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Zheng J, Ju X, Zhang N, Xu D. A novel predefined-time neurodynamic approach for mixed variational inequality problems and applications. Neural Netw 2024; 174:106247. [PMID: 38518707 DOI: 10.1016/j.neunet.2024.106247] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2023] [Revised: 02/20/2024] [Accepted: 03/15/2024] [Indexed: 03/24/2024]
Abstract
In this paper, we propose a novel neurodynamic approach with predefined-time stability that offers a solution to address mixed variational inequality problems. Our approach introduces an adjustable time parameter, thereby enhancing flexibility and applicability compared to conventional fixed-time stability methods. By satisfying certain conditions, the proposed approach is capable of converging to a unique solution within a predefined-time, which sets it apart from fixed-time stability and finite-time stability approaches. Furthermore, our approach can be extended to address a wide range of mathematical optimization problems, including variational inequalities, nonlinear complementarity problems, sparse signal recovery problems, and nash equilibria seeking problems in noncooperative games. We provide numerical simulations to validate the theoretical derivation and showcase the effectiveness and feasibility of our proposed method.
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Affiliation(s)
- Jinlan Zheng
- Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
| | - Xingxing Ju
- College of Electronics and Information Engineering, Sichuan University, Chengdu 610065, China; Shaanxi Key Laboratory of Information Communication Network and Security, Xi'an University of Posts and Telecommunications, Xi'an, Shaanxi 710121, China
| | - Naimin Zhang
- College of Mathematics and Physics, Wenzhou University, Wenzhou 325035, China
| | - Dongpo Xu
- Key Laboratory for Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China.
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2
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Zhang L, Su Y, Wang Z, Wang H. Fixed-time terminal sliding mode control for uncertain robot manipulators. ISA Trans 2024; 144:364-373. [PMID: 37923630 DOI: 10.1016/j.isatra.2023.10.011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2021] [Revised: 08/20/2023] [Accepted: 10/13/2023] [Indexed: 11/07/2023]
Abstract
This paper proposes a fixed-time tracking control for robot manipulators in the presence of parametric uncertainties and disturbances. An auxiliary function is first proposed for constructing a fixed-time sliding manifold. Benefited from this fixed-time sliding manifold, a singularity-free robust control is proposed to evade the effects of algebraic loop problem of the commonly-used sliding mode controls (SMC). The key advantages of the proposed approach are: (i) exact fixed-time stability featuring the convergence time does not relate to the initial conditions and is acquired in advance; (ii) the singularity and algebraic loop problems are eliminated completely; (iii) a simple and intuitive control structure is used for easy implementation of trajectory tracking control for uncertain robot manipulators with faster transient and higher steady-state precision. Simulations and experimental comparisons validate the improved tracking performance of the proposed approach.
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Affiliation(s)
- Liyin Zhang
- School of Automation, Xi'an University of Posts and Telecommunications, Xi'an 710121, China; Xi'an Key Laboratory of Advanced Control and Intelligent Process, China
| | - Yuxin Su
- School of Electro-Mechanical Engineering, Xidian University, Xi'an 710071, China.
| | - Zeng Wang
- Northwest Institutes of Advanced Technology, Xi'an Technological University, Xi'an 710021, China
| | - Huan Wang
- School of Electro-Mechanical Engineering, Xidian University, Xi'an 710071, China
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3
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Truong TN, Vo AT, Kang HJ. A model-free terminal sliding mode control for robots: Achieving fixed-time prescribed performance and convergence. ISA Trans 2024; 144:330-341. [PMID: 37977881 DOI: 10.1016/j.isatra.2023.11.013] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2023] [Revised: 11/06/2023] [Accepted: 11/08/2023] [Indexed: 11/19/2023]
Abstract
This paper introduces a new control strategy for robot manipulators, specifically designed to tackle the challenges associated with traditional model-based sliding mode (SM) controller design. These challenges include the need for accurately computed system models, knowledge of disturbance upper bounds, fixed-time convergence, prescribed performance, and the generation of chattering. To overcome these obstacles, we propose the incorporation of a neural network (NN) that effectively addresses these issues by removing the constraint of a precise system model. Additionally, we introduce a novel fixed-time prescribed performance control (PPC) to enhance response performance and position-tracking accuracy, while effectively limiting overshoot and maintaining steady-state error within the predefined range. To expedite the convergence of the SM surface to its equilibrium point, we introduce a faster terminal sliding mode (TSM) surface and a novel fixed-time reaching control algorithm (RCA) with adaptable factors. By integrating these approaches, we develop a novel control strategy that successfully achieves the desired goals for robot manipulators. The effectiveness and stability of the proposed approach are validated through extensive simulations on a 3-DOF SAMSUNG FARA-AT2 robot manipulator, utilizing both Lyapunov criteria and performance evaluations. The results demonstrate improved convergence rate and tracking accuracy, reduced chattering, and enhanced controller robustness.
