Distributed-observer-based formation tracking control of heterogeneous multi-agent systems through sensory feedback

Cyber-physical systems (CPS) are engineered systems with built-in seamless integration of physical and cyber components. Fundamental developments in sensing, communication, control, and computing technologies endow CPS with flexibility, adaptability, scalability, and robustness. The availability and size of input-output data generated along with the control of CPS bring a unique opportunity for machine learning techniques to advance the theory of dynamical control systems, by learning control rules directly from data. Integration of input-output data into adaptive, robust, predictive, and distributed control policies holds the key to exploiting the potential of learning and optimisation in the CPS designs. There are several challenges related to sampling, transmission, synchronization, as well as associated cyber security when merging contemporary data-based and traditional model-based control techniques for CPS. The overarching goal of this special issue is to bring together innovative developments on the interface between learning, control, and optimisation targeting cyber-physical opportunities emerging from power, transportation, and manufacturing systems. Through a rigorous peer review process, three articles have been accepted, which are summarised below. In the study, "Learning-based distributed adaptive control of heterogeneous multi-agent systems with unknown leader dynamics", the authors develop a distributed adaptive tracking control method for heterogeneous multi-agent systems with unknown leader dynamics in a directed graph. In contrast to the reported leader-following consensus studies, the prior knowledge of the leader is supposed to be cognised by some or all of the followers, the situation that the leader's dynamics are totally unrecognised but can be learned for each individual follower is considered. A data-driven learning algorithm using the system's data is developed to reconstruct the unknown systems matrix. Then, an adaptive distributed dynamic compensator is exploited to provide the leader's state estimation in a directed graph. Afterwards, a dynamic output feedback control law for each agent is projected. Theoretical analysis shows that the proposed algorithms not only ensure that all followers can identify the unknown system matrix but also guarantee that the distributed output leader-following consensus control with heterogeneous dynamics is achieved without any global information. In the study, "Sampled-data synchronisation of singular Markovian jump system (SMJS): application to a DC motor model", the authors consider the sampled-data synchronisation problem for SMJSs subject to aperiodic sampled-data control. Firstly, by constructing mode-dependent one-sided loop-based Lyapunov functional (LBLF) and two-sided LBLF, two different stochastically admissible conditions are suggested for error SMJSs with aperiodic sampled-data. It is guaranteed that the slave system is stochastically synchronised to the master system on the basis of the proposed stochastically admissible conditions. Secondly, two corresponding mode-dependent aperiodic sampled-data controller design approaches are provided for error SMJSs based on two different conditions, respectively. Finally, the validity of these approaches is demonstrated by a DC motor model. It also demonstrated that the two-sided LBLF method possesses a larger upper bound of the sampling period than the one-sided LBLF method. In the study, "Predefined-time distributed event-triggered algorithms for resource allocation", the authors propose a predefined-time distributed algorithm and analyse its convergence by using the Lyapunov stability theory in which the local constraint is ensured by a differential projection operator. Thus, a predefined time is obtained using a time-varying time-based generator. In addition, to reduce the communication consumption between agents, the authors develop a static as well as a dynamic-based event-triggered control scheme, where the information broadcast only occurs at some discrete time instants. Moreover, the three proposed algorithms converge precisely to the global optimal solution. Besides, the Zeno behaviour is excluded in the above static and dynamic event-triggered mechanisms. The guest editors would like to thank the Editor-in-Chief of the IET Cyber-Physical Systems: Theory & Applications, Prof. Shiyan Hu, and the Editorial Office for their great support of our special issue. In addition, we thank all the authors who submitted their quality papers to this special issue, and special thanks go to all anonymous reviewers for their great efforts and time to accomplish their review tasks. Data sharing not applicable. Jian Sun is currently a professor at Beijing Institute of Technology, China. He received the bachelor's degree from the Department of Automation and Electric Engineering, Jilin Institute of Technology, Changchun, China, in 2001, the master's degree from the Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences (CAS), Changchun, in 2004, and the Ph.D. degree from the Institute of Automation, CAS, Beijing, China, in 2007. He was a Research Fellow with the Faculty of Advanced Technology, University of