On the variable structure control approach with sliding modes to robust finite-time consensus problems: A methodological overview based on nonsmooth analysis

Annual Reviews in Control - Tập 55 - Trang 338-355 - 2023
A. Pilloni1, M. Franceschelli1, A. Pisano1, E. Usai1
1Department of Electrical and Electronic Engineering, University of Cagliari, Cagliari, 09123, Italy

Tài liệu tham khảo

Ajina, 2020, Asynchronous distributed event-triggered coordination for multiagent coverage control, IEEE Transactions on Cybernetics, 51, 5941, 10.1109/TCYB.2019.2962772 Bartolini, 1998, Chattering avoidance by second-order sliding mode control, IEEE Transactions on Automatic Control, 43, 241, 10.1109/9.661074 Bauso, 2017, Consensus via multi-population robust mean-field games, Systems & Control Letters, 107, 76, 10.1016/j.sysconle.2017.07.010 Bernuau, 2014, On homogeneity and its application in sliding mode control, Journal of the Franklin Institute, 351, 1866, 10.1016/j.jfranklin.2014.01.007 Biyikoglu, 2007 Bodkhe, 2020, A survey on decentralized consensus mechanisms for cyber physical systems, IEEE Access, 8, 54371, 10.1109/ACCESS.2020.2981415 Boyd, 2006, Randomized gossip algorithms, IEEE Transaction on Information Theory, 52, 2508, 10.1109/TIT.2006.874516 Bullo, 2019 Cao, Y., & Ren, W. (2010). Distributed coordinated tracking via a variable structure approach-part i: Consensus tracking. In IEEE American control conference (pp. 4744–4749). Cao, 2014, Finite-time consensus for multi-agent networks with unknown inherent nonlinear dynamics, Automatica, 50, 2648, 10.1016/j.automatica.2014.08.028 Cao, 2012, An overview of recent progress in the study of distributed multi-agent coordination, IEEE Transactions on Industrial Informatics, 9, 427, 10.1109/TII.2012.2219061 Carli, 2008, Distributed Kalman filtering based on consensus strategies, IEEE Journal on Selected Areas in Communications, 26, 622, 10.1109/JSAC.2008.080505 Chen, 2018, A fixed-time convergent algorithm for distributed convex optimization in multi-agent systems, Automatica, 95, 539, 10.1016/j.automatica.2018.05.032 Chen, 2019, On the control of multi-agent systems: A survey, Foundations and Trends® in Systems and Control, 6, 339, 10.1561/2600000019 Clarke, 1990 Clarke, 1998 Cortés, 2006, Finite-time convergent gradient flows with applications to network consensus, Automatica, 42, 1993, 10.1016/j.automatica.2006.06.015 Cucuzzella, 2018, A robust consensus algorithm for current sharing and voltage regulation in DC microgrids, IEEE Transactions on Control Systems Technology, 27, 1583, 10.1109/TCST.2018.2834878 Dong, 2022, Fixed-time consensus of nonlinear multi-agent systems with stochastically switching topologies, International Journal of Control, 95, 2828, 10.1080/00207179.2021.1939165 Dörfler, 2015, Breaking the hierarchy: Distributed control and economic optimality in microgrids, IEEE Transactions on Control of Network Systems, 3, 241, 10.1109/TCNS.2015.2459391 Dorneanu, 2020, A framework for intelligent monitoring and control of chemical processes with multi-agent systems, 18 Dorneanu, 2018, Towards the cooperative-based control of chemical plants, Computer Aided Chemical Engineering, 43, 1087, 10.1016/B978-0-444-64235-6.50190-X Du, 2017, A distributed finite-time consensus algorithm for higher-order leaderless and leader-following multiagent systems, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 47, 1625, 10.1109/TSMC.2017.2651899 Ferrara, 2022, Multi-scale model based hierarchical control of freeway traffic via platoons of connected and automated vehicles, IEEE Open Journal of Intelligent Transportation Systems, 10.1109/OJITS.2022.3217001 Ferrara, A., & Zambelli, M. (2019). Integral second-order sliding modes for robust prescribed-time leader-follower consensus control with partial information. In Proc. of the IEEE conf. on decision & control (pp. 7863–7868). Filippov, 2013 Franceschelli, 2013, Decentralized estimation of Laplacian eigenvalues in multi-agent systems, Automatica, 49, 1031, 10.1016/j.automatica.2013.01.029 