Abstract
An indirect adaptive consensus control method is presented for multi-agent systems (MASs) with unknown hysteresis states and input. All system states that can be utilized to design the controller are measured by the sensors subjected to hysteresis, and thus, the system state values are inaccurate. Meanwhile, it is difficult to compensate the input hysteresis for it is coupled with the state hysteresis. The unknown function from agent’s neighbors also increases the difficulty of controller design. To eliminate the influence of unknown input hysteresis, an inverse adaptive compensated method is presented. The problem of state hysteresis is addressed by designing two adaptive laws to approximate the upper and lower bounds of unknown hysteresis coefficient. Neural networks are introduced to handle the unknown dynamics of agent and its neighbors. The proposed control scheme can guarantee that the consensus errors of followers converge to a predefined interval of zero asymptotically. In addition, the transient performance of MASs can be further ensured. The simulation examples are included to verify the effectiveness of the presented control approach.
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References
Curtin, T.B., Bellingham, J.G., Catipovic, J., Webb, D.: Autonomous oceanographic sampling networks. Oceanography 6(3), 86–94 (1993)
Meng, D., Jia, Y.: Robust consensus algorithms for multiscale coordination control of multivehicle systems with disturbances. IEEE Trans. Ind. Electron. 63(2), 1107–1119 (2016)
Tomlin, C., Pappas, G., Sastry, S.: Conflict resolution for air traffic management: a study in multiagent hybrid systems. IEEE Trans. Autom. Control 43(4), 509–521 (1998)
Zhang, J., Feng, T., Zhang, H., Wang, X.: The decoupling cooperative control with dominant poles assignment. IEEE Trans. Syst. Man Cybern. Syst. PP, 1–9 (2020). https://doi.org/10.1109/TSMC.2020.3011142
Zhang, J., Chen, Z., Zhang, H., Feng, T.: Coupling effect and pole assignment in trajectory regulation of multi-agent systems. Automatica 125, 109465 (2021). https://doi.org/10.1016/j.automatica.2020.109465
Yu, W., Chen, G., Ming, C.: Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems. Automatica 46(6), 1089–1095 (2010)
Su, H., Chen, G., Wang, X., Lin, Z.: Adaptive second-order consensus of networked mobile agents with nonlinear dynamics. Automatica 47(2), 368–375 (2011)
Tian, Y.P., Liu, C.L.: Consensus of multi-agent systems with diverse input and communication delays. IEEE Trans. Autom. Control 53(9), 2122–2128 (2008)
Zhang, H., Lewis, F.L., Das, A.: Optimal design for synchronization of cooperative systems: state feedback, observer and output feedback. IEEE Trans. Autom. Control 56(8), 1948–1952 (2011)
Jiang, F., Wang, L., Jia, Y.: Consensus in leaderless networks of high-order-integrator agents. In: 2009 American Control Conference, pp. 4458–4463 (2009)
Hua, C.-C., Li, K., Guan, X.-P.: Leader-following output consensus for high-order nonlinear multiagent systems. IEEE Trans. Autom. Control 64(3), 1156–1161 (2018)
Zhang, H., Lewis, F.L.: Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics. Automatica 48(7), 1432–1439 (2012)
Shi, P., Shen, Q.: Cooperative control of multi-agent systems with unknown state-dependent controlling effects. IEEE Trans. Autom. Sci. Eng. 12(3), 827–834 (2015)
