach in the literature. Henceforth, to highlight our contribution, we will show that the results in the work of Ning et al and other fixed‐time consensus protocols, such as in the works of Zuo et al and Wang et al, are subsumed by our approach since our results allow more flexibility in the parameter selection. Besides, contrary to previous fixed‐time consensus protocols, our approach allows to straightforwardly specify the upper bound of the convergence time as a parameter of the consensus protocol.…”

Fixed-Time Consensus Tracking for Multiagent Systems With High-Order Integrator Dynamics

“…As an important performance measure also for coordination control of multi-agent systems, fast convergence is always pursued to achieve better performance and robustness, such as hybrid formation flying [1], consensus subject to switching topology [2], [3]. For a linear consensus protocol proposed for single integrator multiagent systems, Olfati-Saber and Murray have demonstrated in [4] that the algebraic connectivity of an interaction graph, i.e., the second smallest eigenvalue of the graph Laplacian, qualified the convergence rate.…”

A new coordinated path-following control for second-order multi-agent systems

“…Consensus problem [1], [2], [3], [4], [5], which means that the states of all the agents converge to certain quantities of interest, has been widely investigated in recent years. In some applications including formation flying and coordinated tracking, groups of agents are required to agree upon the state of a dynamic leader with local interaction, i.e., consensus tracking problem [6].…”