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Affiliation(s)
- Thanh Nguyen Truong
- School of Electrical Engineering, University of Ulsan, 93 Daehak-ro, Nam-gu, Ulsan, 44610, Republic of Korea.
| | - Anh Tuan Vo
- School of Electrical Engineering, University of Ulsan, 93 Daehak-ro, Nam-gu, Ulsan, 44610, Republic of Korea.
| | - Hee-Jun Kang
- School of Electrical Engineering, University of Ulsan, 93 Daehak-ro, Nam-gu, Ulsan, 44610, Republic of Korea.
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4
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Guan T, Zhang K, Li B, Guan X, Yiu KFC. Adaptive fixed-time sliding mode control for spacecraft reorientation with attitude pointing constraints and disturbance rejection. ISA Trans 2023:S0019-0578(23)00420-2. [PMID: 37806819 DOI: 10.1016/j.isatra.2023.09.013] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2022] [Revised: 07/25/2023] [Accepted: 09/15/2023] [Indexed: 10/10/2023]
Abstract
Spacecraft reorientation with attitude pointing constraints and the uncertainty of inertia and external disturbance is investigated in this paper. By introducing the potential function into the design of non-singular fixed-time sliding mode surface, the proposed controller can achieve fixed-time convergence and the convergence time of attitude error can be predetermined by selecting appropriate parameters. Meanwhile, the attitude pointing constraints can be satisfied all the time. The designed sliding surface and potential function have two equilibrium points, which guarantees the unwinding-free performance. Furthermore, an adaptive sliding mode control scheme is developed to handle the system lumped disturbance. Rigorous Lyapunov analyses are employed to ensure practical fixed-time closed-loop stability in the presence of system disturbance uncertainties and attitude pointing constraints. Therefore, the fixed-time stability, the feasibility of attitude pointing constraints and disturbance rejection are achieved simultaneously with the proposed controller. Numerical simulations are provided to demonstrate the effectiveness and superiority of the proposed method.
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Affiliation(s)
- Tao Guan
- School of Aeronautics and Astronautics, Sichuan University, Chengdu, China.
| | - Kai Zhang
- School of Aeronautics and Astronautics, Sichuan University, Chengdu, China.
| | - Bin Li
- School of Aeronautics and Astronautics, Sichuan University, Chengdu, China.
| | - Xiaoyi Guan
- Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China.
| | - Ka-Fai Cedric Yiu
- Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China.
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5
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Kong F, Zhu Q, Karimi HR. Fixed-time periodic stabilization of discontinuous reaction-diffusion Cohen-Grossberg neural networks. Neural Netw 2023; 166:354-365. [PMID: 37544092 DOI: 10.1016/j.neunet.2023.07.017] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/02/2023] [Revised: 05/22/2023] [Accepted: 07/12/2023] [Indexed: 08/08/2023]
Abstract
This paper aims to study the fixed-time stabilization of a class of delayed discontinuous reaction-diffusion Cohen-Grossberg neural networks. Firstly, by providing some relaxed conditions containing indefinite functions and based on inequality techniques, a new fixed-time stability lemma is given, which can improve the traditional ones. Secondly, based on state-dependent switching laws, the periodic wave solution of the formulated networks is transformed into the periodic solution of ordinary differential system. By utilizing differential inclusions theory and coincidence theorem, the existence of periodic solutions is obtained. Thirdly, based on the new fixed-time stability lemma, the periodic solutions are stabilized at zero in a fixed-time, which is a new topic on reaction-diffusion networks. Moreover, the established criteria are all delay-dependent, which are less conservative than the previous delay-independent ones for ensuring the stabilization of delayed reaction-diffusion networks. Finally, two examples give numerical explanations of the proposed results and highlight the influence of delays.
