Adaptive neural funnel control for a class of pure-feedback nonlinear systems with event-trigger strategy. (English) Zbl 1483.93272
Summary: In this paper, an event-trigger-based adaptive funnel control problem is considered for a class of pure-feedback nonlinear systems. Due to the nonaffine variables existed in the virtual controls of pure-feedback systems, the implicit function theorem and mean-value theorem are adopted to guarantee the existence of the ideal virtual controls, which can be effectively approximated by neural networks. Then, a novel event-triggered control strategy is designed to consume less communication resources. The event-triggered condition depends on the amplitudes of the control input, the tracking error and a fixed threshold, which makes the control more flexible in real applications. Furthermore, the proposed control scheme ensures the transient and steady state performance for the tracking errors by constructing a funnel constraint function. Also, the stability analysis proves that all the signals of the closed-loop system are uniformly ultimately bounded. Finally, the feasibility and effectiveness of the proposed control scheme are verified through the simulation.
MSC:
| 93C40 | Adaptive control/observation systems |
| 93C65 | Discrete event control/observation systems |
| 93B52 | Feedback control |
| 93C10 | Nonlinear systems in control theory |
Keywords:
event-triggered control; backstepping; funnel control; neural network; pure-feedback systemsReferences:
| [1] | Benchlioulis, C.; Rovithakis, G., Robust adaptive control of feedback linearizable MIMO nonlinear systems with prescribed performance, IEEE Transactions on Automatic Control, 53, 9, 2090-2099 (2008) · Zbl 1367.93298 |
| [2] | Chen, B.; Liu, X. P.; Tong, S. C., Adaptive fuzzy output tracking control of MIMO nonlinear uncertain systems, IEEE Transactions on Fuzzy Systems, 15, 2, 287-300 (2007) |
| [3] | Choi, Y. H.; Yoo, S. J., Event-triggered output-feedback tracking of a class of nonlinear systems with unknown time delays, Nonlinear Dynamics, 96, 2, 959-973 (2019) · Zbl 1437.93035 |
| [4] | Ge, S. S.; Wang, C., Adaptive NN control of uncertain nonlinear pure-feedback systems (2002), Pergamon Press · Zbl 0998.93025 |
| [5] | Han, S. I.; Lee, J. M., Improved prescribed performance constraint control for a strict feedback non-linear dynamic system, IET Control Theory & Applications, 7, 14, 1818-1827 (2013) |
| [6] | Han, S. I.; Lee, J. M., Fuzzy echo state neural networks and funnel dynamic surface control for prescribed performance of a nonlinear dynamic system, IEEE Transactions on Industrial Electronics, 61, 2, 1099-1112 (2014) |
| [7] | Ilchman, A.; Ryan, E. P.; Sangwin, C. J., Tracking with prescribed transient behaviour, ESAIM: Control, Optimisation and Calculus of Variations, 7, 471-493 (2002) · Zbl 1044.93022 |
| [8] | Ilchman, A.; Ryan, E. P.; Townsend, P., Tracking control with prescribed transient behaviour for systems of known relative degree, Systems & Control Letters, 55, 5, 396-406 (2006) · Zbl 1129.93502 |
| [9] | Johansson, K. H.; Egerstedt, M.; Lygeros, J.; Sastry, S., On the regularization of Zeno hybrid automata, Systems & Control Letters, 38, 3, 141-150 (1999) · Zbl 0948.93031 |
| [10] | Kristic, M.; Kanellakopoulos, I.; Kokotovic, P. V., Nonlinear and adaptive control design (1995), Wiley |
| [11] | Li, T. S.; Wang, D.; Feng, G.; Tong, S. C., A DSC approach to robust adaptive NN tracking control for strict-feedback nonlinear systems, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 40, 3, 915-927 (2010) |
