Predefined-time hierarchical controller-estimator time-varying formation-containment tracking for multiple Euler-Lagrange systems with two-layer leaders. (English) Zbl 1516.93002
Summary: This paper mainly discusses the problem of the predefined-time time-varying formation-containment tracking (TVFCT) for the multiple Euler-Lagrange systems (MELSs), where the external disturbances are taken into consideration. To cope with the above problem, a two-layer formation-containment tracking (FCT) framework is established, namely, the real leaders’ formation layer and the followers’ containment layer, where the analysis of the system is executed step by step. Meanwhile, the corresponding hierarchical control algorithms based on nonsingular terminal sliding mode are designed for different layers to facilitate the implementation of the TVFCT control problem. With the help of the Lyapunov function and predefined-time stability theory, some sufficient criteria for the convergence of the proposed algorithms are provided. In the end, the simulation results demonstrate the effectiveness of the theoretical results and the designed controller.
References:
| [1] | Olfati-Saber, R.; Murray, R. M., Consensus problems in networks of agents with switching topology and time-delays, IEEE Trans. Autom. Control, 49, 9, 1520-1533 (2004) · Zbl 1365.93301 |
| [2] | Wang, J.; Lv, W.; Jiang, J.; Qin, S.; Li, J., A multi-agent based cellular automata model for intersection traffic control simulation, Physica A, 58, 126356 (2021) |
| [3] | Shen, K.; Wang, M.; Fu, M.; Yi, Y.; Zhang, Y., Observability analysis and adaptive information fusion for integrated navigation of unmanned ground vehicles, IEEE Trans. Ind. Electron., 67, 9, 7659-7668 (2019) |
| [4] | Chen, L.; Liu, Z.; Dang, Q.; Zhao, W.; Wang, G., Robust trajectory tracking control for a quadrotor using recursive sliding mode control and nonlinear extended state observer, Aerosp. Sci. Technol., 128, 107749 (2022) |
| [5] | Li, J.; Sun, T.; Huang, X.; Ma, L.; Lin, Q.; Chen, J.; Victor, V. C.M., A memetic path planning algorithm for unmanned air/ground vehicle cooperative detection systems, IEEE Trans. Autom. Sci. Eng., 19, 4, 2724-2737 (2021) |
| [6] | Liu, X.-K.; Wang, Y.-W.; Xiao, J.-W.; Chi, M., Concentrated differentially private average consensus algorithm for a discrete-time network with heterogeneous dynamics, J. Franklin Inst., 359, 4, 1655-1676 (2022) · Zbl 1483.93581 |
| [7] | Yao, X.-Y.; Park, J. H.; Ding, H.-F.; Ge, M. F., Event-triggered consensus control for networked under-actuated robotic systems, IEEE Trans. Cybern., 52, 5, 2896-2906 (2020) |
| [8] | Han, T.; Guan, Z.-H.; Xiao, B.; Yan, H., Bipartite average tracking for multi-agent systems with disturbances: finite-time and fixed-time convergence, IEEE Trans. Circuits Syst. I Regul. Pap., 68, 10, 4393-4402 (2021) |
| [9] | Han, T.; Zheng, W. X., Bipartite output consensus for heterogeneous multi-agent systems via output regulation approach, IEEE Trans. Circuits Syst. II Express Briefs, 68, 1, 281-285 (2021) |
| [10] | Wang, J.; Xia, J.; Shen, H.; Xing, M.; Park, J. H., \(H{}^\infty\) synchronization for fuzzy Markov jump chaotic systems with piecewise-constant transition probabilities subject to PDT switching rule, IEEE Trans. Fuzzy Syst., 29, 10, 3082-3092 (2020) |
| [11] | Shen, H.; Hu, X.; Wang, J.; Cao, J.; Qian, W., Non-fragile synchronization for Markov jump singularly perturbed coupled neural networks subject to double-layer switching regulation, IEEE Trans. Neural. Netw. Learn. Syst. (2021) |
| [12] | Chang, Z.; Xue, H.; Liang, H.; Zhang, P., Time-varying formation control for nonlinear multi-agent systems against actuator attacks, J. Franklin Inst., 359, 18, 11068-11088 (2022) · Zbl 1504.93015 |
