Distributed adaptive fault-tolerant control of pure-feedback nonlinear multi-agent systems with actuator failures☆
Introduction
Over the past decade, tremendous interests have been aroused about the cooperative control of multi-agent systems (MASs) due to their widespread applications in military and civil affairs, such as multi-mobile robots, spacecraft systems, and sensor networks [1], [2], [3], [4], [5]. Cooperative control methods of linear MASs were reported in [6], [7], [8] and distributed output regulation problems for linear MASs were addressed in Hong et al. [9] and Chopra and Spong [10]. Further extensions of these work were carried out by Kim et al. [11] to the heterogeneous uncertain cases and by Li et al. [12] to the heterogeneous linear discrete-time ones. Since numerous of practical applications are with nonlinear behavior inherently, it has attracted considerable attention to this topic. By introducing internal models, Su and Huang converted the cooperative global robust output regulation issue into a global stabilization problem and reported distributed schemes for second-order heterogeneous nonlinear uncertain MASs [13], nonlinear uncertain MASs with unknown leader [14], minimum phase nonlinear uncertain MASs [15]. In [16], a consensus control strategy was developed for network-connected nonlinear systems whose subsystems were heterogeneous with non-sector-bounded nonlinearities. Shen et al. and Wang et al. investigated distributed consensus tracking control schemes for nonlinear strict-feedback MASs [17] and strict-feedback MASs with unknown control gains [18], respectively. Wang et al. tried to apply their theory results to formation control of nonholonomic mobile robots in [19] where the objectives were in strict-feedback forms. However, the computational burdens might increase drastically by the conventional backstepping approach [20] used in [19], the so-called ‘explosion of complexity’, along with the growth of the order and number of agents. For this case, a cybernetics topology, dynamic surface control (DSC) one, was proposed via a first-order filter at each step instead of repeated differentiation calculation in [21]. On the basis of this idea, some efforts have been made and fruitful results have been obtained for more general systems, such as pure-feedback systems [22], [23], low-triangular systems with time delays [24], [25], [26], and strict-feedback MASs [18], [27], by numbers of scientific researchers.
Another main limitation in [18], [19], [27] regarding consensus control of MASs is that it was assumed that actuators were well working without consideration of their own faults. It is well known that actuators may undergo abrupt failures in practical industrial applications, which might lead to severe deteriorated performance, or even undermine the instability resulting in unpredictable accidents. It is thus essential and significant to design effective fault-tolerance schemes to accommodate actuator failures. Semsar-Kazerooni and Khorasani developed a semi-decentralized optimal consensus proposal for the team behavior of faulty agents in [28]. This result was extended into more general form systems, second-order ones [29], but the shortcoming was that the nonlinear dynamics were not taken into account. Further, Zuo et al. addressed an adaptive fault tolerant tracking consensus control issue in [30] for linear and Lipschitz nonlinear MASs and provided sufficient conditions in the presence of unknown actuator failure. Yang et al. [31] studied a kind of target aggregation affairs for MASs with a time-varying topology in the presence of agent faults. In [32], a fuzzy logical theory was used for achieving consensus for a class of high order MASs with bias actuators and an adaptive fault tolerant proposal was suggested. A cooperative fault-tolerant tracking control strategy and a containment control scheme were presented for a class of MASs and linear MASs subject to parameter uncertainties, external disturbances and actuator faults in [33] and [34], respectively.
The main focus of this paper is on the output tracking consensus fault-tolerant control of a class of pure-feedback nonlinear MASs in the presence of actuator failures and in the leader–follower architecture connected through a directed communication topology. We employ appropriate correlative theorems to transform virtual control variables into dominant affine forms, and adaptive methodologies of NNs are applied to approximate the unknown functions and compensate for the effort of loss effective and bias faults. Combining backstepping methods with DSC technique and algebraic graph theory, a distributed adaptive fault-tolerant control strategy is developed by the relative information of individual agents and their neighbors. The distinct contributions of this paper are summarized as follows: (1) The dynamics of individual agent are non-affine pure-feedback, and this class of follower agents with faulty actuators, such as bias and loss of effectiveness, is more general than the ones in [18], [27]. We consider the complex form and actuator failure in this paper simultaneously, and it is a challenging and formidable task to construct explicit virtual controls for such non-affine systems. (2) Prior knowledge about precise parameters of individual agents are hardly necessary. It is not of requirement of prior information, such as uncertainties, control gains as well as modeling errors, with the help of approximation property of NNs. (3) The norms of weight vectors of NNs are estimated instead of weight vectors themselves. Interestingly, unlike the work reported in [35], [39], it reduces the computational burden considerably by introducing the DSC approach. The control law constructed in this paper seems concise and practical in particular when the order and complexity of the system increases.