Glamorgan, Pontypridd, U.K., from 2008 to 2009. He was a Post-Doctoral Research Fellow with the Beijing Institute of Technology, Beijing, from 2007 to 2010. In 2010, he joined the School of Automation, Beijing Institute of Technology, where he has been a Professor since 2013. His current research interests include networked control systems, time-delay systems, and security of cyber-physical systems. He is also an Editorial Board Member of the IEEE Transactions on Systems, Man, and Cybernetics: Systems, the Journal of Systems Science and Complexity, and Acta Automatica Sinica. Qing-Long Han is Pro Vice-Chancellor (Research Quality) and a Distinguished Professor at Swinburne University of Technology, Melbourne, Australia. He held various academic and management positions at Griffith University and Central Queensland University, Australia. He received the Ph.D. degree in Control Engineering from East China University of Science and Technology in 1997. He has been conducting research in the areas of networked control systems, cyber physical systems, time-delay systems, multi-agent systems, smart grids, offshore structure, unmanned surface vehicles, cyber security, and neural networks. Since 2001, as of 12 August 2021, he has authored or co-authored three hundred and thirty-nine (339) fully-refereed high quality journal articles including one hundred and seventy-six (176) articles in the most prestigious IEEE Transactions, and thirty-seven (37) articles in Automatica. He has also authored or co-authored one hundred and eighty-four (184) international leading conference papers, five (5) monographs, one (1) research-based book chapter, and edited four (4) conference proceedings and ten (10) special issues. His research work has been cited 32,886 times with an h-index of 102, an i10-index of 296 according to Google Scholar. He is a Highly Cited Researcher in the Essential Science Indicator (ESI) field of Engineering (2014–2017), in the ESI Cross-Field (2018) and in both the ESI fields of Engineering and Computer Science (2019–2020) by Clarivate Analytics (Thomson Reuters). He is one of Australia's Top 5 Lifetime Achievers (Research Superstars) in the discipline area of Engineering and Computer Science by The Australian's Research Magazine (2019-2020). He is one of Australia's Top 5 Researchers in Computer Science and Electronics by Guide2Research. He was the recipient of The 2021 M. A. Sargent Medal (the Highest Award of the Electrical College Board of Engineers Australia), The 2020 IEEE Systems, Man, and Cybernetics (SMC) Society Andrew P. Sage Best Transactions Paper Award, The 2020 IEEE Transactions on Industrial Informatics Outstanding Paper Award, and The 2019 IEEE SMC Society Andrew P. Sage Best Transactions Paper Award. He was the recipient of The 2020 IEEE SMC Society Best Associate Editor Award and The 2020 IEEE/CAA Journal of Automatica Sinica Outstanding Associate Editor Award. Professor Han is a Member of the Academia Europaea (The Academy of Europe). He is a Fellow of The Institute of Electrical and Electronic Engineers (IEEE) and a Fellow of The Institution of Engineers Australia. He has served as an AdCom Member of IEEE Industrial Electronics Society (IES), a Member of IEEE IES Fellows Committee, and Chair of IEEE IES Technical Committee on Network-based Control Systems. He has served as Co-Editor-in-Chief of IEEE Transactions on Industrial Informatics (2022–2024), Co-Editor of Australian Journal of Electrical & Electronics Engineering, an Associate Editor for 12 international journals including IEEE Transactions on Cybernetics, IEEE Industrial Electronics Magazine, IEEE/CAA Journal of Automatica Sinica, Control Engineering Practice, Information Sciences, and a Guest Editor for 13 Special Issues. Guo-Ping Liu is currently a chair professor with the Southern University of Science and Technology, China. He received the BEng and MEng degrees from Central South University of Technology (now Central South University, China) in 1982 and 1985, respectively, and the PhD degree from University of Manchester in the UK in 1992. He did the postdoctoral research in the University of York in 1992–1993. He worked as a research fellow with the University of Sheffield in 1994-1996. During 1996–2000, he was a senior engineer with GEC-Alsthom and ALSTOM, and then a principal engineer and a project leader with ABB ALSTOM Power. He was a senior lecturer with the University of Nottingham in 2000–2003, a visiting professor with the Chinese Academy of Sciences in 2001-2005 and with the Harbin Institute of Technology in 2008–2013, and a professor with the University of South Wales in 2004–2019 and with Wuhan University in 2019–2021. Prof Liu's research interests include networked control systems, multi-objective optimal control, nonlinear identification and control, and industrial advanced control applications. He has completed more than 70 research projects as a principal investigator. He is an author of 10 books, 2 edited books, over 330 journal papers and 320 conference papers, and has 14 patents, 34 software copyrights and 2 software products. He was awarded the Alexander von Humboldt Research Fellowship in 1992. He was named a Highly Cited Researcher by Thomson Reuters in 2014 and 2015, by Clarivate Analytics in 2016–2018, and by Elsevier in 2014–2020. He