Neural-Network-Based Control for Discrete-Time Nonlinear Systems with Input Saturation Under Stochastic Communication Protocol

Xueli Wang; Derui Ding; Hongli Dong; Xian-Ming Zhang

doi:10.1109/JAS.2021.1003922

Volume 8 Issue 4

Apr. 2021

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2021 > 8(4): 766-778

Xueli Wang, Derui Ding, Hongli Dong, and Xian-Ming Zhang, "Neural-Network-Based Control for Discrete-Time Nonlinear Systems with Input Saturation Under Stochastic Communication Protocol," IEEE/CAA J. Autom. Sinica, vol. 8, no. 4, pp. 766-778, Apr. 2021. doi: 10.1109/JAS.2021.1003922

Citation:

Xueli Wang, Derui Ding, Hongli Dong, and Xian-Ming Zhang, "Neural-Network-Based Control for Discrete-Time Nonlinear Systems with Input Saturation Under Stochastic Communication Protocol," IEEE/CAA J. Autom. Sinica, vol. 8, no. 4, pp. 766-778, Apr. 2021. doi: 10.1109/JAS.2021.1003922

Citation:

Xueli Wang, Derui Ding, Hongli Dong, and Xian-Ming Zhang, "Neural-Network-Based Control for Discrete-Time Nonlinear Systems with Input Saturation Under Stochastic Communication Protocol," IEEE/CAA J. Autom. Sinica, vol. 8, no. 4, pp. 766-778, Apr. 2021. doi: 10.1109/JAS.2021.1003922

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Neural-Network-Based Control for Discrete-Time Nonlinear Systems with Input Saturation Under Stochastic Communication Protocol

doi: 10.1109/JAS.2021.1003922

1.
Department of Control Science and Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
2.
School of Software and Electrical Engineering, Swinburne University of Technology, Melbourne 3122, Victoria, Australia
3.
Institute of Complex Systems and Advanced Control, Northeast Petroleum University, Daqing 163318, China

Funds: This work was supported in part by the Australian Research Council Discovery Early Career Researcher Award (DE200101128), and Australian Research Council (DP190101557)

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Author Bio:
Xueli Wang received the B.Sc. degree from Qufu Normal University, Qufu, China, in 2013. She is currently a Ph.D. candidate in control science and engineering at University of Shanghai for Science and Technology, Shanghai, China. Her current research interests include networked control systems, adaptive dynamic program, and neural networks. She is a very active reviewer for many international journals

Derui Ding (M’16–SM’20) received both the B.Sc. degree in industry engineering in 2004 and the M.Sc. degree in detection technology and automation equipment in 2007 from Anhui Polytechnic University, Wuhu, China, and the Ph.D. degree in control theory and control engineering in 2014 from Donghua University, Shanghai, China. From July 2007 to December 2014, he was a Teaching Assistant and then a Lecturer in the Department of Mathematics, Anhui Polytechnic University, Wuhu, China. He is currently a Senior Research Fellow with the School of Software and Electrical Engineering, Swinburne University of Technology, Melbourne, Australia. From June 2012 to September 2012, he was a Research Assistant in the Department of Mechanical Engineering, the University of Hong Kong, Hong Kong. From March 2013 to March 2014, he was a Visiting Scholar in the Department of Information Systems and Computing, Brunel University London, UK. His research interests include nonlinear stochastic control and filtering, as well as multi-agent systems and sensor networks. He has published around 80 papers in refereed international journals. He is serving as an Associate Editor for Neurocomputing and IET Control Theory & Applications. He is also a very active reviewer for many international journals

Hongli Dong (SM’16) received the Ph.D. degree in control science and engineering from the Harbin Institute of Technology, Harbin, China, in 2012. From 2009 to 2010, she was a Research Assistant with the Department of Applied Mathematics, City University of Hong Kong, Hong Kong, China. From 2010 to 2011, she was a Research Assistant with the Department of Mechanical Engineering, The University of Hong Kong, Hong Kong, China. From 2011 to 2012, she was a Visiting Scholar with the Department of Information Systems and Computing, Brunel University London, London, UK. From 2012 to 2014, she was an Alexander von Humboldt Research Fellow with the University of DuisburgEssen, Duisburg, Germany. She is currently a Professor with the Institute of Complex Systems and Advanced Control, Northeast Petroleum University, Daqing, China. She is also the Director with the Heilongjiang Provincial Key Laboratory of Networking and Intelligent Control, China. Her current research interests include robust control and networked control systems

