Protocol design for group output consensus of disturbed port-controlled Hamiltonian multi-agent systems

Authors

Baozeng Fu, Xiangyu Wang, Qingzhi Wang

Abstract

This paper considers the group output consensus problem for a class of disturbed port-controlled Hamiltonian multi-agent systems via a composite control method. The composite distributed control protocol is proposed by combining the damping injection and energy shaping method, the finite-time disturbance observer (FTDO) technique and distributed protocol, which makes the closed-loop Hamiltonian multi-agent systems asymptotically stable and the group outputs reach consensus. It is shown that many kinds of disturbances can be estimated accurately via the FTDO. The advantage is that this control scheme exhibits not only better robustness against disturbances, but also the nominal system recovery performance. Two illustrative examples reveal that the designed control protocol is effective.

Citation

• Journal: Journal of the Franklin Institute
• Year: 2021
• Volume: 358
• Issue: 18
• Pages: 9867–9889
• Publisher: Elsevier BV
• DOI: 10.1016/j.jfranklin.2021.10.006

BibTeX

@article{Fu_2021,
  title={{Protocol design for group output consensus of disturbed port-controlled Hamiltonian multi-agent systems}},
  volume={358},
  ISSN={0016-0032},
  DOI={10.1016/j.jfranklin.2021.10.006},
  number={18},
  journal={Journal of the Franklin Institute},
  publisher={Elsevier BV},
  author={Fu, Baozeng and Wang, Xiangyu and Wang, Qingzhi},
  year={2021},
  pages={9867--9889}
}