received the second prize of Chinese National Science and Technology Awards in 2008 and 2015. Prof. Liu was the general chair of the 2007 IEEE International Conference on Networking, Sensing and Control, the 2011 International Conference on Intelligent Control and Information Processing, and the 2012 UKACC International Conference on Control. He has served as an Editor-in-Chief of the International Journal of Automation and Computing in 2004–2021 and an Honorary Editor-in-Chief of the journal "Advances in Internet of Things" since 2011. He is a Fellow of IEEE, a Fellow of IET and a member of the Academy of Europe. Yajun Pan is currently a Professor in the Department of Mechanical Engineering at Dalhousie University, Canada. She received the B.E. degree in Mechanical Engineering from Yanshan University, P.R. China, in 1996, the M.E. degree in Mechanical Engineering from Zhejiang University, P.R. China, in 1999 and the Ph.D degree in Electrical and Computer Engineering from the National University of Singapore, in 2003. After receiving the Ph.D. degree, she was a post-doctoral fellow of CNRS in the Laboratoire d'Automatique de Grenoble, France from 2003 to 2004. In 2004, she held post-doctoral position in the department of Electrical and Computer Engineering at the University of Alberta, Canada. She is currently an Associate Editor of the IEEE Transactions on Industrial Electronics (2019 Present), IEEE Transactions on Cybernetics (2016-Present), and IEEE/ASME Transactions on Mechatronics (2015–2020). She has been the Associate Editor for the Journal of Franklin Institute (2007–2013), International Journal of Advanced Robotics Systems (2014–2018), and the International Journal of Information and Systems Sciences (2009–2017). She is the Editor of the special issue on Advances in Methods for Control over Networks for the Journal of Control Science and Engineering; and the guest editor for the special issue in Advanced Modelling and Control of Complex Mechatronic Systems with Nonlinearity and Uncertainty for IEEE Access (2017–2018). She is a Fellow of Engineering Institute of Canada (FEIC - 2021), a Fellow of the American Society of Mechanical Engineers (ASME - 2017), a Senior Member of the Institute of Electrical and Electronics Engineers (IEEE), a member of Canadian Society of Mechanical Engineering (CSME) and a Registered Professional Engineer in the Province of Nova Scotia, Canada. Dr. Pan was awarded the Research Excellence Award (Junior Category, Academic Year of 2008–2009) in the Faculty of Engineering, Dalhousie University. She has served as the evaluation group member for NSERC Discovery Grant (2017–2020) and also the selection committee member for NSERC RTI grant in 2016–2017. She has served as the Vice-President, Atlantic Region, for Canadian Society of Mechanical Engineering (CSME) from 2018–2020. Tao Yang is a Professor at the State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University. He was an Assistant Professor at the Department of Electrical Engineering, University of North Texas, Denton, USA, from 2016–2019. He received the Ph.D. degree in electrical engineering from Washington State University in 2012. Between August 2012 and August 2014, he was an ACCESS Post-Doctoral Researcher with the ACCESS Linnaeus Centre, Royal Institute of Technology, Sweden. He then joined the Pacific Northwest National Laboratory as a postdoc, and was promoted to Scientist/Engineer II in 2015. His research interests include industrial artificial intelligence, integrated optimization and control, distributed control and optimization with applications to process industries, cyber physical systems, and networked control systems. He is an Associate Editor for IEEE Transactions on Control Systems Technology and IEEE/CAA Journal of Automatica Sinica. He currently is a member of the Technical Committee on Nonlinear Systems and Control, the Technical Committee on Networks and Communication Systems, and the Technical Committee on Smart Grids of the IEEE Control Systems Society, a member of the IEEE Control Systems Society Conference Editorial Board, and a member of the IFAC Technical Committee on Large Scale Complex Systems. He received Ralph E. Powe Junior Faculty Enhancement Award and Best Student Paper award (as an advisor) of the 14th IEEE International Conference on Control & Automation in 2018. Jiahu Qin is currently a Professor with the Department of Automation, University of Science and Technology of China, Hefei, China. He received the first Ph.D. degree in control science and engineering from the Harbin Institute of Technology, Harbin, China, in 2012, and the second Ph.D. degree in systems and control from the Australian National University, Canberra, ACT, Australia, in 2014. His current research interests include multi-agent systems, cyber-physical systems, and complex dynamical networks. Dr. Qin serves as the Deputy Director of Youth Committee of Chinese Association of Automation. He is currently an Associate Editor of IEEE Transactions on Industrial Electronics, IEEE Transactions on Industrial Informatics, Journal of The Franklin Institute, Neurocomputing, Acta Automatica Sinica, IET Cyber-Physical Systems: Theory & Applications, etc. He is a recipient of the 2017 IEEE IES (Industrial Electronics Society) Best Conference Paper Award.

