F. Chen, Y. Cao and W. Ren, “Distributed Average Tracking of Multiple Time-Varying Reference Signals With Bounded Derivatives,” in IEEE Transactions on Automatic Control, vol. 57, no. 12, pp. 3169-3174, Dec. 2012, doi: 10.1109/TAC.2012.2199176.

Distributed Average Tracking of Multiple Time-Varying Reference Signals With Bounded Derivatives

• 1 Introduction
• 2 Problem Descriptions and Mathematical Preliminaries
• • 2.1 Problem Description
  • 2.2 Mathematical Preliminaries
  • • • • • Filippove sense
• 3 Stability Analysis

1 Introduction

2 Problem Descriptions and Mathematical Preliminaries

2.1 Problem Description

參考信號 $r_i(t)$，滿足
$${\dot{r}}_i(t)=f_i(t)$$

其中，$f_i(t)\in {\mathbb{R}}^m$ 可測量并有上界 $\bar{f}$。

2.2 Mathematical Preliminaries

Filippove sense

Filippove sense

3 Stability Analysis

clear clcL = [2 -1 0 0 0 0 0 0 0 -1;-1 2 -1 0 0 0 0 0 0 0;0 -1 2 -1 0 0 0 0 0 0;0 0 -1 2 -1 0 0 0 0 0;0 0 0 -1 2 -1 0 0 0 0;0 0 0 0 -1 2 -1 0 0 0;0 0 0 0 0 -1 2 -1 0 0;0 0 0 0 0 0 -1 2 -1 0;0 0 0 0 0 0 0 -1 2 -1;-1 0 0 0 0 0 0 0 -1 2;]X0 = [0.5913, 1.9835, 0.7023, 0.1437, 0.4684, 1.9726, 0.4777, 1.1766, 1.9707, 0.5860]';alpha = 5;% dotri = i * sin(t) + mod(t,3);% 時間參數 tbegin = 0; tfinal = 4; dT = 0.01; T(1,1) = 0; R(10,1) = 0;% 計算次數 times = (tfinal - tbegin) / dT;for time = 1:1:times% 記錄時間T(1, time+1) = T(1, time) + dT;for i=1:10R(i, time+1) = R(i,time) + dT * i * sin(dT) + mod(dT, 3);end endav = sum(R,1)/10; plot(T,av)

clear clcL = [2 -1 0 0 0 0 0 0 0 -1;-1 2 -1 0 0 0 0 0 0 0;0 -1 2 -1 0 0 0 0 0 0;0 0 -1 2 -1 0 0 0 0 0;0 0 0 -1 2 -1 0 0 0 0;0 0 0 0 -1 2 -1 0 0 0;0 0 0 0 0 -1 2 -1 0 0;0 0 0 0 0 0 -1 2 -1 0;0 0 0 0 0 0 0 -1 2 -1;-1 0 0 0 0 0 0 0 -1 2;]X0 = [0.5913, 1.9835, 0.7023, 0.1437, 0.4684, 1.9726, 0.4777, 1.1766, 1.9707, 0.5860]';alpha = 5;% dotri = i * sin(t) + mod(t,3);% 時間參數 tbegin = 0; tfinal = 4; dT = 0.01; T(1,1) = 0; R(10,1) = 0;% 計算次數 times = (tfinal - tbegin) / dT;for time = 1:1:times% 記錄時間T(1, time+1) = T(1, time) + dT;for i=1:10R(i, time+1) = R(i,time) + dT * i * sin(dT) + mod(dT, 3);end endav = sum(R,1)/10; plot(T,av)

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