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References

• Arcak M (2007) Passivity as a Design Tool for Group Coordination. IEEE Trans Automat Contr 52(8):1380–1390. https://doi.org/10.1109/tac.2007.902733 – 10.1109/tac.2007.902733
• Li, Global analysis of multi-agent systems based on Vicsek’s model. IEEE Trans. Autom. Control (2009)
• Li S, Wang X (2013) Finite-time consensus and collision avoidance control algorithms for multiple AUVs. Automatica 49(11):3359–3367. https://doi.org/10.1016/j.automatica.2013.08.003 – 10.1016/j.automatica.2013.08.003
• Wang X, Wang G, Li S (2020) Distributed Finite-Time Optimization for Integrator Chain Multiagent Systems With Disturbances. IEEE Trans Automat Contr 65(12):5296–5311. https://doi.org/10.1109/tac.2020.2979274 – 10.1109/tac.2020.2979274
• Wang, A distributed fixed-time optimization algorithm for multi-agent systems. Automatica (2020)
• Wang X, Li S, Wang G (2020) Distributed Optimization for Disturbed Second-Order Multiagent Systems Based on Active Antidisturbance Control. IEEE Trans Neural Netw Learning Syst 31(6):2104–2117. https://doi.org/10.1109/tnnls.2019.2951790 – 10.1109/tnnls.2019.2951790
• Olfati-Saber R, Murray RM (2004) Consensus Problems in Networks of Agents With Switching Topology and Time-Delays. IEEE Trans Automat Contr 49(9):1520–1533. https://doi.org/10.1109/tac.2004.834113 – 10.1109/tac.2004.834113
• LUO X-Y, SHAO S-K, GUAN X-P, ZHAO Y-J (2014) Dynamic Generation and Control of Optimally Persistent Formation for Multi-agent Systems. Acta Automatica Sinica 39(9):1431–1438. https://doi.org/10.3724/sp.j.1004.2013.01431 – 10.3724/sp.j.1004.2013.01431
• Wei Ren, Beard RW (2005) Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Trans Automat Contr 50(5):655–661. https://doi.org/10.1109/tac.2005.846556 – 10.1109/tac.2005.846556
• Wang X, Wang G, Li S (2021) Distributed Finite-Time Optimization for Disturbed Second-Order Multiagent Systems. IEEE Trans Cybern 51(9):4634–4647. https://doi.org/10.1109/tcyb.2020.2988490 – 10.1109/tcyb.2020.2988490
• Wang, A modular optimal formation control scheme of multi-agent systems with application to multiple mobile robots. IEEE Trans. Ind. Electron. (2021)
• Wang X, Li S, Lam J (2016) Distributed active anti-disturbance output consensus algorithms for higher-order multi-agent systems with mismatched disturbances. Automatica 74:30–37. https://doi.org/10.1016/j.automatica.2016.07.010 – 10.1016/j.automatica.2016.07.010
• Chopra, Passivity-based control of multi-agent systems. (2006)
• Wang X, Li S, Chen MZQ (2018) Composite Backstepping Consensus Algorithms of Leader–Follower Higher-Order Nonlinear Multiagent Systems Subject to Mismatched Disturbances. IEEE Trans Cybern 48(6):1935–1946. https://doi.org/10.1109/tcyb.2017.2720680 – 10.1109/tcyb.2017.2720680
• Wang G (2019) Distributed control of higher-order nonlinear multi-agent systems with unknown non-identical control directions under general directed graphs. Automatica 110:108559. https://doi.org/10.1016/j.automatica.2019.108559 – 10.1016/j.automatica.2019.108559
• Wang G, Wang C, Cai X (2020) Consensus control of output‐constrained multiagent systems with unknown control directions under a directed graph. Intl J Robust & Nonlinear 30(5):1802–1818. https://doi.org/10.1002/rnc.4852 – 10.1002/rnc.4852
• Wang, Fully distributed low-complexity control for nonlinear strict-feedback multiagent systems with unknown dead-zone inputs. IEEE Trans. Syst. Man Cybern. (2020)
• Li Y, Li H, Sun W (2018) Event-triggered control for robust set stabilization of logical control networks. Automatica 95:556–560. https://doi.org/10.1016/j.automatica.2018.06.030 – 10.1016/j.automatica.2018.06.030
• Li, Protocol design for output consensus of port-controlled Hamiltonian multi-agent systems. Acta Autom. Sin. (2014)
• Wang, Flocking control protocol design for a class of multi-agent systems based on Hamiltonian framework. (2010)
• Maschke, Port-controlled Hamiltonian systems: modeling origins and system theoretic properties. (1992)
• Schaft, The Hamiltonian formulation of energy conserving physical systems with external ports. Arch. Elektron. Bertragungstechnik (1995)
• Cheng D, Astolfi A, Ortega R (2005) On feedback equivalence to port controlled Hamiltonian systems. Systems & Control Letters 54(9):911–917. https://doi.org/10.1016/j.sysconle.2005.02.005 – 10.1016/j.sysconle.2005.02.005
• Sun L, Feng G, Wang Y (2014) Finite-time stabilization and \(H_{\infty}\) control for a class of nonlinear Hamiltonian descriptor systems with application to affine nonlinear descriptor systems. Automatica 50(8):2090–2097. https://doi.org/10.1016/j.automatica.2014.05.031 – 10.1016/j.automatica.2014.05.031
• Fu B, Li S, Wang X, Guo L (2019) Output feedback based simultaneous stabilization of two Port-controlled Hamiltonian systems with disturbances. Journal of the Franklin Institute 356(15):8154–8166. https://doi.org/10.1016/j.jfranklin.2019.02.039 – 10.1016/j.jfranklin.2019.02.039
• Yu H, Yu J, Liu J, Song Q (2012) Nonlinear control of induction motors based on state error PCH and energy-shaping principle. Nonlinear Dyn 72(1-2):49–59. https://doi.org/10.1007/s11071-012-0689-3 – 10.1007/s11071-012-0689-3