Considering that communication between neighboring agents may be cooperative or antagonistic, this study is concerned with the bipartite time-varying output formation tracking (BTVOFT) problem for heterogeneous multi-agent systems (MASs) with multiple leaders on signed digraph. A fully distributed event-triggered output feedback formation tracking (FDETOFFT) control scheme is constructed to address this problem. It is noteworthy that the control scheme does not involve any global information, which enables it to be implemented in a fully distributed fashion. The biggest contribution of this study is to extend event-triggered techniques to the formation tracking control scheme. Compared with previous related works, continuous communication between neighboring agents is avoided. Moreover, it is further proved that no agents exhibit the Zeno behavior.

This paper presents an optimal time-varying output formation tracking control algorithm for heterogeneous linear multi-agent systems (MASs). The outputs of agents are desired to track the virtual leaders' output with a time-varying formation while optimizing cost functions with respect to tracking error and control input. Firstly, distributed trajectory generators are designed to observe the virtual leader's state and produce the desired formation signals for each follower. Then, followers considered to be heterogeneous with dynamics and parameters are driven to track the generated trajectories under optimal control protocols designed by reinforcement learning (RL) technique. Formation tracking controllers are learned by off-policy online data in real-time without requiring any knowledge of the followers' dynamics. Stability and optimality of learning process and tracking algorithm are provided and output regulator equations are also proved to be equivalently solved. Thirdly, a steady-state compensational input is proposed under model-free method to guarantee the tracking error converges to zero asymptotically. Finally, simulation results are provided to verify the effectiveness of proposed control scheme.

This paper studies the multi-tracking control for high-order heterogeneous multi-agent systems under a directed acyclic graph. The authors first convert the multi-tracking control problem for multi-agent systems into the zero steady-state error control problem of some independent subsystems. Based on final-value theorem and Mason's rule, a sufficient condition for achieving the multi-tracking control is proposed. It explicitly reveals how the system dynamic and desired object dynamic jointly affect the multi-tracking control of heterogeneous multi-agent systems. Meanwhile, a new result on the steady-state error for multi-subnetworks is established. Moreover, the multi-tracking control for heterogeneous multi-agent systems with time delay is discussed. Some simulations are performed to illustrate the effectiveness of the theoretical results.

Controllability of heterogeneous multi-agent systems via cooperative output regulation

ABSTRACTIn existing researches on containment control of heterogeneous multi-agent systems (MASs), the solution is usually dependent on the solvability of regulator equations. However, the closed-form solution of many nonlinear regulator equations of systems is rarely obtained. Towards this end, in this paper the containment control problem of heterogeneous discrete-time nonlinear MASs subject to parameter uncertainties is considered, and the power series approach is adopted to solve complex regulator equations by decomposing them into a series of solvable linear equations. Then, a distributed robust control law based on internal model principle is presented by utilising the solution of the linear equations. Theoretical analysis shows that under certain assumptions asymptotic containment control is achieved for the heterogeneous discrete-time nonlinear MASs with sufficiently small parameter perturbations. Finally, a numerical simulation is implemented to verify the proposed control law.