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Affiliation(s)
- Fanchao Kong
- School of Mathematics and Statistics, Anhui Normal University, Wuhu, Anhui 241000, China; MOE-LCSM, School of Mathematical Sciences and Statistics, Hunan Normal University, Changsha 410081, China.
| | - Quanxin Zhu
- MOE-LCSM, School of Mathematical Sciences and Statistics, Hunan Normal University, Changsha 410081, China.
| | - Hamid Reza Karimi
- Department of Mechanical Engineering, Politecnico di Milano, Milan 20156, Italy.
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6
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Zhuang M, Song S. Fixed-time fault-tolerant attitude control for rigid spacecraft with torque saturation. ISA Trans 2023; 139:229-243. [PMID: 37156692 DOI: 10.1016/j.isatra.2023.04.013] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2021] [Revised: 03/08/2023] [Accepted: 04/14/2023] [Indexed: 05/10/2023]
Abstract
This paper investigates the fixed-time attitude control problem for spacecraft under input saturation, actuator faults, and system uncertainties. Three novel saturated fixed-time nonsingular terminal sliding mode surfaces (NTSMSs) are designed, which can keep the system states fixed-time stable after the establishment of their sliding manifolds. Two of them are time-varying and firstly designed. Each of the two NTSMSs has an adjustment parameter that is adjusted dynamically and used to handle saturation and cancel the attitude dynamics. According to other related predesigned parameters, a conservative lower bound of this parameter is obtained. A saturated control scheme is then designed in conjunction with a newly proposed saturated reaching law. A modification strategy is carried out to facilitate the engineering applications of our methods. The fixed-time stability of the closed-loop systems is validated by Lyapunov stable theory. Simulation results validate the effectiveness and superiority of the proposed control scheme.
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Affiliation(s)
- Minglei Zhuang
- Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin, 150001, China; School of Electronic Information Engineering, Inner Mongolia University, Hohhot, 010021, China.
| | - Shenmin Song
- Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin, 150001, China.
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7
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Lv J, Wang C, Kao Y, Jiang Y. A fixed-time distributed extended state observer for uncertain second-order nonlinear system. ISA Trans 2023; 138:373-383. [PMID: 36803780 DOI: 10.1016/j.isatra.2023.02.016] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2022] [Revised: 01/16/2023] [Accepted: 02/10/2023] [Indexed: 06/16/2023]
Abstract
This paper investigates the fixed-time distributed estimation problem for a class of second-order nonlinear systems with uncertain input, unknown nonlinearity and matched perturbation. A fixed-time distributed extended state observer (FxTDESO) consisting of a group of local observer nodes under directed communication topology is proposed, and each node can reconstruct both the full state and unknown dynamics of the system. To achieve fixed-time stability, a Lyapunov function is elaborated, and based on this, sufficient conditions for the existence of the FxTDESO are established. Under time-invariant and time-varying disturbance, the observation errors can converge to the origin and a small region of the origin within a fixed time, respectively, where the upper bound of the settling time (UBST) is irrelevant to the initial conditions. Compared to the existing fixed-time distributed observers, the proposed observer can reconstruct both the unknown states and uncertain dynamics, and only the output of the leader and 1-dimensional output estimates from the neighboring nodes are needed in the observer design which effectively reduces the communication load. The paper also extends previous finite-time distributed extended state observer to the case of time-variant disturbance and eliminates the complex linear matrix equation assumption that guarantees the finite-time stability. Furthermore, the FxTDESO design for a class of high-order nonlinear systems is also discussed. Finally, simulation examples are conducted to demonstrate the effectiveness of the proposed observer.