Xian-Ming Zhang (M’16–SM’18) received the M.Sc. degree in applied mathematics and the Ph.D. degree in control theory and engineering from Central South University, Changsha, China, in 1992 and 2006, respectively. In 1992, he joined Central South University, where he was an Associate Professor with the School of Mathematics and Statistics. From 2007 to 2014, he was a Postdoctoral Research Fellow and a Lecturer with the School of Engineering and Technology, Central Queensland University, Rockhampton, QLD, Australia. From 2014 to 2016, he was a Lecturer with the Griffith School of Engineering, Griffith University, Gold Coast, QLD, Australia. In 2016, he joined the Swinburne University of Technology, Melbourne, VIC, Australia, where he is currently an Associate Professor with the School of Software and Electrical Engineering. His current research interests include H_∞ filtering, event-triggered control, networked control systems, neural networks, distributed systems, and time-delay systems. He was a recipient of the National Natural Science Award (Secondclass) in China in 2013, and the Hunan Provincial Natural Science Award (First-class) in Hunan Province in China in 2011, both jointly with Profs. M. Wu and Y. He. He was also a recipient of the IEEE Transactions on Industrial Informatics Outstanding Paper Award 2020, the Andrew P. Sage Best Transactions Paper Award 2019, and the IET Control Theory and Applications Premium Award 2016. He is acting as an Associate Editor of several international journals, including the IEEE Transactions on Cybernetics, Neural Processing Letters, Journal of the Franklin Institute, International Journal of Control, Automation, and Systems, Neurocomputing
Corresponding author: Derui Ding, e-mail: dding@swin.edu.au
Received Date: 2020-10-23
Accepted Date: 2020-12-06

Available Online: 2020-12-16

Abstract

Abstract

In this paper, an adaptive dynamic programming (ADP) strategy is investigated for discrete-time nonlinear systems with unknown nonlinear dynamics subject to input saturation. To save the communication resources between the controller and the actuators, stochastic communication protocols (SCPs) are adopted to schedule the control signal, and therefore the closed-loop system is essentially a protocol-induced switching system. A neural network (NN)-based identifier with a robust term is exploited for approximating the unknown nonlinear system, and a set of switch-based updating rules with an additional tunable parameter of NN weights are developed with the help of the gradient descent. By virtue of a novel Lyapunov function, a sufficient condition is proposed to achieve the stability of both system identification errors and the update dynamics of NN weights. Then, a value iterative ADP algorithm in an offline way is proposed to solve the optimal control of protocol-induced switching systems with saturation constraints, and the convergence is profoundly discussed in light of mathematical induction. Furthermore, an actor-critic NN scheme is developed to approximate the control law and the proposed performance index function in the framework of ADP, and the stability of the closed-loop system is analyzed in view of the Lyapunov theory. Finally, the numerical simulation results are presented to demonstrate the effectiveness of the proposed control scheme.
- Adaptive dynamic programming (ADP),
- constrained inputs,
- neural network (NN),
- stochastic communication protocols (SCPs),
- suboptimal control

