亚严反馈系统镇定的全驱系统方法

doi:10.7527/S1000-6893.2023.29552

Abstract

Abstract:

This paper proposes a substabilization control method for a class of strict feedback systems with singular value gain functions based on Fully Actuated System （FAS） approach. Firstly， the definition of sub-Strict Feedback System （sub-SFS）， including the feasible set and singular set of this system， is given. Then， it is revealed that the sub-SFS can be transformed into a sub-FAS with high order by model transformation under certain conditions， and the corresponding attraction region is described precisely based on the concepts of substability and substabilization of FAS. Furthermore， by using the control characteristics of FAS， the stabilization control law of the sub-SFS can be explicitly solved in a very simple way， and the linear constant closed-loop control system is obtained. The proposed approach not only greatly reduces the design complexity， but also effectively avoids the controller singularity problem by using the feasibility conditions. Finally， theoretical stability analysis and numerical simulation are conducted to illustrate the effectiveness of the proposed approach.

Key words: sub-strict feedback system, fully-actuated system approach, substability, substabilization, singular value

CLC Number:

V448.2

Guangren DUAN. Fully actuated system approach for stabilization control of sub-strict feedback systems[J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(1): 629552-629552.

Figures/Tables 6

Table 1

Definitions of symbols

符号	定义
$R r$	$r$ 维实向量空间
$R m × n$	$m × n$ 维实矩阵空间
$A - 1$	矩阵 $A$ 的逆矩阵
$A T$	矩阵 $A$ 的转置
$d e t (A)$	矩阵 $A$ 的行列式
$I n$	$n$ 阶单位矩阵
$f n (x)$	函数 $f (x)$ 的 $n$ 阶导数
$Ω \ Θ$	集合 $Θ$ 在集合 $Ω$ 中的补集