Franceschelli, M., Giua, A., & Pisano, A. (2014). Finite-time consensus on the median value by discontinuous control. In 2014 American control conference (pp. 946–951). Franceschelli, 2016, Finite-time consensus on the median value with robustness properties, IEEE Transactions on Automatic Control, 62, 1652, 10.1109/TAC.2016.2590602 Franceschelli, 2013, Finite-time consensus for switching network topologies with disturbances, Nonlinear Analysis. Hybrid Systems, 10, 83, 10.1016/j.nahs.2013.06.004 Franceschelli, 2014, Finite-time consensus with disturbance rejection by discontinuous local interactions in directed graphs, IEEE Transactions on Automatic Control, 60, 1133, 10.1109/TAC.2014.2351431 Fridman, 2016 Gharesifard, 2013, Distributed continuous-time convex optimization on weight-balanced digraphs, IEEE Transactions on Automatic Control, 59, 781, 10.1109/TAC.2013.2278132 Gholami, 2021, Robust distributed secondary voltage restoration control of ac microgrids under multiple communication delays, Energies, 14, 1165, 10.3390/en14041165 Godsil, 2001 Gómez-Gutiérrez, 2020, On finite-time and fixed-time consensus algorithms for dynamic networks switching among disconnected digraphs, International Journal of Control, 93, 2120, 10.1080/00207179.2018.1543896 Gross, 2003 Guan, 2012, Finite-time consensus for leader-following second-order multi-agent networks, IEEE Transactions on Circuits and Systems I: Regular Papers, 59, 2646, 10.1109/TCSI.2012.2190676 Horn, 2012 Huang, 2021, Resource allocation and consensus of blockchains in pervasive edge computing environments, IEEE Transactions on Mobile Computing, 10.1109/TC.2021.3122891 Hui, 2008, Finite-time semistability and consensus for nonlinear dynamical networks, IEEE Transactions on Automatic Control, 53, 1887, 10.1109/TAC.2008.929392 Hui, Q., Haddad, W. M., & Bhat, S. P. (2008b). Semistability theory for differential inclusions with applications to consensus problems in dynamical networks with switching topology. In IEEE American control conf. (pp. 3981–3986). Ishii, 2010, Distributed randomized algorithms for the PageRank computation, IEEE Transactions on Automatic Control, 55, 1987, 10.1109/TAC.2010.2042984 Ishii, 2022, An overview on multi-agent consensus under adversarial attacks Isidori, 2014, Robust output synchronization of a network of heterogeneous nonlinear agents via nonlinear regulation theory, IEEE Transactions on Automatic Control, 59, 2680, 10.1109/TAC.2014.2326213 Jadbabaie, 2003, Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Transactions on Automatic Control, 48, 988, 10.1109/TAC.2003.812781 Jiang, 2016, Robust integral sliding-mode consensus tracking for multi-agent systems with time-varying delay, Asian Journal of Control, 18, 224, 10.1002/asjc.1007 Kameoka, 2022, Cooperative tracking in camera sensor networks with sliding mode control, Advanced Robotics, 1 Lee, 2017, Consensus algorithm-based approach to fundamental modeling of water pipe networks, AIChE Journal, 63, 3860, 10.1002/aic.15760 Lee, 2007, Chattering suppression methods in sliding mode control systems, Annual Reviews in Control, 31, 179, 10.1016/j.arcontrol.2007.08.001 Levant, 1993, Sliding order and sliding accuracy in sliding mode control, International Journal of Control, 58, 1247, 10.1080/00207179308923053 Levant, 2005, Homogeneity approach to high-order sliding mode design, Automatica, 41, 823, 10.1016/j.automatica.2004.11.029 Li, C., Yu, X., Zhou, X., & Ren, W. (2017). A fixed time distributed optimization: A sliding mode perspective. In Proc. of the ann. conf. of the IEEE ind. electron. soc. (pp. 8201–8207). Li, 2009, Mean square average-consensus under measurement noises and fixed topologies: Necessary and sufficient conditions, Automatica, 45, 1929, 10.1016/j.automatica.2009.04.017 Lin, 2016, Distributed continuous-time optimization: nonuniform gradient gains, finite-time convergence, and convex constraint set, IEEE Transactions on Automatic Control, 62, 2239, 10.1109/TAC.2016.2604324 Lin, 2022, An efficient approach to sharing edge knowledge in 5G-enabled industrial internet of things, IEEE Transactions