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Affiliation(s)
- Jixing Lv
- School of Aeronautics, Harbin Institute of Technology, Harbin 150001, China.
| | - Changhong Wang
- School of Aeronautics, Harbin Institute of Technology, Harbin 150001, China.
| | - Yonggui Kao
- School of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, China.
| | - Yushi Jiang
- Beijing Institute of Space Long March Vehicle, Beijing 100076, China.
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8
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Zhang Y, Zhu M, Chen T, Zheng Z. Distributed event-triggered fixed-time formation and trajectory tracking control for multiple stratospheric airships. ISA Trans 2022; 130:63-78. [PMID: 35369992 DOI: 10.1016/j.isatra.2022.03.016] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2021] [Revised: 03/17/2022] [Accepted: 03/17/2022] [Indexed: 06/14/2023]
Abstract
In this study, an event-triggered fixed-time multiple stratospheric airship formation trajectory tracking controller is designed, and it is composed of two parts: the airship leader trajectory tracking controller (ALTTC) and the airship follower formation tracking controller (AFFTC). First, based on the framework of backstepping, the fixed-time ALTTC is designed to allow the trajectory tracking error to converge to zero within a fixed time. Subsequently, the event-triggered fixed-time AFFTC is designed to reduce the formation tracking error to zero within a fixed time. Two event-triggering conditions are designed to reduce the transmission times of control inputs and calculation times of control outputs. The fixed-time stability and the trajectory-tracking and formation-tracking performance of event-triggered closed-loop systems are theoretically shown to be ensured, and Zeno behavior is excluded in the proposed asynchronous event-triggering mechanism. Finally, simulations indicate the effectiveness of the proposed controller.
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Affiliation(s)
- Yifei Zhang
- School of Aeronautic Science and Engineering, PR China
| | - Ming Zhu
- Institute of Unmanned System, PR China
| | - Tian Chen
- School of Electronic and Information Engineering, PR China.
| | - Zewei Zheng
- School of Automation Science and Electrical Engineering Beihang University, Beijing 100191, PR China.
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9
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Lu Q, Chen J, Wang Q, Zhang D, Sun M, Su CY. Practical fixed-time trajectory tracking control of constrained wheeled mobile robots with kinematic disturbances. ISA Trans 2022; 129:273-286. [PMID: 35039151 DOI: 10.1016/j.isatra.2021.12.039] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2021] [Revised: 12/09/2021] [Accepted: 12/31/2021] [Indexed: 06/14/2023]
Abstract
This paper addresses the problem of practical fixed-time trajectory tracking for wheeled mobile robots (WMRs) subject to kinematic disturbances and input saturation. Firstly, considering the under-actuated characteristics of the WMR systems, the WMR model under kinematic disturbances is transformed into a two-input two-output interference system by using a set of output equations. Then, the tracking error state equation with lumped disturbances in the acceleration-level pseudo-dynamic control (ALPDC) structure is established. The lumped disturbances are estimated by a designed fixed-time extended state observer (FESO) without requiring the differentiability of the first-time derivatives of the kinematic disturbances. Meanwhile, a practical fixed-time output feedback control law is developed for trajectory tracking. By resorting to the Lyapunov stability theorem, the fixed-time stability analysis of the closed-loop WMR system in the presence of input saturation is conducted. Finally, simulation results are presented to show the effectiveness of the proposed approach.