Table 1

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

References 36

1	胡寿松. 自动控制原理［M］. 第6版. 北京：科学出版社， 2013.
	HU S S. Principle of automatic control［M］. 6th ed. Beijing： Science Press， 2013 （in Chinese）.
2	李阳，朱家仪，李树民. 非线性控制理论的回顾与展望［J］. 飞航导弹， 2004（11）： 55-58.
	LI Y， ZHU J Y， LI S M. Review and prospect of nonlinear control theory［J］. Winged Missiles Journal， 2004（11）： 55-58 （in Chinese）.
3	ZHANG Y X， GAO J A， CHEN Y M， et al. Adaptive neural network control for visual docking of an autonomous underwater vehicle using command filtered backstepping［J］. International Journal of Robust and Nonlinear Control， 2022， 32（8）： 4716-4738.
4	WEN G X， HAO W， FENG W W， et al. Optimized backstepping tracking control using reinforcement learning for quadrotor unmanned aerial vehicle system［J］. IEEE Transactions on Systems， Man， and Cybernetics： Systems， 2022， 52（8）： 5004-5015.
5	LING S， WANG H Q， LIU P X. Adaptive fuzzy tracking control of flexible-joint robots based on command filtering［J］. IEEE Transactions on Industrial Electronics， 2020， 67（5）： 4046-4055.
6	XIA D D， YUE X K， YIN Y W. Output-feedback asymptotic tracking control for rigid-body attitude via adaptive neural backstepping［J］. ISA Transactions， 2023， 136： 104-113.
7	吴锦，刘勇华，苏春翌，鲁仁全.具有不确定控制增益严格反馈系统的自适应命令滤波控制［J/OL］. 自动化学报，（2021-11-28）［2023-09-08］. .
	WU J， LIU Y H， SU C Y， LU R Q. Adaptive Command Filtered Control of Strict Feedback Systems with Uncertain Control Gains ［J/OL］. Acta Automatica Sinica，（2021-11-28）［2023-09-08］. .
8	YUAN X， CHEN B， LIN C， et al. A concurrent event-triggered approach for fuzzy adaptive control of nonlinear strict-feedback systems［J/OL］. IEEE Transactions on Cybernetics，（2022-11-23）［2023-09-08］. .
9	CHENG H， HUANG X C， CAO H W. Asymptotic tracking control for uncertain nonlinear strict-feedback systems with unknown time-varying delays［J］. IEEE Transactions on Neural Networks and Learning Systems， 2023， 34（12）： 9821-9831.
10	陈建勇，孙明轩. 严格反馈系统约束迭代学习控制［J］. 控制理论与应用， 2021， 38（5）： 561-570.
	CHEN J Y， SUN M X. Constrained iterative learning control of a class of strict-feedback systems［J］. Control Theory & Applications， 2021， 38（5）： 561-570 （in Chinese）.
11	BRIDGES M M， DAWSON D M， ABDALLAH C T. Contril of rigid-link， flexible-joint robots： A survey of backstepping approaches［J］. Journal of Robotic Systems， 1995， 12（3）： 199-216.
12	DENG H， KRSTIĆ M. Stochastic nonlinear stabilization—I： A backstepping design［J］. Systems & Control Letters， 1997， 32（3）： 143-150.
13	王家军，赵光宙，齐冬莲. 反推式控制在永磁同步电动机速度跟踪控制中的应用［J］. 中国电机工程学报， 2004， 24（8）： 95-98.
	WANG J J， ZHAO G Z， QI D L. Speed tracking control of permanent magnet synchronous motor with backstepping［J］. Proceedings of the CSEE， 2004， 24（8）： 95-98. （in Chinese）
14	DENG Y J， ZHANG X K， ZHANG G Q， et al. Adaptive neural tracking control of strict-feedback nonlinear systems with event-triggered state measurement［J］. ISA Transactions， 2021， 117： 28-39.
15	杨俊华，吴捷，胡跃明. 反步方法原理及在非线性鲁棒控制中的应用［J］. 控制与决策， 2002， 17（S1）： 641-647， 653.
	YANG J H， WU J， HU Y M. Backstepping method and its applications to nonlinear robust control［J］. Control and Decision， 2002， 17（S1）： 641-647， 653 （in Chinese）.
16	PENG Z H， WANG D， WANG J. Predictor-based neural dynamic surface control for uncertain nonlinear systems in strict-feedback form［J］. IEEE Transactions on Neural Networks and Learning Systems， 2017， 28（9）： 2156-2167.
17	GE S S， WANG C. Direct adaptive NN control of a class of nonlinear systems［J］. IEEE Transactions on Neural Networks， 2002， 13（1）： 214-221.
18	李铁山，邹早建，罗伟林. 基于DSC后推法的非线性系统的鲁棒自适应NN控制［J］. 自动化学报， 2008， 34（11）： 1424-1430.
	LI T S， ZOU Z J， LUO W L. DSC-backstepping based robust adaptive NN control for nonlinear systems［J］. Acta Automatica Sinica， 2008， 34（11）： 1424-1430 （in Chinese）.
19	LI Y X. Finite time command filtered adaptive fault tolerant control for a class of uncertain nonlinear systems［J］. Automatica， 2019， 106： 117-123.
20	WAN P， ZENG Z G. Adaptive tracking control of state-constrained strict-feedback nonlinear systems using direct method［J］. IEEE Transactions on Systems， Man， and Cybernetics： Systems， 2023， 53（8）： 5116-5126.
21	LI J H， KANG H， KIM M G， et al. Asymptotic trajectory tracking of underactuated non-minimum phase marine vessels［J］. IFAC-PapersOnLine， 2022， 55（31）： 281-286.
22	LI J H. Path tracking of underactuated ships with general form of dynamics［J］. International Journal of Control， 2016， 89（3）： 506-517.
23	LI J H， LEE P M. Path tracking in dive plane for a class of torpedo-type underactuated AUVs［C］∥ 2009 7th Asian Control Conference. Piscataway： IEEE Press， 2009： 360-365.
24	段广仁. 高阶系统方法： I.全驱系统与参数化设计［J］. 自动化学报， 2020， 46（7）： 1333-1345.
	DUAN G R. High-order system approaches： I. Fully-actuated systems and parametric designs［J］. Acta Automatica Sinica， 2020， 46（7）： 1333-1345 （in Chinese）.
25	段广仁. 高阶系统方法： Ⅱ.能控性与全驱性［J］. 自动化学报， 2020， 46（8）： 1571-1581.
	DUAN G R. High-order system approaches： Ⅱ. Controllability and full-actuation［J］. Acta Automatica Sinica， 2020， 46（8）： 1571-1581 （in Chinese）.
26	段广仁. 高阶系统方法： Ⅲ.能观性与观测器设计［J］. 自动化学报， 2020， 46（9）： 1885-1895.
	DUAN G R. High-order system approaches： Ⅲ. Observability and observer design［J］. Acta Automatica Sinica， 2020， 46（9）： 1885-1895 （in Chinese）.
27	DUAN G R. High-order fully actuated system approaches： Part II. Generalized strict-feedback systems［J］. International Journal of Systems Science， 2021， 52（3）： 437-454.
28	DUAN G R. Substability and substabilization： Control of subfully actuated systems［J］. IEEE Transactions on Cybernetics， 2023， 53（11）： 7309-7322.
29	DUAN G R. Fully actuated system approaches for continuous-time delay systems： Part 1. Systems with state delays only［J］. Science China Information Sciences， 2023， 66（1）： 112201.
30	DUAN G R. Discrete-time delay systems： Part 2. Sub-fully actuated case［J］. Science China Information Sciences， 2022， 65（9）： 1-15.
31	DUAN G R. High-order fully actuated system approaches： Part V. Robust adaptive control［J］. International Journal of Systems Science， 2021， 52（10）： 2129-2143.
32	DUAN G R. High-order fully actuated system approaches： Part III. Robust control and high-order backstepping［J］. International Journal of Systems Science， 2021， 52（5）： 952-971.
33	DUAN G R. Robust stabilization of time-varying nonlinear systems with time-varying delays： A fully actuated system approach［J］. IEEE Transactions on Cybernetics， 2023， 53（12）： 7455-7468.
34	段广全，刘国平等．基于全驱系统方法的组合航天器位姿自适应预设性能控制［J/OL］. 航空学报，（2023-08-25）［2023-09-08］. .
	DUAN G Q， LIU G P. Adaptive prescribed performance control for position and attitude of combined spacecraft based on fully actuated system approach ［J/OL］. Acta Aeronautica et Astronautica Sinica，（2023-08-25）［2023-09-08］. （in Chinese）.
35	XU X. High-order fully actuated system models for discrete-time strict-feedback systems with increasing dimensions［C］∥ 2023 2nd Conference on Fully Actuated System Theory and Applications （CFASTA）. Piscataway： IEEE Press， 2023： 66-70.
36	DUAN G. A FAS approach for stabilization of generalized chained forms： Part I. Discontinuous controllers［J/OL］. Science China Information Sciences，（2023-04-07）［2023-09-08］. .