| [13] | Huang, K.-L.; Ge, M.-F.; Liang, C.-D.; Dong, J.-W.; Zhao, X. W., Hierarchical predefined-time control for time-varying formation tracking of multiple heterogeneous Euler-Lagrange agents, Nonlinear Dyn., 105, 4, 3255-3270 (2021) |
| [14] | Zhang, F.; Chen, Y.-Y.; Zhang, Y., Finite-time event-triggered containment control of multiple Euler-Lagrange systems with unknown control coefficients, J. Franklin Inst., 360, 2, 777-791 (2022) · Zbl 1506.93080 |
| [15] | Li, Z.; Cao, L.; Pan, Y.; Zhang, P., Adaptive resilient containment control for nonlower triangular multiagent systems with time-varying delay and sensor faults, J. Franklin Inst., 359, 17, 9759-9781 (2022) · Zbl 1501.93080 |
| [16] | Chen, L.; Li, C.; Guo, Y.; Ma, G.; Li, Y.; Xiao, B., Formation-containment control of multi-agent systems with communication delays, ISA Trans., 128, 32-43 (2021) |
| [17] | Cao, Y.; Stuart, D.; Ren, W.; Meng, Z., Distributed containment control for multiple autonomous vehicles with double-integrator dynamics: algorithms and experiments, IEEE Trans. Control Syst. Technol., 19, 4, 929-938 (2011) |
| [18] | Liu, H.; Xie, G.; Wang, L., Necessary and sufficient conditions for containment control of networked multi-agent systems, Automatica, 48, 7, 1415-1422 (2012) · Zbl 1246.93008 |
| [19] | Hua, Y.; Dong, X.; Han, L.; Li, Q.; Ren, Z., Formation-containment tracking for general linear multi-agent systems with a tracking-leader of unknown control input, Syst. Control Lett., 122, 67-76 (2018) · Zbl 1408.93004 |
| [20] | Zheng, B.; Mu, X., Formation-containment control of second-order multi-agent systems with only sampled position data, Int. J. Syst. Sci., 47, 15, 3609-3618 (2016) · Zbl 1346.93050 |
| [21] | Zhou, S.; Dong, X.; Hua, Y.; Yu, J.; Ren, Z., Predefined formation-containment control of high-order multi-agent systems under communication delays and switching topologies, IET Contr. Theory Appl., 15, 12, 1661-1672 (2021) |
| [22] | Chen, L.; Li, C.; Xiao, B.; Guo, Y., Formation-containment control of networked Euler-Lagrange systems: an event-triggered framework, ISA Trans., 86, 87-97 (2019) |
| [23] | Zhao, J.; Wang, Y.; Wang, Q., Event-triggered formation-containment control for multiple Euler-Lagrange systems with input saturation, J. Chin. Inst. Eng., 45, 4, 313-323 (2022) |
| [24] | Zhou, P.; Chen, B. M., Formation-containment control of Euler-Lagrange systems of leaders with bounded unknown inputs, IEEE Trans. Cybern., 52, 7, 6342-6353 (2020) |
| [25] | Ding, T.-F.; Ge, M.-F.; Liu, Z.-W.; Wang, T.-W.; Hamid, R. K., Lag-bipartite formation tracking of networked robotic systems over directed matrix-weighted signed graphs, IEEE Trans. Cybern., 52, 7, 6759-6770 (2020) |
| [26] | Long, J.; Wang, W.; Liu, K.; Huang, J., Adaptive time-varying formation control of uncertain Euler-Lagrange systems with event-triggered communication, Int. J. Robust Nonlinear Control, 31, 18, 9026-9039 (2021) · Zbl 1527.93217 |
| [27] | Dong, G.; Li, H.; Ma, H.; Lu, R., Finite-time consensus tracking neural network FTC of multi-agent systems, IEEE Trans. Neural Netw. Learn. Syst., 32, 2, 653-662 (2020) |
| [28] | Fan, Y.; Jin, Z.; Luo, X.; Guo, B., Robust finite-time consensus control for Euler-Lagrange multi-agent systems subject to switching topologies and uncertainties, Appl. Math. Comput., 432, 127367 (2022) · Zbl 1510.93017 |
| [29] | Sun, Y.; Chen, L.; Qin, H.; Wang, W., Distributed finite-time coordinated tracking control for multiple Euler-Lagrange systems with input nonlinearity, Nonlinear Dyn., 95, 2395-2414 (2019) · Zbl 1432.93303 |