on Industrial Informatics Mei, 2015, Distributed consensus of second-order multi-agent systems with heterogeneous unknown inertias and control gains under a directed graph, IEEE Transactions on Automatic Control, 61, 2019, 10.1109/TAC.2015.2480336 Meng, 2019, Event-triggered control for semiglobal robust consensus of a class of nonlinear uncertain multiagent systems, IEEE Transactions on Automatic Control, 65, 1683, 10.1109/TAC.2019.2932752 Moreau, 2005, Stability of multiagent systems with time-dependent communication links, IEEE Transactions on Automatic Control, 50, 169, 10.1109/TAC.2004.841888 Moreno, 2012, Strict Lyapunov functions for the super-twisting algorithm, IEEE Transactions on Automatic Control, 57, 1035, 10.1109/TAC.2012.2186179 Nedic, 2009, Distributed subgradient methods for multi-agent optimization, IEEE Transactions on Automatic Control, 54, 48, 10.1109/TAC.2008.2009515 Oh, 2015, A survey of multi-agent formation control, Automatica, 53, 424, 10.1016/j.automatica.2014.10.022 Olfati-Saber, 2007, Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE, 95, 215, 10.1109/JPROC.2006.887293 Olfati-Saber, 2004, Consensus problems in networks of agents with switching topology and time-delays, IEEE Transactions on Automatic Control, 49, 1520, 10.1109/TAC.2004.834113 Orlov, 2008 Orlov, Y., Pilloni, A., Pisano, A., & Usai, E. (2016). Consensus-based leader-follower tracking for a network of perturbed diffusion PDEs via local boundary interaction. In IFAC workshop on control of syst. governed by partial differ. equations, Vol. 49 (pp. 228–233). (8). Paden, 1987, A calculus for computing Filippov’s differential inclusion with application to the variable structure control of robot manipulators, IEEE Transactions on Circuits and Systems I: Regular Papers, 34, 73, 10.1109/TCS.1987.1086038 Pavlov, 2022, Nonlinear integral coupling for synchronization in networks of nonlinear systems, Automatica, 140, 10.1016/j.automatica.2022.110202 Pilloni, 2017, Dynamic involvement of real world objects in the IoT: A consensus-based cooperation approach, MDPI Sensors, 17, 484, 10.3390/s17030484 Pilloni, 2020, Sliding mode-based robustification of consensus and distributed optimization control protocols, IEEE Transactions on Automatic Control, 66, 1207, 10.1109/TAC.2020.2991694 Pilloni, A., Pisano, A., Franceschelli, M., & Usai, E. (2013). Finite-time consensus for a network of perturbed double integrators by second-order sliding mode technique. In Proc. of the IEEE conf. on decision & control (pp. 2145–2150). Pilloni, A., Pisano, A., Franceschelli, M., & Usai, E. (2016a). A discontinuous algorithm for distributed convex optimization. In IEEE int. workshop variable structure syst. (pp. 22–27). Pilloni, A., Pisano, A., Franceschelli, M., & Usai, E. (2016b). Integral sliding modes for the robustification of consensus-based multi-agent based systems. In Int. workshop on variable structure syst. (pp. 222–227). Pilloni, 2015, Consensus-based control for a network of diffusion PDEs with boundary local interaction, IEEE Transactions on Automatic Control, 61, 2708, 10.1109/TAC.2015.2506990 Pilloni, 2017, Voltage restoration of islanded microgrids via cooperative second-order sliding mode control, IFAC World Congress, 50, 9637 Pilloni, 2018, Robust finite-time frequency and voltage restoration of inverter-based microgrids via sliding-mode cooperative control, IEEE Transactions on Industrial Electronics, 65, 907, 10.1109/TIE.2017.2726970 Pisano, 2011, Sliding mode control: A survey with applications in math, Mathematics and Computers in Simulation, 81, 954, 10.1016/j.matcom.2010.10.003 Polyakov, 2015, Finite-time and fixed-time stabilization: Implicit Lyapunov function approach, Automatica, 51, 332, 10.1016/j.automatica.2014.10.082 Polyakov, 2014, Stability notions and Lyapunov functions for sliding mode control systems, Journal of the Franklin Institute, 351, 1831, 10.1016/j.jfranklin.2014.01.002 Rao, 2011, Sliding mode control-based algorithms for consensus in connected swarms, International Journal of Control, 84, 1477, 