Yoo, S.J.: Distributed consensus tracking for multiple uncertain nonlinear strict-feedback systems under a directed graph. IEEE Trans. Neural Netw. Learn. Syst. 24(4), 666–672 (2013)
Chen, B., Liu, X., Liu, K., Lin, C.: Direct adaptive fuzzy control of nonlinear strict-feedback systems. Automatica 45(6), 1530–1535 (2009)
Wang, F., Chen, B., Lin, C., Li, X.: Distributed adaptive neural control for stochastic nonlinear multiagent systems. IEEE Trans. Cybern. 47(7), 1795–1803 (2017)
Lin, Z., Liu, Z., Zhang, Y., Chen, C Philip: Distributed adaptive cooperative control for uncertain nonlinear multi-agent systems with hysteretic quantized input. J. Frankl. Inst. 357(8), 4645–4663 (2020)
Chen, B., Liu, X.P., Ge, S.S., Lin, C.: Adaptive fuzzy control of a class of nonlinear systems by fuzzy approximation approach. IEEE Trans. Fuzzy Syst. 20(6), 1012–1021 (2012)
Liu, Z., Wang, F., Zhang, Y., Chen, X., Chen, C.L.P.: Adaptive fuzzy output-feedback controller design for nonlinear systems via backstepping and small-gain approach. IEEE Trans. Cybern. 44(10), 1714–1725 (2014)
Chen, B., Zhang, H., Lin, C.: Observer-based adaptive neural network control for nonlinear systems in nonstrict-feedback form. IEEE Trans. Neural Netw. Learn. Syst. 27(1), 89–98 (2016)
Shang, Y., Chen, B., Lin, C.: Consensus tracking control for distributed nonlinear multiagent systems via adaptive neural backstepping approach. IEEE Trans. Syst. Man Cybern. Syst. 50(7), 2436–2444 (2020)
Lai, G., Zhang, Y., Liu, Z., Chen, C.P.: Indirect adaptive fuzzy control design with guaranteed tracking error performance for uncertain canonical nonlinear systems. IEEE Trans. Fuzzy Syst. 27(6), 1139–1150 (2018)
Lu, K., Liu, Z., Lai, G., Chen, C.L.P., Zhang, Y.: Adaptive consensus tracking control of uncertain nonlinear multiagent systems with predefined accuracy. IEEE Trans. Cybern. 51(1), 405–415 (2021)
Chen, X., Ozaki, T.: Adaptive control for plants in the presence of actuator and sensor uncertain hysteresis. IEEE Trans. Autom. Control 56(1), 171–177 (2010)
Zhou, J., Wen, C., Li, T.: Adaptive output feedback control of uncertain nonlinear systems with hysteresis nonlinearity. IEEE Trans. Autom. Control 57(10), 2627–2633 (2012)
Tao, G., Kokotovic, P.V.: Adaptive control of plants with unknown hystereses. IEEE Trans. Autom. Control 40(2), 200–212 (1995)
Su, C.-Y., Wang, Q., Chen, X., Rakheja, S.: Adaptive variable structure control of a class of nonlinear systems with unknown Prandtl–Ishlinskii hysteresis. IEEE Trans. Autom. Control 50(12), 2069–2074 (2005)
Zhang, X., Li, Z., Su, C.-Y., Lin, Y., Fu, Y.: Implementable adaptive inverse control of hysteretic systems via output feedback with application to piezoelectric positioning stages. IEEE Trans. Ind. Electron. 63(9), 5733–5743 (2016)
Yu, Z., Li, S., Yu, Z., Li, F.: Adaptive neural output feedback control for nonstrict-feedback stochastic nonlinear systems with unknown backlash-like hysteresis and unknown control directions. IEEE Trans. Neural Netw. Learn. Syst. 29(4), 1147–1160 (2018)
Zhou, Q., Wang, W., Ma, H., Li, H.: Event-triggered fuzzy adaptive containment control for nonlinear multiagent systems with unknown Bouc–Wen hysteresis input. IEEE Trans. Fuzzy Syst. 29(4), 731–741 (2021)
Tao, G., Kokotovic, P.V.: Adaptive Control of Systems with Actuator and Sensor Nonlinearities. Wiley & Sons, Inc., Hoboken (1996)
Dong, R., Tan, Y.: A model based predictive compensation for ionic polymer metal composite sensors for displacement measurement. Sens. Actuators A Phys. 224, 43–49 (2015)
