Guaranteed cost consensus for multi‐agent systems with switching topologies

Abstract

Guaranteed cost consensus problems for multi-agent systems with switching topologies are investigated. Firstly, guaranteed cost consensus for multi-agent systems is introduced based on state errors among neighboring agents and control inputs of all agents, where a tradeoff between the consensus regulation performance and the control effort is considered. Then, a sufficient condition for guaranteed cost consensus is given by the state-space decomposition approach and the Lyapunov method, where an upper bound of the cost function is determined and an approach is proposed to determine the control gain. It is worth mentioning that the criterions for guaranteed cost consensus are only dependent on the maximum eigenvalue of the Laplacian matrices of switching topologies. Finally, numerical simulations are given to demonstrate theoretical results. more challenging. Cao and Ren [16] studied the consensus problems with undirected and directed topologies with a sampled-data setting. In [17], the consensus for multi-agent systems with directed topologies was considered. Xi et al. [18] investigated consensus problems by the partial stability method, where the interaction topologies for multi-agent systems were directed. In [19], linear matrix inequality (LMI) criterions for consensus problems of multi-agent systems with bounded time-varying delays were presented. In [20], the cases with unbounded time-varying delays were dealt with. Ma and Zhang [21] showed that both the dynamic structure of each agent and interaction topologies impact on the consensualizability properties of multi-agent systems.It should be pointed out that consensus problems for multi-agent systems with switching topologies are more complicated because the neighboring set of each agent is time varying. The consensus problems for multi-agent systems were studied in [22], where it was assumed that all the possible topologies were undirected and connected. Su and Huang [23] relaxed the connection conditions in [22] to the joint connection cases. In [24][25][26][27][28][29], consensus problems for multi-agent systems with switching directed topologies were investigated. In [24], it was shown that consensus can be achieved asymptotically if the joint topology of the directed topologies had a spanning tree frequently enough as multi-agent systems evolve. Xiao and Wang [25] investigated consensus problems with bounded time-varying delays based on the properties of non-negative matrices. In [26], sufficient conditions for consensus of multi-agent systems with constant time delays and finite timevarying delays were given by LMIs. The consensus control problems for discrete-time multi-agent systems with stochastic noises were considered in [27]. Münz et al. [28] addressed the cases with arbitrarily large time delays, where a spanning tree should be contained in the joint topology of switching topologies in finite time. The paper [29] was devoted to the consensus problem of multiagent systems with switching topologies, where external disturbance was considered. It s...

Guaranteed cost formation control for multi-agent systems: Consensus approach

“…Then, the time derivative of V (t) = V (κ e (t)) with respect to t along the trajectory of system (16) iṡ…”

“…Then,V (t)| (16) ≤ 0 andV (t)| (16) = 0 if and only if κ e (t) ≡ 0. Moreover, by the convex property of Linear Matrix Inequalities, if Θ i < 0 (i = 2, N) thenΘ i < 0 (i = 2, 3, · · · , N).…”

“…By Definition 1, Θ i < 0 (i = 2, N) can ensure that multi-agent system (8) achieves consensus. From (35) and˙ (t) ≤ 0, one has (16) .…”

“…To this end, the guaranteed cost consensus algorithm is an effective approach. In [15] and [16], the guaranteed cost consensus problems for first-order multi-agent systems with fixed and switching topologies were investigated, respectively. The influence of time delays on the guaranteed cost consensus was analyzed in [17].…”

Guaranteed cost control of mobile sensor networks with Markov switching topologies

“…Based on nonnegative matrix theory, [20] and [21] investigated consensus control of multi-agent systems under dynamic topology. [22] considered a tradeoff between system performance and control effort of multi-agent systems with switching topologies. In some cases, due to random network conditions or environmental factors (e.g., sea wave, the wind and weather condition, [23]), an MSN may experience a randomly switching communication topology.…”