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References

[1]	M. Mazouchi, M. B. N. Sistani, and S. K. H. Sani, “A novel distributed optimal adaptive control algorithm for nonlinear multi-agent differential graphical games,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 1, pp. 331–341, Jan. 2018.
[2]	Y. J. Liu, L. Tang, S. Tong, C. L. Chen, and D. J. Li, “Reinforcement learning design-based adaptive tracking control with less learning parameters for nonlinear discrete-time MIMO systems,” IEEE Trans. Neural Netw. Learn. Syst., vol. 26, no. 1, pp. 165–176, Jan. 2015.
[3]	R. Song and L. Zhu, “Optimal fixed-point tracking control for discrete-time nonlinear systems via ADP,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 3, pp. 657–666, May 2019.
[4]	L. Sun, and Z. Zheng, “Disturbance-observer-based robust backstepping attitude stabilization of spacecraft under input saturation and measurement uncertainty,” IEEE Trans. Ind. Electron., vol. 64, no. 10, pp. 7994–8002, 2017.
[5]	D. Wang, H. He, X. Zhong, and D. Liu, “Event-driven nonlinear discounted optimal regulation involving a power system application,” IEEE Trans. Ind. Electron., vol. 64, no. 10, pp. 8177–8186, 2017.
[6]	H. Li, Y. Wu and M. Chen, “Adaptive fault-tolerant tracking control for discrete-time multi-agent systems via reinforcement learning algorithm,” IEEE Trans. Cybern., to be published. DOI: 10.1109/TCYB.2020.2982168.
[7]	T. Wang, H. Gao, and J. Qiu, “A combined adaptive neural network and nonlinear model predictive control for multirate networked industrial process control,” IEEE Trans. Ind. Electron., vol. 27, no. 2, pp. 416–425, 2016.
[8]	H. Zhang, Y. Luo, and D. Liu, “Neural-network-based near-optimal control for a class of discrete-time affine nonlinear systems with control constraints,” IEEE Trans. Neural Netw., vol. 20, no. 9, pp. 1490–1503, 2009.
[9]	Z. Shi and Z. Wang, “Optimal control for a class of complex singular system based on adaptive dynamic programming,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 1, pp. 188–197, Jan. 2019.
[10]	R. Song, Q. Wei, H. Zhang, and F. L. Lewis, “Discrete-time non-zero-sum games with completely unknown dynamics,” IEEE Trans. Cybern., vol. 99, pp. 1–15, 2019. doi: 10.1109/TCYB.2019.2957406
[11]	Q. Wei, and D. Liu, “Data-driven neuro-optimal temperature control of waterCgas shift reaction using stable iterative adaptive dynamic programming,” IEEE Trans. Ind. Electron., vol. 61, no. 11, pp. 6399–6408, 2014.
[12]	P. J. Werbos, “Foreword-ADP: the key direction for future research in intelligent control and understanding brain intelligence,” IEEE Trans. Syst. Man,Cybern. Part B, vol. 38, pp. 898–900, 2008.
[13]	D. P. Bertsekas and J. N. Tsitsiklis, “Neuro-Dynamic Programming,” Athena Scientific, USA, Belmont, MA, 1996.
[14]	R. S. Sutton and A. G. Barto, “Reinforcement Learning: An Introduction”, Cambridge, MA, USA: MIT Press, 1998.
[15]	A. Al-Tamimi, F. L. Lewis, and M. Abu-Khalaf, “Discrete-time nonlinear HJB solution using approximate dynamic programming: convergence proof,” IEEE Trans. Syst. Man,Cybern. Part B, vol. 38, no. 4, pp. 943–949, 2008.
[16]	A. Heydari, “Stability analysis of optimal adaptive control under value iteration using a stabilizing initial policy,” IEEE Trans. Neural Netw. Learn. Syst., vol. 29, no. 9, pp. 4522–4527, Sept. 2018.
[17]	Q. Wei, D. Liu, and H. Lin, “Value iteration adaptive dynamic programming for optimal control of discrete-time nonlinear systems,” IEEE Trans. Cybern., vol. 46, pp. 840–853, 2016.
[18]	W. B. Powell, “Approximate Dynamic Programming,” IHoboken, NJ, USA: Wiley, 2007.
[19]	D. V. Prokhorov and D. C. Wunsch, “Adaptive critic designs,” IEEE Trans. Neural Netw., vol. 8, no. 5, pp. 997–1007, 1997.
[20]	X. Zhong, N. Zhen, and H. He, “A theoretical foundation of goal representation heuristic dynamic programming,” IEEE Trans. Neural Netw. Learn. Syst, vol. 27, no. 12, pp. 2513–2525, 2017.
[21]	Y. Yuan, Z. Wang, P. Zhang, and H. Liu, “Near-optimal resilient control strategy design for state-saturated networked systems under stochastic communication protocol,” IEEE Trans. Cybern., vol. 49, no. 8, pp. 1–13, 2018.
[22]	M. Abu-Khalaf and F. L. Lewis, “Nearly optimal control laws for nonlinear systems with saturating actuators using a neural network HJB approach,” Automatica, vol. 41, no. 5, pp. 779–791, 2005.
[23]	X. Yang and B. Zhao, “Optimal neuro-control strategy for nonlinear systems with asymmetric input constraints,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 2, pp. 575–583, Mar. 2020.
[24]	D. Liu, X. Yang, D. Wang, and Q. Wei, “Reinforcement-learning-based robust controller design for continuous-time uncertain nonlinear systems subject to input constraints,” IEEE Trans. Cybern., vol. 45, no. 7, pp. 1372–1385, Jul. 2015.