| [30] | Yang, H.; Ye, D., Time-varying formation tracking control for high-order nonlinear multi-agent systems in fixed-time framework, Appl. Math. Comput., 377, 125119 (2020) · Zbl 1508.93022 |
| [31] | Zhao, X.-F.; Han, T.; Zhan, X.-S.; Yan, H., Distributed estimator-based fixed-time bipartite consensus of multiple Euler-Lagrange systems over a signed digraph, IEEE Trans. Circuits Syst. II Express Briefs, 69, 6, 2847-2851 (2022) |
| [32] | Fang, X.; Fan, H.; Liu, L.; Wang, B., Adaptive fixed-time fault-tolerant control of saturated MIMO nonlinear systems with time-varying state constrains, Nonlinear Dyn., 110, 3463-3483 (2022) |
| [33] | Jimenez-Rodriguez, E.; Munoz-Vazquez, A. J.; Sanchez-Torres, J. D.; Defoort, M.; Loukianov, A. G., A Lyapunov-like characterization of predefined-time stability, IEEE Trans. Autom. Control, 65, 11, 4922-4927 (2020) · Zbl 1536.93760 |
| [34] | Liang, C.-D.; Ge, M.-F.; Liu, Z.-W.; Ling, G.; Liu, P., Predefined-time formation tracking control of networked marine surface vehicles, Control Eng. Pract., 107, 104682 (2021) |
| [35] | Zhao, X.-F.; Han, T.; Xiao, B.; Yan, H.; Ge, M.-F.; Liang, C. D., Task-space time-varying formation tracking for networked heterogeneous Euler-Lagrange systems via hierarchical predefined-time control approach, Nonlinear Dyn., 109, 2675-2692 (2022) |
| [36] | Li, S.; Nian, X.; Deng, Z.; Chen, Z., Predefined-time distributed optimization of general linear multi-agent systems, Inf. Sci., 584, 111-125 (2022) · Zbl 1532.93318 |
| [37] | Ouyang, Y.; Lei, X.; Lu, D.; Sun, C., Neural network-based finite-time distributed formation-containment control of two-layer quadrotor UAVs, IEEE Trans. Syst. Man Cybern. Syst., 52, 8, 4836-4848 (2021) |
| [38] | Hua, M.; Ding, H.; Yao, X.-Y.; Zhang, X., Distributed fixed-time formation-containment control for multiple Euler-Lagrange systems with directed graphs, Int. J. Control Autom. Syst., 19, 2, 837-849 (2021) |
| [39] | Chen, L.-M.; Li, C.-J.; Mei, J.; Ma, G. F., Adaptive cooperative formation-containment control for networked Euler-Lagrange systems without using relative velocity information, IET Contr. Theory Appl., 11, 9, 1450-1458 (2017) |
| [40] | Liang, C.-D.; Ge, M.-F.; Liu, Z.-W.; Ling, G.; Zhao, X. W., A novel sliding surface design for predefined-time stabilization of Euler-Lagrange systems, Nonlinear Dyn., 106, 1, 445-458 (2021) |
| [41] | Li, C.; Chen, L.; Guo, Y.; Ma, G., Formation-containment control for networked Euler-Lagrange systems with input saturation, Nonlinear Dyn., 91, 2, 1307-1320 (2018) · Zbl 1390.34074 |
| [42] | Munoz-Vazquez, A. J.; Sanchez-Torres, J. D.; Rodriguez, E. J.; Loukianov, A., Predefined-time robust stabilization of robotic manipulators, IEEE/ASME Trans. Mechatron., 24, 3, 1033-1040 (2019) |
| [43] | Liao, R.; Han, L.; Dong, X.; Li, Q.; Ren, Z., Finite-time formation-containment tracking for second-order multi-agent systems with a virtual leader of fully unknown input, Neurocomputing, 415, 234-246 (2020) |
| [44] | Li, D.; Zhang, W.; He, W.; Li, C.; Ge, S. S., Two-layer distributed formation-containment control of multiple Euler-Lagrange systems by output feedback, IEEE Trans. Cybern., 49, 2, 675-687 (2018) |
| [45] | Wang, Y.-W.; Zeng, Z.-H.; Liu, X.-K.; Liu, Z. W., Input-to-state stability of switched linear systems with unstabilizable modes under dos attacks, Automatica, 146, 110607 (2022) · Zbl 1504.93324 |
| [46] | Tian, Y.; Yan, H.; Zhang, H.; Zhan, X.; Peng, Y., Resilient static output feedback control of linear semi-Markov jump systems with incomplete semi-Markov kernel, IEEE Trans. Autom. Control, 66, 9, 4274-4281 (2021) · Zbl 1471.93104 |
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