Event-Triggered H∞ Control for Continuous-Time Nonlinear System via Concurrent Learning

IEEE Transactions on Systems, Man, and Cybernetics: Systems

Volumn 47, Issue 7, 2017, Pages 1071-1081

  Zhang, Qichao ^a   Zhao, Dongbin ^a   Zhu, Yuanheng ^a  

^a INSTITUTE OF AUTOMATION   (China)

Author keywords

Concurrent learning; event triggered control; H optimal control; neural networks (NNs); zero sum (ZS) game

Indexed keywords

CONTINUOUS TIME SYSTEMS; CONTROLLERS; EDUCATION; LEARNING ALGORITHMS; NONLINEAR SYSTEMS; OPTIMAL CONTROL SYSTEMS;

CONCURRENT LEARNING; EVENT-TRIGGERED CONTROLS; NEURAL NETWORKS (NNS); OPTIMAL CONTROLS; ZERO SUMS;

CONCURRENCY CONTROL;

EID: 85021653031     PISSN: 21682216     EISSN: 21682232     Source Type: Journal    
DOI: 10.1109/TSMC.2016.2531680     Document Type: Article

References (47)

1. S. P. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA, USA: SIAM, 1994.
2. S. Hussain, S. Q. Xie, and P. K. Jamwal, "Robust nonlinear control of an intrinsically compliant robotic gait training orthosis," IEEE Trans. Syst., Man, Cybern., Syst., vol. 43, no. 3, pp. 655-665, May 2013.
3. K. Zhou and J. C. Doyle, Essentials of Robust Control. Upper Saddle River, NJ, USA: Prentice Hall, 1998.
4. A. J. van der Schaft, "L2-gain analysis of nonlinear systems and nonlinear state-feedback H∞ control," IEEE Trans. Autom. Control, vol. 37, no. 6, pp. 770-784, Jun. 1992.
5. M. R. James and J. S. Baras, "Robust H∞ output feedback control for nonlinear systems," IEEE Trans. Autom. Control, vol. 40, no. 6, pp. 1007-1017, Jun. 1995.
6. T. Başar and P. Bernhard, H∞ Optimal Control and Related Minimax Design Problems: A Dynamic Game Approach. Boston, MA, USA: Birkhäuser, 1995.
7. T. Başar and G. J. Olsder, Dynamic Noncooperative Game Theory. Philadelphia, PA, USA: SIAM, 1995.
8. D. Zhao and Y. Zhu, "MEC - A near-optimal online reinforcement learning algorithm for continuous deterministic systems," IEEE Trans. Neural Netw. Learn. Syst., vol. 26, no. 2, pp. 346-356, Feb. 2015.
9. D. P. Bertsekas, M. L. Homer, D. A. Logan, S. D. Patek, and N. R. Sandell, "Missile defense and interceptor allocation by neurodynamic programming," IEEE Trans. Syst., Man, Cybern. A, Syst., Humans, vol. 30, no. 1, pp. 42-51, Jan. 2000.
10. D. Liu, H. Li, and D. Wang, "Online synchronous approximate optimal learning algorithm for multi-player non-zero-sum games with unknown dynamics," IEEE Trans. Syst., Man, Cybern., Syst., vol. 44, no. 8, pp. 1015-1027, Aug. 2014.
11. D. Zhao, Z. Xia, and D. Wang, "Model-free optimal control for affine nonlinear systems with convergence analysis," IEEE Trans. Autom. Sci. Eng., vol. 12, no. 4, pp. 1461-1468, Oct. 2015.
12. Y. Zhu and D. Zhao, "A data-based online reinforcement learning algorithm satisfying probably approximately correct principle," Neural Comput. Appl., vol. 26, no. 4, pp. 775-787, 2015.
13. D. Zhao, X. Bai, F.-Y. Wang, J. Xu, and W. Yu, "DHP method for ramp metering of freeway traffic," IEEE Trans. Intell. Transp. Syst., vol. 12, no. 4, pp. 990-999, Dec. 2011.
14. B. Wang, D. Zhao, A. Cesare, and D. Liu, "Dual heuristic dynamic programming for nonlinear discrete-time uncertain systems with state delay," Neurocomputing, vol. 134, pp. 222-229, Jun. 2014.
15. A. Al-Tamimi, M. Abu-Khalaf, and F. L. Lewis, "Adaptive critic designs for discrete-time zero-sum games with application to H∞ control," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 37, no. 1, pp. 240-247, Feb. 2007.