10.1080/00207179.2011.602834 Rubagotti, 2011, Integral sliding mode control for nonlinear systems with matched and unmatched perturbations, IEEE Transactions on Automatic Control, 56, 2699, 10.1109/TAC.2011.2159420 Sanai Dashti, Z. A. Z., Seatzu, C., & Franceschelli, M. (2019). Dynamic Consensus on the Median Value in Open Multi-Agent Systems. In 2019 IEEE 58th conference on decision and control (pp. 3691–3697). Shevitz, 1994, Lyapunov stability theory of nonsmooth systems, IEEE Transactions on Automatic Control, 39, 1910, 10.1109/9.317122 Shi, 2013, Robust consensus for continuous-time multiagent dynamics, SIAM Journal on Control and Optimization, 51, 3673, 10.1137/110841308 Simpson-Porco, 2013, Synchronization and power sharing for droop-controlled inverters in islanded microgrids, Automatica, 49, 2603, 10.1016/j.automatica.2013.05.018 Smith, 2021, Cooperative control of microgrids: A review of theoretical frameworks, applications and recent developments, MDPI Energies, 14, 8026, 10.3390/en14238026 Song, 2010, Second-order leader-following consensus of nonlinear multi-agent systems via pinning control, Systems & Control Letters, 59, 553, 10.1016/j.sysconle.2010.06.016 Utkin, 1977, Variable structure systems with sliding modes, IEEE Transactions on Automatic Control, 22, 212, 10.1109/TAC.1977.1101446 Utkin, 2013 Utkin, 2002, Sliding mode control in electro-mechanical systems, Mathematioal Problem in Engnieering, 8, 451, 10.1080/10241230306724 Utkin, V., & Shi, J. (1996). Integral sliding mode in systems operating under uncertainty conditions. In Proc. of the IEEE conf. on decision & control, Vol. 4 (pp. 4591–4596). (1). Van Vleck, 1966, The spectrum of clipped noise, Proceedings of the IEEE, 54, 2, 10.1109/PROC.1966.4567 Vasca, 2021, Practical consensus in bounded confidence opinion dynamics, Automatica, 129, 10.1016/j.automatica.2021.109683 Wang, J., & Elia, N. (2011). A control perspective for centralized and distributed convex optimization. In Proc. of the IEEE joint conf. on decision & control and European control conf. (pp. 3800–3805). Wang, 2008, Finite-time consensus for multi-agent networks with second-order agent dynamics, IFAC Proceedings Volumes, 41, 15185, 10.3182/20080706-5-KR-1001.02568 Wen, 2014, Distributed consensus of multi-agent systems with general linear node dynamics and intermittent communications, International Journal of Robust and Nonlinear Control, 24, 2438, 10.1002/rnc.3001 Wooldridge, 2009 Wu, 2020, Vision-based trajectory tracking control of quadrotors using super twisting sliding mode control, Cyber-Physical Systems, 6, 207, 10.1080/23335777.2020.1727960 Xiao, 2009, Finite-time formation control for multi-agent systems, Automatica, 45, 2605, 10.1016/j.automatica.2009.07.012 Xie, 2020, Global consensus of multi-agent systems with intermittent directed communication in the presence of actuator saturation, International Journal of Robust and Nonlinear Control, 30, 8469, 10.1002/rnc.5255 Xie, 2022, Global smooth leaderless consensus control of high-order nonholonomic chained systems, International Journal of Control, 95, 81, 10.1080/00207179.2020.1779957 Xu, 2020, A Markovian jump system approach to consensus of heterogeneous multiagent systems with partially unknown and uncertain attack strategies, International Journal of Robust and Nonlinear Control, 30, 3039, 10.1002/rnc.4923 Yu, 2015, Finite-time consensus for second-order multi-agent systems with disturbances by integral sliding mode, Automatica, 54, 158, 10.1016/j.automatica.2015.02.001 Zambelli, 2021, Sliding modes in consensus control, 181 Zhang, 2021, Robust h 2 consensus for multi-agent systems with parametric uncertainties, IEEE Transactions on Circuits and Systems II: Express Briefs, 68, 2473 Zhou, 2012, Flocking of multi-agent dynamical systems based on pseudo-leader mechanism, Systems & Control Letters, 61, 195, 10.1016/j.sysconle.2011.10.006 Zou, 2019, Finite-time consensus of second-order switched nonlinear multi-agent systems, IEEE Transactions on Neural Networks and Learning Systems, 31, 1757, 10.1109/TNNLS.2019.2920880