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Affiliation(s)
- Qun Lu
- College of Electrical Engineering, Yancheng Institute of Technology, Yancheng 224003, China
| | - Jian Chen
- College of Electrical Engineering, Yancheng Institute of Technology, Yancheng 224003, China
| | - Qianjin Wang
- College of Electrical Engineering, Yancheng Institute of Technology, Yancheng 224003, China
| | - Dan Zhang
- Zhejiang Provincial United Key Laboratory of Embedded Systems, Zhejiang University of Technology, Hangzhou 310023, China.
| | - Mingxuan Sun
- Zhejiang Provincial United Key Laboratory of Embedded Systems, Zhejiang University of Technology, Hangzhou 310023, China
| | - Chun-Yi Su
- Department of Mechanical, Industrial, and Aerospace Engineering, Concordia University, Montreal, QC H3G 1M8, Canada
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10
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Wang Y, Zhu S, Shao H, Feng Y, Wang L, Wen S. Comprehensive analysis of fixed-time stability and energy cost for delay neural networks. Neural Netw 2022; 155:413-421. [PMID: 36115166 DOI: 10.1016/j.neunet.2022.08.024] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2022] [Revised: 08/04/2022] [Accepted: 08/25/2022] [Indexed: 10/31/2022]
Abstract
This paper focuses on comprehensive analysis of fixed-time stability and energy consumed by controller in nonlinear neural networks with time-varying delays. A sufficient condition is provided to assure fixed-time stability by developing a global composite switched controller and employing inequality techniques. Then the specific expression of the upper of energy required for achieving control is deduced. Moreover, the comprehensive analysis of the energy cost and fixed-time stability is investigated utilizing a dual-objective optimization function. It illustrates that adjusting the control parameters can make the system converge to the equilibrium point under better control state. Finally, one numerical example is presented to verify the effectiveness of the provided control scheme.
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Affiliation(s)
- Yuchun Wang
- School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, China; School of Arts and Science, Suqian University, Suqian, 223800, China.
| | - Song Zhu
- School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, China.
| | - Hu Shao
- School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, China.
| | - Yu Feng
- China Coal Transportation and Marketing Association, Beijing, 100013, China.
| | - Li Wang
- School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, China; School of Arts and Science, Suqian University, Suqian, 223800, China.
| | - Shiping Wen
- Center for Artificial Intelligence, University of Technology Sydney, Sydney, 2007, Australia.
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11
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Alipour M, Malekzadeh M, Ariaei A. Practical fractional-order nonsingular terminal sliding mode control of spacecraft. ISA Trans 2022; 128:162-173. [PMID: 34763885 DOI: 10.1016/j.isatra.2021.10.022] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2021] [Revised: 10/21/2021] [Accepted: 10/21/2021] [Indexed: 06/13/2023]
Abstract
In this study, a new adaptive fractional-order nonsingular terminal sliding mode (AFONTSM) controller is presented. A novel multi-purpose sliding surface is constructed, with the aim of bringing the reaction wheels in to rest after every attitude stabilization maneuver, utilizing the fractional-order difference of the quaternion error and the reaction wheels angular momentum error. The closed-loop system's practical fixed-time stability is investigated using the Lyapunov theorem under uncertainty and external disturbance. The AFONTSM controller's performance is compared with the existing nonsingular terminal sliding mode (NTSM), full-order NTSM, and fractional-order sliding mode controllers. Finally, the proposed AFONTSM controller's effectiveness is studied in close-to-reality situations through practical experiments on the spacecraft attitude control subsystem simulator under internal/external disturbance and uncertainty; then, the results are compared with previous studies.
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Affiliation(s)
- Milad Alipour
- Department of Mechanical Engineering, University of Isfahan, Iran.
| | | | - Alireza Ariaei
- Department of Mechanical Engineering, University of Isfahan, Iran.
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12
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Cui L, Jin N, Chang S, Zuo Z, Zhao Z. Fixed-time ESO based fixed-time integral terminal sliding mode controller design for a missile. ISA Trans 2022; 125:237-251. [PMID: 34303528 DOI: 10.1016/j.isatra.2021.06.039] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/11/2020] [Revised: 06/26/2021] [Accepted: 06/26/2021] [Indexed: 06/13/2023]
Abstract
This paper studies a novel fixed-time extended state observer based fixed-time integral terminal sliding mode controller for partial integrated guidance and control design. Firstly, a class of arbitrary-order systems with fixed-time stability is proposed by utilizing homogeneous approach, whose upper bound of convergence time is given. Then, an arbitrary-order fixed-time integral terminal sliding mode control is designed based on the proposed arbitrary-order fixed-time stable system, which avoids the singular problem. Subsequently, this paper constructs a new fixed-time extended state observer to further actively compensate for the disturbance caused by unknown target acceleration. Finally, numerical simulations show the effectiveness of the proposed controller.
