Exponential consensus of discrete-time non-linear multi-agent systems via relative state-dependent impulsive protocols

Event‐based impulsive consensus for delayed multi‐agent systems

“…The initial state of the agents is (x T 1 (t), x T 2 (t), x T 3 (t), x T 4 (t), x T 5 (t), x T 6 (t)) = (−1.2 cos t, −1.5t, 1.3 cos t, t, −1.1, 1.8t, 1.2 cos t, −1.6t, −1.3 cos t, −1.4t, 0.8 cos t, 1.2t), −0.3 ≤ t ≤ 0, thus we have N ∑ i=1 ξ i ||e i (t 0 )|| 2 = 1.4419. Let t 0 = 0, then under the eventtriggering condition (17) one can obtain the eventtriggering impulsive time series {t k }. Figure 2 shows the triggering impulsive instants under different parameters 𝜎 which plays a decisive role.…”

“…It has been proven to be more significant and efficient than continuous control schemes, especially for some practical systems which can't bear continuous control inputs, such as the money supply control in financial market [12] and the ecological control in pest management systems [13,14]. Due to its high efficiency and energy-saving advantage, impulsive control has been preferred by many researchers when investigating the consensus problems of networked systems [10,[15][16][17]. For example, Liu et al applied hybrid pinning impulsive control method in Liu et al [10] to make the states of all agents to reach consensus on zero for nonlinear multi-agent system with a directed spanning tree.…”

“…For example, Liu et al applied hybrid pinning impulsive control method in Liu et al [10] to make the states of all agents to reach consensus on zero for nonlinear multi-agent system with a directed spanning tree. Based on impulsive control scheme, the leader-following consensus and exponential consensus of nonlinear multi-agent systems was concerned in He et al [16] and Han et al [17], respectively. It should be mentioned that the aforementioned studies on the impulsive consensus of MASs were time-scheduled, which assume that the impulsive time instants is known ahead of time and periodic sampling.…”

Iterative learning control for multi-agent systems with impulsive consensus tracking

“…In this regard, Cui conducted related research in [6]. However, very few existing papers considered the consensus problem of MASs with impulse, for examples, [8,14,16,21,32,35,36,38], in the conventional consensus framework. In addition, impulsive control approach is advantageous in simplicity and flexibility for such kind of systems because the standard continuous state information is not required.…”

Fully relative state constraint impulsive consensus of nonlinear multi‐agent systems via state‐dependent impulsive protocols

“…In paper [29], second-order impulsive consensus of multi-agent systems with time delays was proposed only by the position information. The author used the relative states of any two agents to design the impulsive surface for achieving consensus of discrete-time nonlinear multi-agent systems in paper [30]. Compared with [11,27] of fixed-time impulses, the variable impulsive strategies in paper [30] are wider applications in real world.…”