| [12] | Li, Y. M.; Sui, S.; Tong, S. C., Adaptive fuzzy control design for stochastic nonlinear switched systems with arbitrary switchings and unmodeled dynamics, IEEE Transactions on Cybernetics, 47, 2, 403-414 (2017) |
| [13] | Liang, H. J.; Guo, X. Y.; Pan, Y. N.; Huang, T. W., Event-triggered fuzzy bipartite tracking control for network systems based on distributed reduced-order observers, IEEE Transactions on Fuzzy Systems (2020) |
| [14] | Liu, Z. C.; Dong, X. M.; Xue, J. P.; Li, H. B.; Chen, Y., Adaptive neural control for a class of pure-feedback nonlinear systems via dynamic surface technique, IEEE Transactions on Neural Networks and Learning Systems, 27, 9, 1969-1975 (2016) |
| [15] | Liu, X. P.; Wang, H. Q.; Gao, C.; Chen, M., Adaptive fuzzy funnel control for a class of strict feedback nonlinear systems, Neurocomputing, 241, 71-80 (2017) |
| [16] | Liu, Y. R.; Wang, Z. D.; Yuan, Y.; Liu, W. B., Event-triggered partial-nodes-based state estimation for delayed complex networks with bounded distributed delays, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 49, 6, 1088-1098 (2019) · doi:10.1109/TSMC.2017.2720121 |
| [17] | Pan, Y. N.; Du, P. G.; Xue, H.; Lam, H. K., Singularity-free fixed-time fuzzy control for robotic systems with user-defined performance, IEEE Transactions on Fuzzy Systems (2020) |
| [18] | Ploycarpou, M. M.; Ioannou, P. A., A robust adaptive nonlinear control design, Automatica, 32, 3, 423-427 (1996) · Zbl 0847.93031 |
| [19] | Postoyan, R.; Tabuada, P.; Nešić, D.; Anta, A., A framework for the event-triggered stabilization of nonlinear systems, IEEE Transactions on Automatic Control, 60, 4, 982-996 (2015) · Zbl 1360.93567 |
| [20] | Qiu, J.; Sun, K.; Rudas, I. J.; Gao, H., Command filter-based adaptive NN control for MIMO nonlinear systems with full state constraints and actuator hysteresis, IEEE Transactions on Cybernetics (2019) |
| [21] | Qiu, J.; Sun, K.; Wang, T.; Gao, H., Observer-based fuzzy adaptive event-triggered control for pure-feedback nonlinear systems with prescribed performance, IEEE Transactions on Fuzzy Systems, 27, 11, 2152-2162 (2019) · doi:10.1109/TFUZZ.2019.2895560 |
| [22] | Ren, B.; Ge, S. S.; Tee, K. P.; Lee, T. H., Adaptive neural control for output feedback nonlinear systems using a barrier Lyapunov function, IEEE Transactions on Neural Networks, 21, 8, 1339-1345 (2010) |
| [23] | Ren, H. R.; Karimi, H. R.; Lu, R. Q.; Wu, Y. Q., Synchronization of network systems via aperiodic sampled-data control with constant delay and application to unmanned ground vehicles, IEEE Transactions on Industrial Electronics), 67, 6, 4980-4990 (2019) · doi:10.1109/TIE.2019.2928241 |
| [24] | Ren, H. R.; Lu, R. Q.; Xiong, J. L.; Wu, Y. Q.; Shi, P., Optimal filtered and smoothed estimators for discrete-time linear systems with multiple packet dropouts under Markovian communication constraints, IEEE Transactions on Cybernetics (2019) |
| [25] | Sahoo, A.; Xu, H.; Jagannathan, S., Neural network-based event-triggered state feedback control of nonlinear continuous-time systems, IEEE Transactions on Neural Networks and Learning Systems, 27, 3, 497-509 (2016) |
| [26] | Tabuada, P., Event-triggered real-time scheduling of stabilizing control tasks, IEEE Transactions on Automatic Control, 52, 9, 1680-1685 (2007) · Zbl 1366.90104 |
| [27] | Tallapragada, P.; Chopra, N., Decentralized event-triggering for control of nonlinear systems, IEEE Transactions on Automatic Control, 59, 12, 3312-3324 (2014) · Zbl 1360.93441 |
| [28] | Tee, K. P.; Ge, S. S.; Tay, E. H., Barrier Lyapunov functions for the control of output-constrained nonlinear systems, Automatica, 45, 4, 918-927 (2009) · Zbl 1162.93346 |
