Event-triggered \(H_\infty\) consensus for uncertain nonlinear systems using integral sliding mode based adaptive dynamic programming. (English) Zbl 1525.93239
Summary: This paper studies a robust optimal consensus problem for uncertain nonlinear multi-agent systems, where the uncertainties include both input and external disturbances. Adaptive distributed observer, integral sliding mode control and \(H_\infty\) adaptive dynamic programming are integrated to obtain a sub-optimal control protocol for each follower. Firstly, an adaptive distributed observer is designed for state estimation of the leader, which serves as the reference of the ADP algorithm. Then, an \(H_\infty\) ADP algorithm is presented to make each follower track the reference in real-time. An integral sliding manifold-based discontinuous control is designed to eliminate the matched uncertainty, and continuous control is obtained by solving the Hamilton-Jacobi-Isaac equation under the \(H_\infty\) tracking framework. Two event-triggered rules are developed to relieve the communication pressure. For simplicity, a critic-only structure is used to numerically implement the proposed algorithm, and a concurrent learning technique is employed to update weights of neural networks. All signals in the closed-loop system are proven to be uniformly ultimately bounded. Finally, a simulation is conducted to demonstrate demonstrates the effectiveness of the method.
MSC:
| 93C65 | Discrete event control/observation systems |
| 93B36 | \(H^\infty\)-control |
| 93D50 | Consensus |
| 93A16 | Multi-agent systems |
| 93C41 | Control/observation systems with incomplete information |
| 93C10 | Nonlinear systems in control theory |
| 93B12 | Variable structure systems |
| 93C40 | Adaptive control/observation systems |
| 90C39 | Dynamic programming |
Keywords:
multi-agent systems; adaptive dynamic programming; event-triggered control; \(H_\infty\) control; concurrent learningReferences:
| [1] | Abouheaf, M. I.; Lewis, F. L.; Vamvoudakis, K. G.; Haesaert, S.; Babuska, R., Multi-agent discrete-time graphical games and reinforcement learning solutions, Automatica, 50, 12, 3038-3053 (2014) · Zbl 1367.91032 |
| [2] | Bidram, A.; Davoudi, A.; Lewis, F. L.; Guerrero, J. M., Distributed cooperative secondary control of microgrids using feedback linearization, IEEE Transactions on Power Systems, 28, 3, 3462-3470 (2013) |
| [3] | Cai, H.; Huang, J., Output based adaptive distributed output observer for leader-follower multiagent systems, Automatica, 125, Article 109413 pp. (2021) · Zbl 1461.93247 |
| [4] | Cai, H.; Su, Y.; Huang, J., Cooperative control of multi-agent systems: Distributed-observer and distributed-internal-model approaches (2022), Springer Nature · Zbl 1503.93002 |
| [5] | Chen, Z.; Chen, S.-Z.; Chen, K.; Zhang, Y., Constrained decoupling adaptive dynamic programming for a partially uncontrollable time-delayed model of energy systems, Information Sciences, 608, 1352-1374 (2022) · Zbl 1542.90244 |
| [6] | Chen, Z., Chen, S.-Z., Zhang, Y., Deng, Q., & Zeng, X. (0000). Online and hard constrained adaptive dynamic programming algorithm for energy storage control in smart buildings. Optimal Control Applications and Methods. · Zbl 1531.93201 |
| [7] | Chen, C.; Lewis, F. L.; Li, X., Event-triggered coordination of multi-agent systems via a Lyapunov-based approach for leaderless consensus, Automatica, 136, Article 109936 pp. (2022) · Zbl 1480.93260 |
| [8] | Chen, W.; Li, T., Distributed economic dispatch for energy internet based on multiagent consensus control, IEEE Transactions on Automatic Control, 66, 1, 137-152 (2021) · Zbl 1536.93789 |
| [9] | Chen, K.; Wang, J.; Zhao, Z.; Lai, G.; Lyu, Y., Output consensus of heterogeneous multiagent systems: A distributed observer-based approach, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 52, 1, 370-376 (2022) |
| [10] | Dong, L.; Zhong, X.; Sun, C.; He, H., Adaptive event-triggered control based on heuristic dynamic programming for nonlinear discrete-time systems, IEEE Transactions on Neural Networks and Learning Systems, 28, 7, 1594-1605 (2017) |
| [11] | Dong, L.; Zhong, X.; Sun, C.; He, H., Event-triggered adaptive dynamic programming for continuous-time systems with control constraints, IEEE Transactions on Neural Networks and Learning Systems, 28, 8, 1941-1952 (2017) |
| [12] | Fu, H.; Chen, X.; Wang, W.; Wu, M., Observer-based adaptive synchronization control of unknown discrete-time nonlinear heterogeneous systems, IEEE Transactions on Neural Networks and Learning Systems, 33, 2, 681-693 (2022) |
