Necessary and sufficient conditions of stationary average consensus for second-order multi-agent systems

Stationary average consensus for high‐order multi‐agent systems

“…Primary studies on the consensus problem have focused on models with first‐order dynamics [6–11]. Consensus protocols for second‐order dynamics have been presented in [12–18]. For instance, the work of Ren [12] has focused on designing consensus protocols for formation control of second‐order MASs.…”

“…The stationary consensus problem is aimed at reaching agreement on a common constant value for the positions of agents while the remaining states (velocity, acceleration, and higher‐order states) all converge to zero [14–18, 22–25]. This strategy has applications in flocking, formation, and rendezvous position control of MASs.…”

“…Ren [16] has proposed protocols for both stationary and dynamic consensus problems in second‐order MASs under undirected networks. Synthesising protocols for discrete‐time second‐order MASs have been studied in [17, 18] in order to achieve stationary consensus.…”

“…The main limitation of the designed protocol in all the previous works [14–18, 22–24] is that the agreed position of the agents is a linear function of initial states (e.g., positions, velocities, and higher‐order states) and also coefficients of protocols, which does not necessarily respect the physical constraints of the position. For instance, take the altitude consensus problem in an MAS composed of unmanned helicopters with third‐order dynamics in which the designed protocol may result in negative or too high altitudes which are not accessible by the UAVs.…”