| [29] | Tong, S. C.; Li, Y. M., Robust adaptive fuzzy backstepping output feedback tracking control for nonlinear system with dynamic uncertainties, Science China Information Sciences, 53, 2, 307-324 (2010) · Zbl 1497.93134 |
| [30] | Tong, S. C.; Li, Y. M., Observer-based adaptive fuzzy backstepping control of uncertain nonlinear pure-feedback systems, Science China Information Sciences, 57, 1, 1-14 (2014) · Zbl 1331.93136 |
| [31] | Wang, C.; Hill, D. J.; Ge, S. S.; Chen, G. R., An ISS-modular approach for adaptive neural control of pure-feedback systems, Automatica, 42, 5, 723-731 (2006) · Zbl 1137.93367 |
| [32] | Wang, F.; Liu, Z.; Zhang, Y.; Chen, C. L. P., Adaptive fuzzy control for a class of stochastic pure-feedback nonlinear systems with unknown hysteresis, IEEE Transactions on Fuzzy Systems, 24, 1, 140-152 (2016) |
| [33] | Wang, H. Q.; Bai, W.; Liu, P. X. P., Finite-time adaptive fault-tolerant control for nonlinear systems with multiple faults, IEEE/CAA Journal of Automatica Sinica, 6, 6, 1417-1427 (2019) |
| [34] | Wang, H. Q.; Chen, B.; Lin, C., Adaptive neural tracking control for a class of perturbed pure-feedback nonlinear systems, Nonlinear Dynamics, 72, 1-2, 207-220 (2013) · Zbl 1268.92015 |
| [35] | Wang, H. Q.; Liu, S. W.; Yang, X. B., Adaptive neural control for non-strict-feedback nonlinear systems with input delay, Information Sciences, 514, 605-616 (2020) · Zbl 1461.93408 |
| [36] | Wang, L. C.; Wang, Z. D.; Huang, T. W.; Wei, G. L., An event-triggered approach to state estimation for a class of complex networks with mixed time delays and nonlinearities, IEEE Transactions on Cybernetics, 46, 11, 2497-2508 (2016) |
| [37] | Wang, W.; Liang, H. J.; Pan, Y. N.; Li, T. S., Prescribed performance adaptive fuzzy containment control for nonlinear multiagent systems using disturbance observer, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 49, 6, 1088-1098 (2020) · doi:10.1109/tcyb.2020.2969499 |
| [38] | Xie, X.; Yue, D.; Peng, C., Relaxed real-time scheduling stabilization of discrete-time Takagi-Sugeno fuzzy systems via a alterable-weights-based ranking wwitching mechanism, IEEE Transactions on Fuzzy Systems, 26, 6, 3808-3819 (2018) |
| [39] | Xie, X.; Zhou, Q.; Yue, D.; Li, H. Y., Relaxed control design of discrete-time Takagi-Sugeno fuzzy systems: An event-triggered real-time scheduling approach, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 48, 12, 2251-2262 (2018) |
| [40] | Xing, L. T.; Wen, C. Y.; Liu, Z. T.; Su, H. Y.; Cai, J. P., Adaptive compensation for actuator failures with event-triggered input, Automatica, 85, 129-136 (2017) · Zbl 1375.93084 |
| [41] | Xing, L. T.; Wen, C. Y.; Liu, Z. T.; Su, H. Y.; Cai, J. P., Event-triggered adaptive control for a class of uncertain nonlinear systems, IEEE Transactions on Automatic Control, 62, 4, 2071-2076 (2017) · Zbl 1366.93305 |
| [42] | Zhang, T.; Ge, S. S.; Hang, C. C., Adaptive neural network control for strict-feedback nonlinear systems using backstepping design, Automatica, 36, 12, 1835-1846 (2000) · Zbl 0976.93046 |
| [43] | Zhang, T. P.; Ge, S. S., Adaptive dynamic surface control of nonlinear systems with unknown dead zone in pure feedback form, Automatica, 44, 7, 1895-1903 (2008) · Zbl 1149.93322 |
| [44] | Zhao, S.; Liang, H.; Du, P.; Qi, S., Adaptive NN finite-time tracking control of output constrained nonlinear system with input saturation, Nonlinear Dynamics, 92, 4, 1845-1856 (2018) · Zbl 1398.93178 |
| [45] | Zhu, Z. C.; Pan, Y. N.; Zhou, Q.; Lu, C. X., Event-triggered adaptive fuzzy control for stochastic nonlinear systems with unmeasured states and unknown backlash-like hysteresis, IEEE Transactions on Fuzzy Systems (2020) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