| [13] | Jiang, Y.; Fan, J.; Gao, W.; Chai, T.; Lewis, F. L., Cooperative adaptive optimal output regulation of nonlinear discrete-time multi-agent systems, Automatica, 121, Article 109149 pp. (2020) · Zbl 1448.93159 |
| [14] | Jiang, H.; Gibson, N., Semismooth Newton methods with a shooting-like technique for solving a constrained free-boundary HJB equation, Journal of Computational and Applied Mathematics, 391, Article 113428 pp. (2021) · Zbl 1459.91160 |
| [15] | Jiao, Q.; Modares, H.; Xu, S.; Lewis, F. L.; Vamvoudakis, K. G., Multi-agent zero-sum differential graphical games for disturbance rejection in distributed control, Automatica, 69, 24-34 (2016) · Zbl 1338.93023 |
| [16] | Lewis, F.; Jagannathan, S.; Yesildirak, A., Neural network control of robot manipulators and non-linear systems (2020), CRC Press |
| [17] | Lewis, F. L.; Vrabie, D., Reinforcement learning and adaptive dynamic programming for feedback control, IEEE Circuits and Systems Magazine, 9, 3, 32-50 (2009) |
| [18] | Lewis, F. L.; Vrabie, D.; Vamvoudakis, K. G., Reinforcement learning and feedback control: Using natural decision methods to design optimal adaptive controllers, IEEE Control Systems Magazine, 32, 6, 76-105 (2012) · Zbl 1395.93584 |
| [19] | Li, S.; Durdevic, P.; Yang, Z., Trajectory tracking of underactuated VTOL aerial vehicles with unknown system parameters via IRL, IEEE Transactions on Automatic Control, 67, 6, 3043-3050 (2022) · Zbl 1537.93364 |
| [20] | Liu, M.; Wan, Y.; Lopez, V. G.; Lewis, F. L.; Hewer, G. A.; Estabridis, K., Differential graphical game with distributed global Nash solution, IEEE Transactions on Control of Network Systems, 8, 3, 1371-1382 (2021) |
| [21] | Liu, D.; Xue, S.; Zhao, B.; Luo, B.; Wei, Q., Adaptive dynamic programming for control: A survey and recent advances, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 51, 1, 142-160 (2021) |
| [22] | Lopez, V. G.; Lewis, F. L.; Wan, Y.; Liu, M.; Hewer, G.; Estabridis, K., Stability and robustness analysis of minmax solutions for differential graphical games, Automatica, 121, Article 109177 pp. (2020) · Zbl 1448.91048 |
| [23] | Lu, K.; Liu, Z.; Wang, Y.; Chen, C. L.P.; Zhang, Y., Adaptive neural design of consensus controllers for nonlinear multiagent systems under switching topologies, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 1-12 (2022) |
| [24] | Luo, B.; Wu, H.-N.; Huang, T.; Liu, D., Reinforcement learning solution for HJB equation arising in constrained optimal control problem, Neural Networks, 71, 150-158 (2015) · Zbl 1397.49044 |
| [25] | Modares, H.; Lewis, F. L.; Jiang, Z.-P., \(H{}_\infty\) tracking control of completely unknown continuous-time systems via off-policy reinforcement learning, IEEE Transactions on Neural Networks and Learning Systems, 26, 10, 2550-2562 (2015) |
| [26] | Qian, Y.-Y.; Liu, M.; Wan, Y.; Lewis, F. L.; Davoudi, A., Distributed adaptive Nash equilibrium solution for differential graphical games, IEEE Transactions on Cybernetics, 1-13 (2021) |
| [27] | Sharifi, E.; Damaren, C. J., A numerical approach to hybrid nonlinear optimal control, International Journal of Control, 94, 12, 3349-3362 (2021) · Zbl 1478.93301 |
| [28] | Shi, J.; Yue, D.; Xie, X., Optimal leader-follower consensus for constrained-input multiagent systems with completely unknown dynamics, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 52, 2, 1182-1191 (2022) |
| [29] | Tabuada, P., Event-triggered real-time scheduling of stabilizing control tasks, IEEE Transactions on Automatic Control, 52, 9, 1680-1685 (2007) · Zbl 1366.90104 |
| [30] | Tan, L. N., Event-triggered distributed \(H{}_\infty\) constrained control of physically interconnected large-scale partially unknown strict-feedback systems, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 51, 4, 2444-2456 (2021) |
| [31] | Utkin, V., & Shi, J. (1996). Integral sliding mode in systems operating under uncertainty conditions. In Proceedings of 35th IEEE conference on decision and control, vol. 4 (pp. 4591-4596). |
| [32] | Vamvoudakis, K. G.; Ferraz, H., Model-free event-triggered control algorithm for continuous-time linear systems with optimal performance, Automatica, 87, 412-420 (2018) · Zbl 1378.93083 |
| [33] | Vamvoudakis, K. G.; Lewis, F. L.; Hudas, G. R., Multi-agent differential graphical games: Online adaptive learning solution for synchronization with optimality, Automatica, 48, 8, 1598-1611 (2012) · Zbl 1267.93190 |
