Parallel Control for Optimal Tracking via Adaptive Dynamic Programming

Jingwei Lu; Qinglai Wei; Fei-Yue Wang

doi:10.1109/JAS.2020.1003426

Volume 7 Issue 6

Oct. 2020

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2020 > 7(6): 1662-1674

Jingwei Lu, Qinglai Wei and Fei-Yue Wang, "Parallel Control for Optimal Tracking via Adaptive Dynamic Programming," IEEE/CAA J. Autom. Sinica, vol. 7, no. 6, pp. 1662-1674, Nov. 2020. doi: 10.1109/JAS.2020.1003426

Citation:

Jingwei Lu, Qinglai Wei and Fei-Yue Wang, "Parallel Control for Optimal Tracking via Adaptive Dynamic Programming," IEEE/CAA J. Autom. Sinica, vol. 7, no. 6, pp. 1662-1674, Nov. 2020. doi: 10.1109/JAS.2020.1003426

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Parallel Control for Optimal Tracking via Adaptive Dynamic Programming

doi: 10.1109/JAS.2020.1003426

Jingwei Lu^{1, 2
,},
Qinglai Wei^{1, 2
,},
Fei-Yue Wang^{2, 3, 4
,}

1.
The School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing 100049, China
2.
The State Key Laboratory for Management and Control of Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China
3.
The Institute of Systems Engineering, Macau University of Science and Technology, Macau 999078, China
4.
Qingdao Academy of Intelligent Industries, Qingdao 266109, China

Funds:

the National Key Reseanch and Development Program of China 2018AAA0101502

the National Key Reseanch and Development Program of China 2018YFB1702300

the National Natural Science Foundation of China 61722312

the National Natural Science Foundation of China 61533019

the National Natural Science Foundation of China U1811463

the National Natural Science Foundation of China 61533017

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Author Bio:

Jingwei Lu received the bachelor degree in automation from University of Science and Technology Liaoning, Anshan, China, in 2014, and the master degree in control science and engineering from Beihang University, Beijing, China, in 2017. He was an assistant engineer with the AVIC Manufacturing Technology Institute, Beijing, China, from 2017 to 2019. He is currently pursuing the Ph.D. degree with the School of Artificial Intelligence, University of Chinese Academy of Sciences, and the State Key Laboratory for Management and Control of Complex Systems, Institute of Automation, Chinese Academy of Sciences. His research interests include optimal control, neural networks-based control, reinforcement learning, adaptive dynamic programming, and their industrial applications

Qinglai Wei (M'11-SM'20) received the B.S. degree in automation, and the Ph.D. degree in control theory and control engineering, from Northeastern University, Shenyang, China, in 2002 and 2009, respectively. From 2009-2011, he was a Postdoctoral Fellow with the State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China. He is currently a Professor of the institute and the Associate Director of the laboratory. He has authored four books, and published over 80 international journal papers. His research interests include adaptive dynamic programming, neural-networks-based control, optimal control, nonlinear systems and their industrial applications.
He is the Secretary of IEEE Computational Intelligence Society (CIS) Beijing Chapter since 2015. He was guest editors for several international journals. He was a recipient of IEEE/CAA Journal of Automatica Sinica Best Paper Award, IEEE System, Man, and Cybernetics Society Andrew P. Sage Best Transactions Paper Award, IEEE Transactions on Neural Networks and Learning Systems Outstanding Paper Award, the Outstanding Paper Award of Acta Automatica Sinica, IEEE 6th Data Driven Control and Learning Systems Conference (DDCLS2017) Best Paper Award, and Zhang Siying Outstanding Paper Award of Chinese Control and Decision Conference (CCDC). He was a recipient of Shuang-Chuang Talents in Jiangsu Province, China, Young Researcher Award of Asia Pacific Neural Network Society (APNNS), Young Scientst Award and Yang Jiachi Tech Award of Chinese Association of Automation (CAA). He is a Board of Governors (BOG) member of the International Neural Network Society (INNS) and a council member of CAA

