Jiang Y, Ji L, Pu X, et al. Group consensus for discrete-time heterogeneous multiagent systems with input and communication delays[J]. Complexity, 2018, 2018.

文章目錄

• 1 Introduction
• 2 Preliminaries and problem statements
• • 2.1 Graph theory and interconnection topology
  • 2.2 Discrete-time heterogeneous multiagent system
• 3 Main resultes
• • 3.1 Couple-group consensus for discrete-time heterogeneous MASs with multiple time delays under bipartite digraph
  • 3.2 Group consensus for discrete-time heterogeneous MASs with multiple time-delays under digraph with in-degree balance
• 4 Simulation

1 Introduction

2 Preliminaries and problem statements

2.1 Graph theory and interconnection topology

2.2 Discrete-time heterogeneous multiagent system

Assume the second-order agents are $1,2,?,n$
$$\begin{array}{rl}{x}_i(k+1)& =x_i(k)+v_i(k)\\ v_i(k+1)& =v_i(k)+u_i(k),i\in {\sigma }_1\end{array}$$

the first-order agents are $n+1,n+2,?,n+m$
$$\begin{array}{r}{x}_l(k+1)=x_l(k)+u_l(k),l\in {\sigma }_2\end{array}$$

3 Main resultes

3.1 Couple-group consensus for discrete-time heterogeneous MASs with multiple time delays under bipartite digraph

$$u_i(k)=?\alpha [\sum _{j\in N_i}{a}_{ij}[x_j(k?{\tau }_{ij})+x_i(k?\tau )]]?\beta v_i(k?\tau ),i\in {\sigma }_1$$

$$u_l(k)=?\gamma [\sum _{j\in N_l}{a}_{lj}[x_j(k?{\tau }_{lj})+x_l(k?\tau )]],l\in {\sigma }_2$$

3.2 Group consensus for discrete-time heterogeneous MASs with multiple time-delays under digraph with in-degree balance

4 Simulation

Example 19

先忽略時滯的情況：

下邊是考慮時滯的情況，首先是 ${\tau }_1=1,{\tau }_2=4.5,{\tau }_3=4.5,{\tau }_4=4.5,{\tau }_5=1,{\tau }_{ij}=1$

首先是 ${\tau }_1=1,{\tau }_2=4.5,{\tau }_3=4.5,{\tau }_4=4.5,{\tau }_5=4.5,{\tau }_{ij}=1$

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