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This paper investigates the adaptive consensus for networked mobile agents with heterogeneous nonlinear dynamics. Using tools from matrix, graph, and Lyapunov stability theories, sufficient consensus conditions are obtained under adaptive control protocols for both first-order and second-order cases. We design an adaptive strategy on the coupling strengths, which can guarantee that the consensus conditions do not require any global information except a connection assumption. The obtained results are also extended to networked mobile agents with identical nonlinear dynamics via adaptive pinning control. Finally, numerical simulations are presented to illustrate the theoretical findings.

In recent years, distributed cooperative control for multiagent systems has been intensively investigated by researchers from various disciplines. This is due to its broad potential applications in sensor networks, combat intelligence, surveillance, and so forth [

Consensus is one of the most fundamental problems in distributed cooperative control, which means that the states of the agents reach an agreement on a common physical quantity of interest by implementing an appropriate consensus protocol based on the information from local neighbors. Numerous interesting results about consensus algorithm were presented in the past decade. The earlier studies on consensus problem are mainly about multiagent systems with first-order dynamics [

However, in reality, mobile agents may be governed by more complicated intrinsic dynamics, so second-order consensus problems for multiagent with nonlinear dynamics have been investigated [

The rest of the paper is organized as follows. In Section

In this section, some notations and preliminaries are introduced. The following notations are used throughout this paper.

Let

Before moving on, some assumptions and Lemmas are introduced.

Suppose that the undirected graph

If

The matrix

If a scalar function

In this section, consensus conditions for both first-order and second-order multiagent systems with heterogeneous nonlinear dynamics are obtained by designing pinning-like adaptive control protocols. Pinning-like adaptive consensus for first-order multiagent systems with heterogeneous nonlinear dynamics is investigated in the first subsection and the second-order case is investigated in the second subsection. For the first-order case, the

For the second-order case, the

In this subsection, we investigate consensus criteria for first-order multiagent systems with heterogeneous nonlinear dynamics via distributed adaptive pinning control.

As mentioned in many literatures, consensus or synchronization for networked systems with nonidentical nodes cannot be realized without control if the nonidentical dynamic functions do not have a common solution. Thereby, a distributed adaptive pinning-like control protocol is proposed, under which leader-following consensus for networked system (

The following assumption is necessary for our main results.

For arbitrary

From Lemmas

The controlled network for system (

Suppose that Assumptions

Let

Differentiating

From Theorem

According to Theorem

Suppose that the topology is undirected and connected and

In this subsection, we investigate second-order consensus of networked nonlinear multiagent system (

For every

Choosing

Let

Under consensus protocol (

Suppose that Assumptions

Let

Consider the following Lyapunov function candidate:

Differentiating

From Theorem

When all the nonlinear function

Suppose that Assumptions

In this section, several simulation results are presented to illustrate the previous theoretical results.

We choose a network with 4 nodes and the reference node is chosen as

In Figure

State trajectories of the four nodes with the reference state.

Trajectories of the adaptive gains.

The topology is chosen the same as Example

The nonlinear dynamic functions are chosen as

Trajectories for position.

Trajectories for velocity.

Trajectories of the adaptive gains.

Adaptive consensus for networked mobile agents with heterogeneous nonlinear dynamics was investigated in this paper. Sufficient consensus conditions for both first-order and second-order networked mobile agents with heterogeneous nonlinear dynamics were obtained. By designing an adaptive strategy on the coupling strengths, the consensus can be achieved without requiring any global information except a connection assumption. We also extended the results to the consensus for nonlinear mobile agents with identical nonlinear dynamics. Simulation examples were given to demonstrate the feasibility and effectiveness of the proposed consensus scheme.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work is supported by National Natural Science Foundation (NNSF) of China under Grant no. 61174075, 51375186, Natural Science Foundation of Ministry of Education in Hunan Province (12C0077), and NSF of Hunan University of Technology (2012HZX18).