Section snippets
Preliminaries and problem formulation
We consider a class of nonlinear MASs in leader–follower architecture, and the dynamics of the ith follower, who are in non-affine pure-feedback form and with actuator faults, are:where and are state variables and output signal of the ith followers, respectively, , , are state
Control law design
In this part, we develop and analyze the adaptive fault-tolerant control scheme for MASs (1). To facilitate the illustration and analysis of the design procedure and stability, the following notations are given:where is an intermediate variable from a low-pass filter which will be illustrated later.
Step i, 1: The time-derivative of iswhere .
Since
Multi-one-link manipulators
Consider a group of one-link manipulators and dynamics that are described as follows:where qi, , , Ii and Vi represent angular position, velocity, acceleration, motor current and input voltage for the ith agent, respectively. And the parameters are , , , , and . By noting , , and , the above equation (54) can be expressed in the form (1) as
Conclusion
This paper provides a formal analysis about the distributed adaptive fault-tolerant control performance of non-affine MASs under a directed topology. The results are obtained by combining the DSC technology with adaptive methodologies of NNs, algebraic graph theory as well as appropriate correlative theorems. It is shown that the output consensus target can be achieved in spite of loss of effectiveness and bias faults. Further extension of this work would be concentrated on event-triggered
Acknowledgment
The authors would like to thank anonymous reviewers and editors for their constructive suggestions to improve this paper.
Yang Yang was born in Taixing, Jiangsu Province, China. He received B.E., M.E. and Ph.D. degrees in Automatic Control from Dalian Maritime University, China, in 2008, 2010, and 2013, respectively. He has been the recipient of National Scholarship for Ph.D. Candidates and HOSCO Special Award. Currently, he is with College of Automation, Nanjing University of Posts and Telecommunications, as a Lecturer and serves as a Reviewer for various peer-reviewed journals, including Circuits, Systems &
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2020, Communications in Nonlinear Science and Numerical SimulationCitation Excerpt :Therefore, it is essential to solve consensus problem for MASs with actuator failure. Recently, amount of results have been studied for fault-tolerant control and fault detection in linear and nonlinear MASs, such as [42,43]. In [42], the authors considered the consensus tracking problem for a pure-feedback nonlinear MAS with actuator failures via distributed adaptive fault-tolerant control.
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2019, Nonlinear Analysis: Hybrid SystemsCitation Excerpt :The nonlinearities of multi-agent systems considered in [15–18] are required to satisfy the matching conditions on the control input. Thus, distributed fault-tolerant consensus tracking problems of multi-agent systems with unmatched nonlinearities were studied in [19–21] where the actuator faults were only treated in [19,20] and the faults in both system nonlinearities and actuators were considered in [21]. Despite these progresses, all the aforementioned results related to nonlinear multi-agent systems only provide the distributed consensus tracking solutions in the presence of non-switched nonlinearities and faults.
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Yang Yang was born in Taixing, Jiangsu Province, China. He received B.E., M.E. and Ph.D. degrees in Automatic Control from Dalian Maritime University, China, in 2008, 2010, and 2013, respectively. He has been the recipient of National Scholarship for Ph.D. Candidates and HOSCO Special Award. Currently, he is with College of Automation, Nanjing University of Posts and Telecommunications, as a Lecturer and serves as a Reviewer for various peer-reviewed journals, including Circuits, Systems & Signal Processing, Annual Reviews in Control, International Journal of Systems Science, Neurocomputing, Journal of Systems and Control Engineering, IEEE/CAA Journal of Automatica Sinica. His research interests include nonlinear control theory and intelligent control.
Dong Yue received the Ph.D. degree from the South China University of Technology, Guangzhou, China, in 1995. He is currently a Professor and Dean of Institute of Advanced Technology, Nanjing University of Posts and Telecommunications and also a Changjiang Professor with the Department of Control Science and Engineering, Huazhong University of Science and Technology. He is currently an Associate Editor of the IEEE Control Systems Society Conference Editorial Board and also an Associate Editor of the IEEE Transactions on Neural Networks and Learning Systems and the International Journal of Systems Science. Up to now, he has published more than 100 papers in international journals, domestic journals, and international conferences. His research interests include analysis and synthesis of networked control systems, multi-agent systems, optimal control of power systems, and internet of things.
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This work is supported in part by the National Natural Science Foundation of China (Grant nos. 61533010, 61374055 and 61503194), in part by the Ph.D. Programs Foundation of Ministry of Education of China (Grant no. 20110142110036), in part by the Natural Science Foundation of Jiangsu Province (Grant nos. BK20131381 and BK20140877), in part by Project Funded by China Postdoctoral Science Foundation (Grant no. 2015M571788), in part by Jiangsu Planned Projects for Postdoctoral Research Funds (Grant no. 1402066B), in part by the Foundation of the Key Laboratory of Marine Dynamic Simulation and Control for the Ministry of Transport (DMU) (Grant no. DMU-MSCKLT2016005), and in part by the Scientific Foundation of Nanjing University of Posts and Telecommunications (NUPTSF) (Grant no. NY214076).