【Paper】2021_Observer-based distributed consensus for multi-agent systems with directed networks and

2024-06-02 02:39:46

Shuzhen Yu, Zhiyong Yu, Haijun Jiang, Xuehui Mei, Observer-based distributed consensus for multi-agent systems with directed networks and input saturation, Neurocomputing, Volume 420, 2021, Pages 111-123.

文章目录

1. Introduction
2. Preliminaries
6. Numerical example

1. Introduction

2. Preliminaries

x˙i(t)=Axi(t)+Bσˉ(ui(t))yi(t)=Cxi(t)(1)\begin{aligned} \dot{x}_i(t) & = A x_i (t) + B \bar{\sigma} (u_i(t)) \\ y_i(t) &= C x_i(t) \\ \end{aligned} \tag{1}x˙i(t)yi(t)=Axi(t)+Bσˉ(ui(t))=Cxi(t)(1)

σˉ(ui)=[sat(ui1),sat(ui2),⋯,sat(uim)]Tsat(uij)=sign(uij)min⁡{∣uij∣,ϖ}\begin{aligned} \bar{\sigma} (u_{i}) &= [ \textbf{sat}(u_{i1}), \textbf{sat}(u_{i2}), \cdots, \textbf{sat}(u_{im}) ]^\text{T} \\ \textbf{sat}(u_{ij}) &= \textbf{sign}(u_{ij}) \min\{|u_{ij}|, \varpi\} \end{aligned}σˉ(ui)sat(uij)=[sat(ui1),sat(ui2),⋯,sat(uim)]T=sign(uij)min{∣uij∣,ϖ}

x^˙i(t)=Ax^i(t)+Bui(t)−K(yi(t)−Cx^i(t))ui(t)=−BTP(ς)[∑j∈Niaij(x^i(t)−x^j(t))](2)\begin{aligned} \dot{\hat{x}}_i(t) & = A \hat{x}_i (t) + B u_i(t) - K (y_i(t) - C \hat{x}_i(t) ) \\ u_i(t) &= -B^\text{T} P(\varsigma) [\sum_{j\in N_i} a_{ij} (\hat{x}_i(t) - \hat{x}_j(t)) ] \\ \end{aligned} \tag{2}x^˙i(t)ui(t)=Ax^i(t)+Bui(t)−K(yi(t)−Cx^i(t))=−BTP(ς)[j∈Ni∑aij(x^i(t)−x^j(t))](2)

6. Numerical example

Example 1.

Example 2.

替换了 P(0.3)P(0.3)P(0.3) 参数矩阵后：

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