[25]	Y. J. Liu, S. Li, S. Tong, and C. L. P. Chen, “Neural approximation-based adaptive control for a class of nonlinear nonstrict feedback discrete-time systems,” IEEE Trans. Neural Netw. Learn. Syst., vol. 28, no. 7, pp. 1531–1541, Jul. 2017.
[26]	H. Xu, Q. Zhao, and S. Jagannathan, “Finite-horizon near-optimal output feedback neural network control of quantized nonlinear discrete-time systems with input constraint,” IEEE Trans. Neural Netw. Learn. Syst., vol. 26, no. 8, pp. 1776–1788, Aug. 2015.
[27]	Y. Zhu, D. Zhao, H. He, and J. Ji, “Event-triggered optimal control for partially unknown constrained-input systems via adaptive dynamic programming,” IEEE Trans. Ind. Electron., vol. 64, no. 5, pp. 4101–4109, 2017.
[28]	H. Modares, F. L. Lewis, and M. 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, 2013.
[29]	D. Ding, Q. L. Han, X. Ge, and J. Wang, “Secure state estimation and control of cyber-physical systems: A survey,” IEEE Trans. Syst. Man, Cybern.: Syst., to be published. DOI: 10.1109/TSMC.2020.3041121.
[30]	V. Ugrinovskii and E. Fridman, “A round-robin type protocol for distributed estimation with $\substack{ H_{\infty} }$ consensus,” Syst. Control Lett., vol. 69, pp. 103–110, 2014.
[31]	G. Walsh, H. Ye, and L. Bushnell, “Stability analysis of networked control systems,” IEEE Trans. Control Syst. Tech., vol. 10, no. 3, pp. 438–446, 2002.
[32]	L. Zou, Z. Wang, and H. Gao, “Observer-based $ \substack{H_{\infty} }$ Control of networked systems with stochastic communication protocol: The finite-horizon case,” Automatica, vol. 63, pp. 366–373, 2016.
[33]	H. Ma, H. Li, R. Lu, and T. Huang, “Adaptive event-triggered control for a class of nonlinear systems with periodic disturbances,” Sci China Inf. Sci., vol. 63, no. 5, pp. 157–171, 2020.
[34]	Z. Wang, Q. Wei, and D. Liu, “Event-triggered adaptive dynamic programming for discrete-time multi-player games,” Inf. Sci., vol. 506, pp. 457–470, Jan. 2020.
[35]	D. Ding, Z. Wang, and Q. L. Han, “Neural-network-based consensus control for multi-agent systems with input constraints: The event-triggered case,” IEEE Trans. Cybern., vol. 50, no. 8, pp. 1–12, 2019.
[36]	X. Zhong, H. He, H. Zhang, and Z. Wang, “Optimal control for unknown discrete-time nonlinear Markov jump systems using adaptive dynamic programming,” IEEE Trans. Neural Netw. Learn. Syst., vol. 25, no. 12, pp. 2141–2155, 2014.
[37]	D. Ding, Z. Wang, and Q. L. Han, “Neural-network-based output-feedback control with stochastic communication protocols,” Automatica, vol. 106, pp. 221–229, Aug. 2019.
[38]	N. Azevedo, D. Pinheiro, and G.-W. Weber, “Dynamic programming for a Markov-switching jump-diffusion,” J Comput. Appl. Math., vol. 267, no. 6, pp. 1–19, Sep. 2014.
[39]	M. C. F. Donkers, W. P. M. H. Heemels, and D. Bernardini, A. Bemporad, and V. Shneer, “Stability analysis of stochastic networked control systems,” Automatica, vol. 48, no. 4, pp. 917–925, 2012.
[40]	T. Dierks, B. T. Thumati, and S. Jagannathan, “Optimal control of unknown affine nonlinear discrete-time systems using offline-trained neural networks with proof of convergence,” Neural Networks, vol. 22, no. 5–6, pp. 851–860, 2009.
[41]	B. Lincoln and A. Rantzer, “Relaxing dynamic programming,” IEEE Trans. Autom. Control, vol. 51, no. 8, pp. 1249–1260, Aug. 2006.
[42]	J. Song, Y. Niu, and Y. Zou, “Convergence analysis for an identifier-based adaptive dynamic programming algorithm,” In Proc. the 34th Chinese Control Conf., 2015.
[43]	D. Liu, D. Wang, and X. Yang, “An iterative adaptive dynamic programming algorithm for optimal control of unknown discrete-time nonlinear systems with constrained inputs,” Inf. Sci., vol. 220, no. 1, pp. 331–342, 2013.
[44]	D. Liu and Q. Wei, “Policy iteration adaptive dynamic programming algorithm for discrete-time nonlinear Systems,” IEEE Trans. Neural Netw. Learn. Syst., vol. 25, no. 3, pp. 621–634, 2014.

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An NN-based identifier with a robust term is presented to approximate the unknown nonlinear system, where weight update rules are constructed by an additional tunable parameter;
A value iterative ADP algorithm is proposed to solve the suboptimal control issue of protocol-induced switching systems with saturation constraints in an off-line way;
The convergence of the ADP algorithm is discussed and further performed via an actor-critic NN scheme;
A set of conditions are derived to check the stability of both identification error dynamics and updated error dynamics of NN weights.

Neural-Network-Based Control for Discrete-Time Nonlinear Systems with Input Saturation Under Stochastic Communication Protocol

doi: 10.1109/JAS.2021.1003922

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