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Affiliation(s)
- Lei Cui
- School of Electrical and Information Engineering, Tianjin University, Tianjin, 300072, China.
| | - Nan Jin
- School of Electrical and Information Engineering, Tianjin University, Tianjin, 300072, China.
| | - Shaoping Chang
- School of Electrical and Information Engineering, Tianjin University, Tianjin, 300072, China.
| | - Zhiqiang Zuo
- School of Electrical and Information Engineering, Tianjin University, Tianjin, 300072, China.
| | - Zhengen Zhao
- College of Automation Engineering, Institute of Flight Control, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China.
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13
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Ni J. Fixed-time terminal sliding mode tracking protocol design for high-order multiagent systems with directed communication topology. ISA Trans 2022; 124:444-457. [PMID: 32115190 DOI: 10.1016/j.isatra.2020.02.022] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2019] [Revised: 02/22/2020] [Accepted: 02/22/2020] [Indexed: 06/10/2023]
Abstract
This paper presents a novel fixed-time consensus tracking protocol for high order multi-agent system (MAS) with directed communication topology. A new distributed observer is proposed such that fixed-time leader's state estimation can be achieved, which overcomes the difficulty arising from asymmetry of communication topology. A series of terminal sliding surfaces are constructed and a singularity-free sliding mode fixed-time tracking protocol is developed. It is proved that the proposed tracking protocol achieves fixed-time consensus tracking. Particularly, we can obtain the controller gain from the pre-specified time, which helps to tune the gain in accordance with consensus time requirement. Moreover, a less conservative convergence time bound estimation is attained. Simulation examples demonstrate the effectiveness of the presented scheme.
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Affiliation(s)
- Junkang Ni
- Department of Electrical Engineering, School of Automation, Northwestern Polytechnical University, Xi'an 710072, China.
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14
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Zhuang M, Tan L, Song S. Fixed-time attitude coordination control for spacecraft with external disturbance. ISA Trans 2021; 114:150-170. [PMID: 33419570 DOI: 10.1016/j.isatra.2020.12.048] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2020] [Revised: 12/18/2020] [Accepted: 12/25/2020] [Indexed: 06/12/2023]
Abstract
This paper studies the fixed-time stability of attitude coordination control for spacecraft formation flying (SFF) in the presence of some external disturbance. Firstly, to ensure that the states converge to the origin within a fixed time, a novel nonsingular terminal sliding mode surface (NTSMS) is designed. The convergence time is bounded by some predefined constants. Secondly, an attitude synchronization controller is proposed based on the designed NTSMS, which guarantees the fixed-time stability of SFF under an undirected communication topology. Finally, a fixed-time adaptive control law is designed for cases in which the boundary of the external disturbance is unknown. The fixed-time stability is guaranteed by a revised form of the proposed NTSMS. Simulation results show that the proposed controllers provide fixed-time stability and outperform existing finite-time controllers.
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Affiliation(s)
- Minglei Zhuang
- Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin, 150001, China.
| | - Liguo Tan
- Research Center of Basic Space Science, Harbin Institute of Technology, Harbin 150001, China.
| | - Shenmin Song
- Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin, 150001, China.
