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... implies that each converges to some finite value. . Remark 3: It is worth mentioning that the adaptive scheme in (14) for updating the coupling gains is partly inspired by the adaptive strategies in =-=[25]-=-–[27], which however are applicable only to the case without a leader or the case of a leader with zero control input. Compared to the static controller (4), the adaptive controller (14) requires neit...

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... deterministic linear dynamics. A more interesting scenario is that agents have uncertain general nonlinear dynamics. Nevertheless, such a scenario has rarely been considered. Some exceptions include =-=[20]-=- for leadless consensus and [21,22] for leader-following consensus, where the solution was given under the restrictive assumption that nonlinear dynamics should satisfy a global Lipschitz-type conditi...

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... K. The same difficulty arises for other consensus and synchronization problems, which are often handled by estimating λ2 or employing adaptive technique for tuning the gain k; see, for example, [1], =-=[8]-=-. In the context of adaptive control the above result is a typical “high gain” approach: choosing the feedback gain k sufficiently large leads to an arbitrarily accurate tracking of a desired trajecto...

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...rameter multiplying agent input signal) is known, and it is the same for all agents. They proved the interesting result that each agent state converges toward the average of its neighbors’ states. In =-=[24]-=- the consensus problemwith a general linear model and Lipschitz nonlinear dynamics is considered. The authors analyze an undirected graph and assume that the linear dynamics are known. The proposed co...

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... more local controllers. To ensure overall system stability, the Lyapunov function approach is widely used to drive the subsystem states to zero according to selected non-negative potential functions =-=[1]-=-. For optimal control, minimization of convergence speed [2] and minimization of the sum of convex cost functions for individual subsystems [3] were also studied. The distributed model predictive cont...

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...quilibrium, in most cases, is oscillatory). Another interesting result appears in [5] that discusses the oscillatory synchronization of multiple pendulums. Other results (see, e.g., [16], [17], [18], =-=[19]-=-) can also realize certain kind of oscillatory synchronization due to the explicit inclusion/presence of Lipschitz nonlinearity in the closed-loop network dynamics. Most of the above results under the...

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...mented by the agents in a fully distributed fashion, i.e., using only the local information of its own and neighbors. To overcome this limitation, an adaptive static consensus protocol is proposed in =-=[21]-=-, which is motivated by the adaptive strategies for synchronization of complex networks in [22]. Similar adaptive schemes are presented to achieve second-order consensus with inherent nonlinear dynami...

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...d adaptive controllers are proposed, which implement adaptive laws to update the time-varying coupling weights between neighboring agents. Similar adaptive protocols have been also presented in [15], =-=[16]-=-, [17], [18] to solve the leaderless and leader-follower consensus problems. It is worth noting that the adaptive controllers in [6] are applicable to only the case where the graph among the agents ar...

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...each agent in a fully distributed fashion, i.e., using only the local information of its own and neighbors. To overcome this limitation, distributed adaptive consensus protocols are proposed in [12], =-=[13]-=-. Similar adaptive schemes are presented to achieve second-order August 21, 2014 DRAFT 3consensus with nonlinear dynamics in [14], [15]. Note that the protocols in [12], [13], [14], [15] are applicabl...

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...ledge of the eigenvalues of the Laplacianmatrix of the communication graph, which is actually global information. To overcome this limitation, distributed adaptive consensus protocols are proposed in =-=[22,23]-=-. For the case where there exists a leader with possibly nonzero control input, distributed controllers are proposed in [24,23] to solve the leaderfollower consensus problem. A common assumption in [9...