• Fu B, Li S, Guo L, Yang J, Lan Q (2017) Finite-time stabilization of port-controlled Hamiltonian systems with nonvanishing disturbances. Transactions of the Institute of Measurement and Control 40(10):2973–2981. https://doi.org/10.1177/0142331217712381 – 10.1177/0142331217712381
• Fu B, Wang Q, He W (2018) Nonlinear Disturbance Observer-Based Control for a Class of Port-Controlled Hamiltonian Disturbed Systems. IEEE Access 6:50299–50305. https://doi.org/10.1109/access.2018.2868919 – 10.1109/access.2018.2868919
• Sun W, Fu B (2016) Adaptive control of time‐varying uncertain non‐linear systems with input delay: a Hamiltonian approach. IET Control Theory & Appl 10(15):1844–1858. https://doi.org/10.1049/iet-cta.2015.1165 – 10.1049/iet-cta.2015.1165
• Cao Z, Hou X, Zhao W (2016) A Family of Robust Simultaneous Controllers With Tuning Parameters Design for a Set of Port‐Controlled Hamiltonian Systems. Asian Journal of Control 19(1):151–163. https://doi.org/10.1002/asjc.1341 – 10.1002/asjc.1341
• Fu, Global output regulation for a class of single input port-controlled Hamiltonian disturbed systems. Appl. Math. Comput. (2018)
• Ortega R, Spong MW, Gomez-Estern F, Blankenstein G (2002) Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment. IEEE Trans Automat Contr 47(8):1218–1233. https://doi.org/10.1109/tac.2002.800770 – 10.1109/tac.2002.800770
• Cheng, Decentralized adaptive consensus control for multi-manipulator system with uncertain dynamics. (2008)
• Ren, Robust adaptive control for robotic systems with input time-varying delay using Hamiltonian method. IEEE/CAA J. Autom. Sin. (2018)
• Sun W, Wu Y, Wang L (2019) Trajectory tracking of constrained robotic systems via a hybrid control strategy. Neurocomputing 330:188–195. https://doi.org/10.1016/j.neucom.2018.11.008 – 10.1016/j.neucom.2018.11.008
• Xu T, Yu H, Yu J, Meng X (2020) Adaptive Disturbance Attenuation Control of Two Tank Liquid Level System With Uncertain Parameters Based on Port-Controlled Hamiltonian. IEEE Access 8:47384–47392. https://doi.org/10.1109/access.2020.2979352 – 10.1109/access.2020.2979352
• Ren Y, Chen M, Wu Q (2018) Disturbance observer-based boundary control for a suspension cable system moving in the horizontal plane. Transactions of the Institute of Measurement and Control 41(2):340–349. https://doi.org/10.1177/0142331218759823 – 10.1177/0142331218759823
• Sun W, Lv X, Wang K, Wang L (2019) Observer-based output feedback stabilisation and \(\mathcal{L}_{2}\) -disturbance attenuation of uncertain Hamiltonian systems with input and output delays. International Journal of Systems Science 50(14):2565–2578. https://doi.org/10.1080/00207721.2019.1671532 – 10.1080/00207721.2019.1671532
• Godsil, (2001)
• Wang, Finite-time stabilization of port-controlled Hamiltonian systems with application to nonlinear affine systems. (2008)
• Chen W-H, Yang J, Guo L, Li S (2016) Disturbance-Observer-Based Control and Related Methods—An Overview. IEEE Trans Ind Electron 63(2):1083–1095. https://doi.org/10.1109/tie.2015.2478397 – 10.1109/tie.2015.2478397
• Du, Finite-time synchronization of a class of second-order nonlinear multi-agent systems using output feedback control. IEEE Trans. Circuits Syst. I (2014)
• Guo L, Cao S (2014) Anti-disturbance control theory for systems with multiple disturbances: A survey. ISA Transactions 53(4):846–849. https://doi.org/10.1016/j.isatra.2013.10.005 – 10.1016/j.isatra.2013.10.005
• Li, (2014)
• Wang X, Li S, Yu X, Yang J (2017) Distributed Active Anti-Disturbance Consensus for Leader-Follower Higher-Order Multi-Agent Systems With Mismatched Disturbances. IEEE Trans Automat Contr 62(11):5795–5801. https://doi.org/10.1109/tac.2016.2638966 – 10.1109/tac.2016.2638966
• Yang, Optimized active disturbance rejection control for DC-DC buck converters with uncertainties using a reduced-order GPI observer. IEEE Trans. Circuits Syst. I (2018)
• Levant A (2003) Higher-order sliding modes, differentiation and output-feedback control. International Journal of Control 76(9-10):924–941. https://doi.org/10.1080/0020717031000099029 – 10.1080/0020717031000099029
• Shtessel YB, Shkolnikov IA, Levant A (2007) Smooth second-order sliding modes: Missile guidance application. Automatica 43(8):1470–1476. https://doi.org/10.1016/j.automatica.2007.01.008 – 10.1016/j.automatica.2007.01.008
• Li, Finite-time stability of cascaded time-varying systems. Int. J. Control (2007)
• Wang J, Ding X, Wang C, Liang L, Hu H (2021) Affine formation control for multi-agent systems with prescribed convergence time. Journal of the Franklin Institute 358(14):7055–7072. https://doi.org/10.1016/j.jfranklin.2021.07.019 – 10.1016/j.jfranklin.2021.07.019
• Tang W, Wu J, Liu N, Mo H (2021) Distributed data driven control for multi-agent consensus with unknown system dynamics. Journal of the Franklin Institute 358(14):7013–7031. https://doi.org/10.1016/j.jfranklin.2021.07.017 – 10.1016/j.jfranklin.2021.07.017
• Zhang Z, Zhang S, Li H, Yan W (2020) Cooperative robust optimal control of uncertain multi-agent systems. Journal of the Franklin Institute 357(14):9467–9483. https://doi.org/10.1016/j.jfranklin.2020.07.021 – 10.1016/j.jfranklin.2020.07.021