Fei-Yue Wang (S'87-M'89-SM'94-F'03) received his Ph.D. degree in computer and systems engineering from the Rensselaer Polytechnic Institute, Troy, NY, USA, in 1990. He joined The University of Arizona in 1990 and became a Professor and the Director of the Robotics and Automation Laboratory and the Program in Advanced Research for Complex Systems. In 1999, he founded the Intelligent Control and Systems Engineering Center at the Institute of Automation, Chinese Academy of Sciences (CAS), Beijing, China, and in 2002, was appointed as the Director of the Key Laboratory of Complex Systems and Intelligence Science, CAS. In 2011, he became the State Specially Appointed Expert and the Director of the State Key Laboratory for Management and Control of Complex Systems.
His current research focuses on methods and applications for parallel intelligence, social computing, and knowledge automation. He is a Fellow of INCOSE, IFAC, ASME, and AAAS. In 2007, he received the National Prize in Natural Sciences of China and became an Outstanding Scientist of ACM for his work in intelligent control and social computing. He received the IEEE ITS Outstanding Application and Research Awards in 2009 and 2011, respectively. In 2014, he received the IEEE Norbert Wiener Award. Since 1997, he has been serving as the General or Program Chair of over 30 IEEE, INFORMS, IFAC, ACM, and ASME conferences. He was the President of the IEEE ITS Society from 2005 to 2007, the Chinese Association for Science and Technology, USA, in 2005, the American Zhu Kezhen Education Foundation from 2007 to 2008, the Vice President of the ACM China Council from 2010 to 2011, the Vice President and the Secretary General of the Chinese Association of Automation from 2008-2018. He was the Founding Editor-in-Chief (EiC) of the International Journal of Intelligent Control and Systems from 1995 to 2000, the IEEE ITS Magazine from 2006 to 2007, the IEEE/CAA Journal of Automatica Sinica from 2014-2017, and the China's Journal of Command and Control from 2015-2020. He was the EiC of the IEEE Intelligent Systems from 2009 to 2012, the IEEE Transactions on Intelligent Transportation Systems from 2009 to 2016, and is the EiC of the IEEE Transactions on Computational Social Systems since 2017, and the Founding EiC of China's Journal of Intelligent Science and Technology since 2019. Currently, he is the President of CAA's Supervision Council, IEEE Council on RFID, and Vice President of IEEE Systems, Man, and Cybernetics Society
Corresponding author:
Qinglai Wei. e-mail: qinglai.wei@ia.ac.cn
Recommended by Associate Editor Mangchu Zhou.
Received Date: 2020-09-01
Accepted Date: 2020-10-12

Abstract

Abstract

This paper studies the problem of optimal parallel tracking control for continuous-time general nonlinear systems. Unlike existing optimal state feedback control, the control input of the optimal parallel control is introduced into the feedback system. However, due to the introduction of control input into the feedback system, the optimal state feedback control methods can not be applied directly. To address this problem, an augmented system and an augmented performance index function are proposed firstly. Thus, the general nonlinear system is transformed into an affine nonlinear system. The difference between the optimal parallel control and the optimal state feedback control is analyzed theoretically. It is proven that the optimal parallel control with the augmented performance index function can be seen as the suboptimal state feedback control with the traditional performance index function. Moreover, an adaptive dynamic programming (ADP) technique is utilized to implement the optimal parallel tracking control using a critic neural network (NN) to approximate the value function online. The stability analysis of the closed-loop system is performed using the Lyapunov theory, and the tracking error and NN weights errors are uniformly ultimately bounded (UUB). Also, the optimal parallel controller guarantees the continuity of the control input under the circumstance that there are finite jump discontinuities in the reference signals. Finally, the effectiveness of the developed optimal parallel control method is verified in two cases.
- Adaptive dynamic programming (ADP),
- nonlinear optimal control,
- parallel controller,
- parallel control theory,
- parallel system,
- tracking control,
- neural network (NN)

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Recommended by Associate Editor Mangchu Zhou.

References(56)