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15
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Shao X, Tian B, Yang W. Fixed-time trajectory following for quadrotors via output feedback. ISA Trans 2021; 110:213-224. [PMID: 33092865 DOI: 10.1016/j.isatra.2020.10.039] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/21/2020] [Revised: 10/09/2020] [Accepted: 10/10/2020] [Indexed: 06/11/2023]
Abstract
A fixed-time trajectory following problem for quadrotors via output feedback is concerned. Based on the inner-outer separation design philosophy, the under-actuated quadrotor is formulated as a hierarchical structure composed by position and attitude dynamics. With an emphasis on removing the demand on unmeasured velocity and eliminating the negative effect of disturbances, fixed-time extended state observers utilizing two kinds of polynomial feedback terms are proposed to simultaneously identify unavailable velocity states and unknown uncertainties with a fixed-time estimation capability. With these observation results, a velocity free fixed-time control protocol is synthesized to enable a satisfied trajectory regulation with a uniform convergence time independent of initial positions, such that a prescribed fixed-time stability and enhanced robustness can be obtained with chattering-free inputs. By virtue of bi-limit homogeneity properties, all error variables of the resultant quadrotor system are demonstrated to be fixed-time convergent. Eventually, the benefits of developed algorithm are illustrated via simulations.
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Affiliation(s)
- Xingling Shao
- Key Laboratory of Instrumentation Science & Dynamic Measurement, Ministry of Education, North University of China, Taiyuan 030051, China; National Key Laboratory for Electronic Measurement Technology, School of Instrument and Electronics, North University of China, Taiyuan 030051, China.
| | - Biao Tian
- Key Laboratory of Instrumentation Science & Dynamic Measurement, Ministry of Education, North University of China, Taiyuan 030051, China; National Key Laboratory for Electronic Measurement Technology, School of Instrument and Electronics, North University of China, Taiyuan 030051, China
| | - Wei Yang
- Key Laboratory of Instrumentation Science & Dynamic Measurement, Ministry of Education, North University of China, Taiyuan 030051, China; National Key Laboratory for Electronic Measurement Technology, School of Instrument and Electronics, North University of China, Taiyuan 030051, China
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16
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Tran XT, Oh H. A modified generic second order algorithm with fixed-time stability. ISA Trans 2021; 109:72-80. [PMID: 33059902 DOI: 10.1016/j.isatra.2020.10.021] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2019] [Revised: 10/14/2019] [Accepted: 10/04/2020] [Indexed: 06/11/2023]
Abstract
This paper introduces a modified second order sliding mode algorithm with fixed-time stability analysis based on the Lyapunov function approach. An existing second order sliding mode algorithm is generalized, which provides superior features on convergence rate, accuracy, and robustness against a class of perturbations. The performance of the proposed algorithm is compared with existing algorithms through designing observers first. Then, the proposed algorithm-based controller which displays the fixed-time convergence property is designed to validate its effectiveness and to confirm the theoretical analysis.
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Affiliation(s)
- Xuan-Toa Tran
- NTT Hi-Tech Institute, Nguyen Tat Thanh University, 300A Nguyen Tat Thanh Street, Ho Chi Minh City, Viet Nam
| | - Hyondong Oh
- School of Mechanical, Aerospace and Nuclear Engineering, Ulsan National Institute of Science and Technology, Ulsan 44919, South Korea.
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Chen C, Li L, Peng H, Yang Y, Mi L, Zhao H. A new fixed-time stability theorem and its application to the fixed-time synchronization of neural networks. Neural Netw 2020; 123:412-9. [PMID: 31945620 DOI: 10.1016/j.neunet.2019.12.028] [Citation(s) in RCA: 64] [Impact Index Per Article: 16.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2019] [Revised: 11/01/2019] [Accepted: 12/27/2019] [Indexed: 11/24/2022]
Abstract
In this paper, we derive a new fixed-time stability theorem based on definite integral, variable substitution and some inequality techniques. The fixed-time stability criterion and the upper bound estimate formula for the settling time are different from those in the existing fixed-time stability theorems. Based on the new fixed-time stability theorem, the fixed-time synchronization of neural networks is investigated by designing feedback controller, and sufficient conditions are derived to guarantee the fixed-time synchronization of neural networks. To show the usability and superiority of the obtained theoretical results, we propose a secure communication scheme based on the fixed-time synchronization of neural networks. Numerical simulations illustrate that the new upper bound estimate formula for the settling time is much tighter than those in the existing fixed-time stability theorems. Moreover, the plaintext signals can be recovered according to the new fixed-time stability theorem, while the plaintext signals cannot be recovered according to the existing fixed-time stability theorems.
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