Lei, H., Sharif, M.A., Tan, X.: Dynamics of omnidirectional IPMC sensor: experimental characterization and physical modeling. IEEE/ASME Trans. Mechatron. 21(2), 601–612 (2015)
Seco, F., Martín, J.M., Pons, J.L., Jiménez, A.R.: Hysteresis compensation in a magnetostrictive linear position sensor. Sens. Actuators A Phys. 110(1–3), 247–253 (2004)
Freeman, R.: Global internal stabilizability does not imply global external stabilizability for small sensor disturbances. IEEE Trans. Autom. Control 40(12), 2119–2122 (1995)
Chen, C., Wen, C., Liu, Z., Xie, K., Zhang, Y., Chen, C.P.: Adaptive consensus of nonlinear multi-agent systems with non-identical partially unknown control directions and bounded modelling errors. IEEE Trans. Autom. Control 62(9), 4654–4659 (2016)
Liu, Z., Lu, K., Lai, G., Chen, C.L.P., Zhang, Y.: Indirect fuzzy control of nonlinear systems with unknown input and state hysteresis using an alternative adaptive inverse. IEEE Trans. Fuzzy Syst. 29(3), 500–514 (2021)
Sanner, R.M., Slotine, J.-J.E.: Gaussian networks for direct adaptive control. In: 1991 American Control Conference, pp. 2153–2159 (1991)
Chen, C.P., Wen, G.-X., Liu, Y.-J., Wang, F.-Y.: Adaptive consensus control for a class of nonlinear multiagent time-delay systems using neural networks. IEEE Trans. Neural Netw. Learn. Syst. 25(6), 1217–1226 (2014)
Ikhouane, F., MañOsa, V., Rodellar, J.: Adaptive control of a hysteretic structural system. Automatica 41(2), 225–231 (2005)
Chen, X., Hisayama, T., Su, C.-Y.: Pseudo-inverse-based adaptive control for uncertain discrete time systems preceded by hysteresis. Automatica 45(2), 469–476 (2009)
Parlangeli, G., Corradini, M.L.: Output zeroing of MIMO plants in the presence of actuator and sensor uncertain hysteresis nonlinearities. IEEE Trans. Autom. Control 50(9), 1403–1407 (2005)
Zhang, J., Torres, D., Ebel, J.L., Sepúlveda, N., Tan, X.: A composite hysteresis model in self-sensing feedback control of fully integrated v02 microactuators. IEEE/ASME Trans. Mechatron. 21(5), 2405–2417 (2016)
Rakotondrabe, M.: Bouc–Wen modeling and inverse multiplicative structure to compensate hysteresis nonlinearity in piezoelectric actuators. IEEE Trans. Autom. Sci. Eng. 8(2), 428–431 (2010)
Zhou, J., Wen, C., Zhang, Y.: Adaptive backstepping control of a class of uncertain nonlinear systems with unknown backlash-like hysteresis. IEEE Trans. Autom. Control 49(10), 1751–1759 (2004)
Krstic, M., Kokotovic, P.V., Kanellakopoulos, I.: Nonlinear and Adaptive Control Design. Wiley & Sons, Inc., Hoboken (1995)
Chen, B., Liu, K., Liu, X., Shi, P., Lin, C., Zhang, H.: Approximation-based adaptive neural control design for a class of nonlinear systems. IEEE Trans. Cybern. 44(5), 610–619 (2013)
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This work was supported in part by Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme, and in part by the National Key Research and Development Program of China under Project 2020AAA0108303.
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Lin, Z., Liu, Z., Zhang, Y. et al. Adaptive neural consensus tracking control for multi-agent systems with unknown state and input hysteresis. Nonlinear Dyn 105, 1625–1641 (2021). https://doi.org/10.1007/s11071-021-06652-4
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DOI: https://doi.org/10.1007/s11071-021-06652-4