16. A. Al-Tamimi, F. L. Lewis, and M. Abu-Khalaf, "Model-free Q-learning designs for linear discrete-time zero-sum games with application to H-infinity control," Automatica, vol. 43, no. 3, pp. 473-481, 2007.
17. Q.-L. Wei, H.-G. Zhang, and L.-L. Cui, "Data-based optimal control for discrete-time zero-sum games of 2-D systems using adaptive critic designs," Acta Autom. Sinica, vol. 35, no. 6, pp. 682-692, 2009.
18. D. Liu, H. Li, and D. Wang, "Neural-network-based zero-sum game for discrete-time nonlinear systems via iterative adaptive dynamic programming algorithm," Neurocomputing, vol. 110, pp. 92-100, Jun. 2013.
19. H. Zhang, C. Qin, B. Jiang, and Y. Luo, "Online adaptive policy learning algorithm for H∞ state feedback control of unknown affine nonlinear discrete-time systems," IEEE Trans. Cybern., vol. 44, no. 12, pp. 2706-2718, Dec. 2014.
20. S. Mehraeen, T. Dierks, S. Jagannathan, and M. L. Crow, "Zero-sum two-player game theoretic formulation of affine nonlinear discrete-time systems using neural networks," in Proc. Int. Joint Conf. Neural Netw. (IJCNN), Barcelona, Spain, 2010, pp. 1-8.
21. M. Abu-Khalaf, F. L. Lewis, and J. Huang, "Policy iterations on the Hamilton-Jacobi-Isaacs equation for H∞ state feedback control with input saturation," IEEE Trans. Autom. Control, vol. 51, no. 12, pp. 1989-1995, Dec. 2006.
22. M. Abu-Khalaf, F. L. Lewis, and J. Huang, "Neurodynamic programming and zero-sum games for constrained control systems," IEEE Trans. Neural Netw., vol. 19, no. 7, pp. 1243-1252, Jul. 2008.
23. D. Vrabie and F. Lewis, "Adaptive dynamic programming for online solution of a zero-sum differential game," J. Control Theory Appl., vol. 9, no. 3, pp. 353-360, 2011.
24. H. Li, D. Liu, and D. Wang, "Integral reinforcement learning for linear continuous-time zero-sum games with completely unknown dynamics," IEEE Trans. Autom. Sci. Eng., vol. 11, no. 3, pp. 706-714, Jul. 2014.
25. K. G. Vamvoudakis and F. L. Lewis, "Online solution of nonlinear two-player zero-sum games using synchronous policy iteration," Int. J. Robust Nonlin. Control, vol. 22, no. 13, pp. 1460-1483, 2012.
26. H. Modares, F. L. Lewis, and M. B. N. Sistani, "Online solution of nonquadratic two-player zero-sum games arising in the H∞ control of constrained input systems," Int. J. Adapt. Control Signal Process., vol. 28, nos. 3-5, pp. 232-254, 2014.
27. H. Zhang, Q. Wei, and D. Liu, "An iterative adaptive dynamic programming method for solving a class of nonlinear zero-sum differential games," Automatica, vol. 47, no. 1, pp. 207-214, 2011.
28. H.-N.Wu and B. Luo, "Neural network based online simultaneous policy update algorithm for solving the HJI equation in nonlinear H∞ control," IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 12, pp. 1884-1895, Dec. 2012.
29. W. P. M. H. Heemels, M. C. F. Donkers, and A. R. Teel, "Periodic event-triggered control for linear systems," IEEE Trans. Autom. Control, vol. 58, no. 4, pp. 847-861, Apr. 2013.
30. Q. Liu, Z. Wang, X. He, and D. H. Zhou, "Event-based distributed filtering with stochastic measurement fading," IEEE Trans. Ind. Informat., vol. 11, no. 6, pp. 1643-1652, Dec. 2015, doi: 10.1109/TII.2015.2444355.
31. H. Dong, Z. Wang, S. X. Ding, and H. Gao, "On H∞ estimation of randomly occurring faults for a class of nonlinear time-varying systems with fading channels," IEEE Trans. Autom. Control, vol. 61, no. 2, pp. 479-484, Feb. 2016, doi: 10.1109/TAC.2015.2437526.