Distributed model reference adaptive containment control of heterogeneous multi-agent systems with unknown uncertainties and directed topologies

Event-based formation control of heterogeneous multiagent systems with leader agent of nonzero input

In this paper, the problem of formation control of heterogeneous multi-agent systems is investigated. The heterogeneous multi-agent system is composed of first-order and second-order agents, where the second-order agents cannot obtain the velocity information. Firstly, without considering the input saturation, the distributed formation control protocols are designed for multi-agent systems with static leader and active leader respectively. By using Lyapunov stability theory and LaSalle's invariance principle, the protocols are proved to be effective. Then due to the actor saturation, the formation protocols for multi-agent systems with input saturation based on distributed observers and auxiliary systems are presented. Finally, the simulation results are given to illustrate the effectiveness of the proposed protocols.

This article studies the robust model predictive control of heterogeneous multi-agent systems with polytopic uncertainties and time delay. Moreover, some constraints on the amplitude of the control inputs are considered for each agent. The proposed distributed controllers are designed as state feedback. The goal is to design the feedback gains such that the multiagent system achieves consensus in the presence of time-delay and model uncertainties. For this purpose, an optimization problem is proposed, and by using the constrained robust model predictive control and the appropriate Lyapunov–Krasovskii functional, sufficient conditions are obtained to solve the optimization problem through solving the linear matrix inequalities. In this regard, a theorem is presented, and it is proved that the consensus errors converge to zero. Finally, the effectiveness of the proposed method is illustrated using numerical simulations.

This note considers the formation control of heterogeneous multi-agent systems with time delay, in which all agents are divided into a leader and followers. Here, the output regulation method is employed such that followers track the leader and finally converge to a desired formation as there exists communication time-delay. For this purpose, a distributed observer is proposed for each follower to estimate the state of the leader, and then employ a feedback controller to update its states. As the distances among followers and leader are predefined, we have shown that the considered heterogeneous multi-agent systems with time-delay can achieve the desired formation. Simulation example is included to illustrate the validity of the proposed method.

This article considers the distributed adaptive fault-tolerant control problem for heterogeneous linear multiagent systems with actuator faults and nonuniform time-varying communication delays. First, novel distributed switching observers are proposed to estimate the system matrix and the state of the exosystem. The observers allow each agent to share its information with its underlying neighbors only at sampled instants of time, thus making a distinct difference from the existing results that require the exosystem matrix to be accessible to all agents at every continuous instant of time. Second, a sufficient condition is derived such that the observer error systems are exponentially stable under the influence of communication delays among interacting agents. Third, new distributed adaptive fault-tolerant controllers, which promise fewer adaptive parameters, are presented to compensate for the actuator faults. It is shown that the developed controllers are capable to effectively and efficiently solve the cooperative fault-tolerant output regulation problem with reduced computational complexity. Finally, three illustrative examples, including an inverted pendulum system, an electronic double-integrator circuit system, and an AC microgrid system, are presented to show the validity and efficiency of the developed method.

Adaptive Formation Tracking Control of Directed Networked Vehicles in a Time-Varying Flowfield

Adaptive output containment control of heterogeneous multi-agent systems with unknown leaders

Aiming at the fault-tolerant output consensus problem of heterogeneous multi-agent systems with external finite energy interference in the case of simultaneous additive and multiplicative faults of the actuators, this paper proposes a fault-tolerant output control strategy combining fixed-time feedforward control and adaptive state feedback control. First, a fully distributed adaptive fixed-time observer is designed for the follower, so that each follower can estimate the leader state and the state matrix within a fixed time. Then, combined with the output adjustment equation with fault matrix, a distributed adaptive fault-tolerant output consensus control scheme is proposed to compensate for the impact of fault on the system, and the sufficient conditions for consensus system output are deduced by using Lyapunov stability theory. Finally, the effectiveness and feasibility of the proposed method are verified by a heterogeneous multi-agent faulty system composed of a leader and four followers.