[1]	Ximing CUI, Zhipeng QIU, Jia WEI, Chi ZHANG, Kai SONG, Zhe LI, Shupeng WANG. Data-driven method for characterization of structural steel surface stress of magnetic Barkhausen noise [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(8): 427237-427237.
[2]	Xiaoxu HE, Pei LEI, Deng PAN, Yang YANG, Xiankun LI, Zhenbo DENG. Posture and position computing method for aircraft component based on PSO and WSVD [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(7): 427162-427162.
[3]	HAO Zhenyang, WANG Tao, CAO Xin, ZHU Tao. Decoupling control strategy of position loop for vibration damping electric actuator [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(8): 325884-325884.
[4]	QI Liangang, HAN Yanze, WANG Yani, GUO Qiang, Kaliuzhny MYKOLA. Multi-component LFM interference suppression method based on chirp rate turning point and FrFT [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(8): 326840-326840.
[5]	LI Baoguo, ZHANG Cheng'an, XU Jianqiu. A radar-embedded communication waveform design method based on SVD [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(7): 325401-325401.
[6]	CUI Zhizhuo, DU Fuzhou, XIONG Tao. Analysis and coordination of assembly deviation of multi plane-and-holes assembly based on orientation points group [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(7): 421899-421899.
[7]	NING Fangli, ZHANG Chao, PAN Feng, LIU Yong, WEI Juan. Compressive sensing algorithm for sound source location of aircraft landing gear [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(5): 121810-121810.
[8]	YU Jia, YANG Pengfei, YAN De. Influence analysis of hypersonic flight vehicle model uncertainty [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015, 36(1): 192-200.
[9]	Dai Yuting;Wu Zhigang;Yang Chao. Quantification Analysis of Uncertain Flutter Risks [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2010, 31(9): 1788-1795.
[10]	Yang Zhichun;Gu Yingsong;Xia Wei. New Type of Flutter Solution Based on Matrix Singularity [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2009, 30(6): 985-989.
[11]	Gong Xiaolin;Fang Jiancheng. Application of SVDbased R-T-S Optimal Smoothing Algorithm to POS for Airborne SAR Motion Compensation [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2009, 30(2): 311-318.
[12]	HE Jin;LIU Zhong. DOA Estimation in Impulsive Noise Environments Using Fractional Lower Order Spatial-Temporal Matrix [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2006, 27(1): 104-108.
[13]	FAN Zi-qiang;FANG Zhen-ping. ROBUST, NONLINEAR CONTROL DESIGN FOR A POSTSTALL MANEUVER AIRCRAFT [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2002, 23(3): 193-196.
[14]	Yu Jing;Bao Ming. RESEARCH ON THE LOCATION OF COHERENT MECHANICAL NOISE SOURCES [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 1999, 20(2): 114-117.
[15]	Wu Bin;Cheng Peng. STABILITY MARGIN ANALYSIS OF THE MULTILOOP FLIGHT CONTROL SYSTEMS [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 1998, 19(6): 18-22.

Fully actuated system approach for stabilization control of sub-strict feedback systems

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 6

References 36

Related Articles 15

Recommended Articles

Metrics

Comments