32. K. G. Vamvoudakis, "Event-triggered optimal adaptive control algorithm for continuous-time nonlinear systems," IEEE/CAA J. Autom. Sinica, vol. 1, no. 3, pp. 282-293, Jul. 2014.
33. X. Zhong, Z. Ni, H. He, X. Xu, and D. Zhao, "Event-triggered reinforcement learning approach for unknown nonlinear continuous-time system," in Proc. Int. Joint Conf. Neural Netw. (IJCNN), Beijing, China, 2014, pp. 3677-3684.
34. A. Sahoo, H. Xu, and S. Jagannathan, "Neural network-based eventtriggered state feedback control of nonlinear continuous-time systems," IEEE Trans. Neural Netw. Learn. Syst., vol. 27, no. 3, pp. 497-509, Mar. 2016, doi: 10.1109/TNNLS.2015.2416259.
35. A. Sahoo, H. Xu, and S. Jagannathan, "Near optimal event-triggered control of nonlinear discrete-time systems using neurodynamic programming," IEEE Trans. Neural Netw. Learn. Syst., vol. 29, no. 9, pp. 1801-1815, Aug. 2015, doi: 10.1109/TNNLS.2015.2453320.
36. G. Chowdhary and E. Johnson, "Concurrent learning for convergence in adaptive control without persistency of excitation," in Proc. IEEE Conf. Decis. Control (CDC), Atlanta, GA, USA, 2010, pp. 3674-3679.
37. P. A. Ioannou and B. Fidan, Adaptive Control Tutorial (Advances in Design and Control). Philadelphia, PA, USA: SIAM, 2006.
38. H. Modares, F. L. Lewis, and M.-B. Naghibi-Sistani, "Adaptive optimal control of unknown constrained-input systems using policy iteration and neural networks," IEEE Trans. Neural Netw. Learn. Syst., vol. 24, no. 10, pp. 1513-1525, Oct. 2013.
39. H. Modares, F. L. Lewis, and M.-B. Naghibi-Sistani, "Integral reinforcement learning and experience replay for adaptive optimal control of partially-unknown constrained-input continuous-time systems," Automatica, vol. 50, no. 1, pp. 193-202, 2014.
40. S. Yasini, A. Karimpour, M.-B. Naghibi-Sistani, and H. Modares, "Online concurrent reinforcement learning algorithm to solve twoplayer zero-sum games for partially unknown nonlinear continuous-time systems," Int. J. Adapt. Control Signal Process., vol. 29, no. 4, pp. 473-493, 2015.
41. S. Yasini, M. B. N. Sistani, and A. Kirampor, "Reinforcement learning and neural networks for multi-agent nonzero-sum games of nonlinear constrained-input systems," Int. J. Mach. Learn. Cybern., pp. 1-14, Oct. 2014, doi: 10.1007/s13042-014-0300-y.
42. S. Yasini, M. B. N. Sistani, and A. Karimpour, "Approximate dynamic programming for two-player zero-sum game related to H∞ control of unknown nonlinear continuous-time systems," Int. J. Control Autom. Syst., vol. 13, no. 1, pp. 99-109, 2015.
43. R. Kamalapurkar, J. R. Klotz, and W. E. Dixon, "Concurrent learningbased approximate feedback-Nash equilibrium solution of N-player nonzero-sum differential games," IEEE/CAA J. Autom. Sinica, vol. 1, no. 3, pp. 239-247, Jul. 2014.
44. X. Yang, D. Liu, and Q. Wei, "Online approximate optimal control for affine non-linear systems with unknown internal dynamics using adaptive dynamic programming," IET Control Theory Appl., vol. 8, no. 16, pp. 1676-1688, Nov. 2014.
45. H. K. Khalil, Nonlinear Systems. Upper Saddle River, NJ, USA: Prentice Hall, 2002.
46. B. A. Finlayson, The Method of Weighted Residuals and Variational Principles, vol. 73. Philadelphia, PA, USA: SIAM, 2013.
47. H. Zhang, L. Cui, and Y. Luo, "Near-optimal control for nonzerosum differential games of continuous-time nonlinear systems using single-network ADP," IEEE Trans. Cybern., vol. 43, no. 1, pp. 206-216, Feb. 2013.