| [34] | Wang, J.; Gong, Q.; Huang, K.; Liu, Z.; Chen, C. L.P.; Liu, J., Event-triggered prescribed settling time consensus compensation control for a class of uncertain nonlinear systems with actuator failures, IEEE Transactions on Neural Networks and Learning Systems, 1-11 (2021) |
| [35] | Wang, D.; He, H.; Liu, D., Improving the critic learning for event-based nonlinear \(H{}_\infty\) control design, IEEE Transactions on Cybernetics, 47, 10, 3417-3428 (2017) |
| [36] | Wang, H.; Li, M., Model-free reinforcement learning for fully cooperative consensus problem of nonlinear multiagent systems, IEEE Transactions on Neural Networks and Learning Systems, 33, 4, 1482-1491 (2022) |
| [37] | Wang, D.; Mu, C.; Liu, D.; Ma, H., On mixed data and event driven design for adaptive-critic-based nonlinear \(H{}_\infty\) control, IEEE Transactions on Neural Networks and Learning Systems, 29, 4, 993-1005 (2018) |
| [38] | Wang, D.; Mu, C.; Zhang, Q.; Liu, D., Event-based input-constrained nonlinear \(H{}_\infty\) state feedback with adaptive critic and neural implementation, Neurocomputing, 214, 848-856 (2016) |
| [39] | Wang, Z.; Xu, Y.; Lu, R.; Peng, H., Finite-time state estimation for coupled Markovian neural networks with sensor nonlinearities, IEEE Transactions on Neural Networks and Learning Systems, 28, 3, 630-638 (2017) |
| [40] | Xue, S.; Luo, B.; Liu, D., Event-triggered adaptive dynamic programming for zero-sum game of partially unknown continuous-time nonlinear systems, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 50, 9, 3189-3199 (2020) |
| [41] | Yang, H.; Han, Q.-L.; Ge, X.; Ding, L.; Xu, Y.; Jiang, B., Fault-tolerant cooperative control of multiagent systems: A survey of trends and methodologies, IEEE Transactions on Industrial Informatics, 16, 1, 4-17 (2020) |
| [42] | Yang, D.; Li, T.; Xie, X.; Zhang, H., Event-triggered integral sliding-mode control for nonlinear constrained-input systems with disturbances via adaptive dynamic programming, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 50, 11, 4086-4096 (2020) |
| [43] | Yang, D.; Li, T.; Zhang, H.; Xie, X., Event-trigger-based robust control for nonlinear constrained-input systems using reinforcement learning method, Neurocomputing, 340, 158-170 (2019) |
| [44] | Yang, Y.; Modares, H.; Vamvoudakis, K. G.; Yin, Y.; Wunsch, D. C., Dynamic intermittent feedback design for \(H{}_\infty\) containment control on a directed graph, IEEE Transactions on Cybernetics, 50, 8, 3752-3765 (2020) |
| [45] | Yao, Z.; Yao, J., Toward reliable designs of data-driven reinforcement learning tracking control for Euler-Lagrange systems, Neural Networks, 153, 564-575 (2022) · Zbl 1522.93078 |
| [46] | Yu, T.; Liu, J.; Zeng, Q.; Wu, L., Dissipativity-based filtering for switched genetic regulatory networks with stochastic disturbances and time-varying delays, IEEE/ACM Transactions on Computational Biology and Bioinformatics, 18, 3, 1082-1092 (2021) |
| [47] | Zhang, J.; Zhang, H.; Feng, T., Distributed optimal consensus control for nonlinear multiagent system with unknown dynamic, IEEE Transactions on Neural Networks and Learning Systems, 29, 8, 3339-3348 (2018) |
| [48] | Zhang, H.; Zhang, J.; Yang, G.-H.; Luo, Y., Leader-based optimal coordination control for the consensus problem of multiagent differential games via fuzzy adaptive dynamic programming, IEEE Transactions on Fuzzy Systems, 23, 1, 152-163 (2015) |
| [49] | Zhang, S.; Zhao, B.; Liu, D.; Zhang, Y., Observer-based event-triggered control for zero-sum games of input constrained multi-player nonlinear systems, Neural Networks, 144, 101-112 (2021) · Zbl 1526.93166 |
| [50] | Zhang, Y.; Zhao, B.; Liu, D.; Zhang, S., Event-triggered control of discrete-time zero-sum games via deterministic policy gradient adaptive dynamic programming, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 52, 8, 4823-4835 (2022) |
| [51] | Zhang, Q.; Zhao, D.; Zhu, Y., Event-triggered \(H{}_\infty\) control for continuous-time nonlinear system via concurrent learning, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 47, 7, 1071-1081 (2017) |
| [52] | Zhao, J.; Gan, M.; Zhang, C., Event-triggered \(H{}_\infty\) optimal control for continuous-time nonlinear systems using neurodynamic programming, Neurocomputing, 360, 14-24 (2019) |
| [53] | Zhao, W.; Liu, H.; Lewis, F. L., Data-driven fault-tolerant control for attitude synchronization of nonlinear quadrotors, IEEE Transactions on Automatic Control, 66, 11, 5584-5591 (2021) · Zbl 1536.93193 |
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.
