﻿ 基于预设性能的非仿射非线性系统自适应有限时间控制
 控制与决策  2020, Vol. 35 Issue (5): 1259-1264 0

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CHEN Ming, LI Xiao-hua. Adaptive finite-time tracking control for nonaffine nonlinear systems based on prescribed performance[J]. Control and Decision, 2020, 35(5): 1259-1264. DOI: 10.13195/j.kzyjc.2018.1127.
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### 文章历史

Adaptive finite-time tracking control for nonaffine nonlinear systems based on prescribed performance
CHEN Ming , LI Xiao-hua
School of Electronic and Inforamtion Engineering, Uniersity of Science and Technology Liaoning, Anshan 114051, China
Abstract: By combining prescribed performance and finite-time control, an adaptive finite-time tracking control method is proposed for a class of nonaffine nonlinear systems with dead zones. Based on the Backstepping technology, the fuzzy logic system and the finite-time Lyapunov stability theory, the sufficient conditions for the semi-global practical finite-time stable (SGFPS) and design steps are given. The control strategy can maintain that the output error converges to the predefined region in a finite time, as well as guarantee that the prescribed performance are achieved, such as the convergence speed, the maximum overshoot and the steady-error. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.
Keywords: finite-time control    prescribed performance    Backstepping    nonaffine nonlinear systems    adaptive control    tracking control
0 引言

1 预备知识与问题描述 1.1 预备知识

 (1)

 (2)

 (3)

 (4)

 (5)
1.2 问题描述

 (6)

 (7)

gr(u)、gl(u)是连续光滑函数, brbl是未知常数.

 (8)

 (9)

 (10)

 (11)

2 预设性能函数及误差变换

 (12)

 (13)

 (14)

ϵ(t)求一阶导数, 有

 (15)

, 显见ϕ>0, 且0＜ϕlϕϕu.

3 主要成果

 (16)

 (17)

step 1:考虑式(17)中的第一个子系统, 构造Lyapunov函数

 (18)

 (19)

 (20)

 (21)

, 将式(21)代入(19), 得

 (22)

 (23)
 (24)

 (25)

 (26)

step i (2≤in-1):选择第i个子系统的李亚普诺夫函数为

 (27)

 (28)

 (29)
 (30)

 (31)

step n:定义最后一个子系统的Lyaponov函数

 (32)

 (33)

 (34)
 (35)

 (36)

 (37)

K1=2γmin{kj}, 将式(37)代入(36), 并根据, 得到

 (38)

 (39)

 (40)

ϕuK0=K2, ς=min{min{σjγ}, K2, K1}, 易得

 (41)

 (42)

 (43)

4 仿真分析

 (44)

 (45)

 图 1 输出响应曲线
 图 2 跟踪误差响应曲线
 图 3 x2、x3响应曲线
 图 4 控制输入u响应曲线

 图 5 ai、σi取值一定, Γi取值不同时的跟踪曲线比较
5 结论

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