References

[1]	F.-Y. Wang, "Parallel system methods for management and control of complex systems, " Control and Decision, vol. 19, no. 5, pp. 485-489, May 2004. https://www.researchgate.net/publication/266537911_Parallel_system_methods_for_management_and_control_of_complex_systems
[2]	F.-Y. Wang, "Parallel control and management for intelligent transportation systems: concepts, architectures, and applications, " IEEE Trans. Intell. Transp. Syst., vol. 11, no. 3, pp. 630-638, Sep. 2010. https://www.researchgate.net/publication/220108880_Parallel_Control_and_Management_for_Intelligent_Transportation_Systems_Concepts_Architectures_and_Applications
[3]	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, no. 3, pp. 840-853, Mar. 2016. https://www.researchgate.net/publication/283624374_Value_Iteration_Adaptive_Dynamic_Programming_for_Optimal_Control_of_Discrete-Time_Nonlinear_Systems
[4]	D. Liu, Q. Wei, D. Wang, X. Yang, and H. Li, Adaptive Dynamic Programming with Applications in Optimal Control. Cham, Switzerland: Springer, 2017.
[5]	Y. Li, T, Yang, and S. Tong, "Adaptive neural networks finite-time optimal control for a class of nonlinear systems, " IEEE Trans. Neural. Netw. Learn. Syst., in press, doi: 10.1109/TNNLS.2019.2955438
[6]	H. Zhang, L. Jiang, J. Liu, and F. Qu, "Data recovery of magnetic flux leakage data gaps using multifeature conditional risk, " IEEE Trans. Autom. Sci. Eng.,, in press, doi: 10.1109/TASE.2020.2994659
[7]	Q. Wei, R. Song, Z. Liao, B. Li, and F. L. Lewis, "Discrete-time impulsive adaptive dynamic programming, " IEEE Trans. Cybern., in press, doi: 10.1109/TCYB.2019.2906694
[8]	R. Song, J. Li, F. L. Lewis, "Robust optimal control for disturbed nonlinear zero-sum differential games based on Single NN and Least-Squares, " IEEE Trans. Syst., Man, Cybern., Syst., in press, doi: 10.1109/TSMC.2019.2897379
[9]	R. Song, Q. L. Wei, H. Zhang, F. L. Lewis, "Discrete-time non-zero-sum games with completely unknown dynamics, " IEEE Trans. Cybern., in press, doi: 10.1109/TCYB.2019.2957406
[10]	P. J. Werbos, "Advanced forecasting methods for global crisis warning and models of intelligence, " Gen. Syst. Yearbook, vol. 22, pp. 25-38, 1977.
[11]	P. J. Werbos, "Approximate dynamic programming for real-time control and neural modeling, " in Handbook of Intelligent Control, D. A. White and D. A. Sofge, Eds. New York: Van Nostrand Reinhold, 1992. https://www.researchgate.net/publication/243651581_Approximate_dynamic_programming_for_real-time_control_and_neural_modeling
[12]	F. L. Lewis, D. Vrabie, and V. L. Syrmos, Optimal Control. Hoboken, NJ, USA: Wiley, 2013.
[13]	H. Zhang, K. Zhang, G. Xiao, and H. Jiang, "Robust optimal control scheme for unknown constrained-input nonlinear systems via a plug-n-play event-sampled critic-only algorithm, " IEEE Trans. Syst., Man, Cybern., Syst.,, in press, doi: 10.1109/TSMC.2018.2889377
[14]	Q. Wei, Z. Liao, R. Song, P. Zhang, Z. Wang, and J. Xiao, "Self-learning optimal control for ice storage air conditioning systems via data-based adaptive dynamic programming, " IEEE Trans. Ind. Electron., in press 2020. DOI: 10.1109/TIE.2020.2978699
[15]	Y.-M. Li, X. Min, and S. Tong, "Adaptive fuzzy inverse optimal control for uncertain strict-feedback nonlinear systems, " IEEE Trans. Neural. Netw. Learn. Syst., vol. 28, no. 10, pp. 2363-2374, Oct. 2020.
[16]	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. B. Cybern., vol. 38, no. 4, pp. 943-949, Aug. 2008. http://med.wanfangdata.com.cn/Paper/Detail/PeriodicalPaper_PM18632382
[17]	F. L. Lewis and D. Vrabie, "Reinforcement learning and adaptive dynamic programming for feedback control, " IEEE Circuits Syst. Mag., vol. 9, no. 3, pp. 32-50, Jul. 2009. Reinforcement learning and adaptive dynamic programming for feedback control
[18]	F.-Y. Wang, N. Jin, D. Liu, and Q. Wei, "Adaptive dynamic programming for finite-horizon optimal control of discrete-time nonlinear systems with ε-error bound, " IEEE Trans. Neural. Netw. Learn. Syst., vol. 22, no. 1, pp. 24-36, Jan. 2011. http://med.wanfangdata.com.cn/Paper/Detail/PeriodicalPaper_PM20876014
[19]	T. Dierks and S. Jagannathan, "Online optimal control of affine nonlinear discrete-time systems with unknown internal dynamics by using time-based policy update, " IEEE Trans. Neural. Netw. Learn. Syst., vol. 23, no. 7, pp. 1118-1129, Jul. 2012. https://pubmed.ncbi.nlm.nih.gov/24807137/
[20]	C. Mu, D. Wang, and H. He, "Data-driven finite-horizon approximate optimal control for discrete-time nonlinear systems using iterative HDP approach, " IEEE Trans. Cybern., vol. 48, no. 10, pp. 2948-2961, Oct. 2018. https://pubmed.ncbi.nlm.nih.gov/29028219/
[21]	L. Dong, J. Yan, X. Yuan, H. He, and C. Sun, "Functional nonlinear model predictive control based on adaptive dynamic programming, " IEEE Trans. Cybern., vol. 49, no. 12, pp. 4206-4218, Dec. 2019. https://www.researchgate.net/publication/327089881_Functional_Nonlinear_Model_Predictive_Control_Based_on_Adaptive_Dynamic_Programming
[22]	Q. Wei, Z. Liao, Z. Yang, B. Li, and D. Liu, "Continuous-time time-varying policy iteration, " IEEE Trans. Cybern., in press, doi: 10.1109/TCYB.2019.2926631
[23]	Q. Wei, H. Li, X. Yang, and H. He, "Continuous-time distributed policy iteration for multicontroller nonlinear systems, " IEEE Trans. Cybern., in press, doi: 10.1109/TCYB.2020.2979614
[24]	Q. Wei, H. Li, X. Yang, and H. He, "Continuous-time distributed policy iteration for multicontroller nonlinear systems, " IEEE Trans. Cybern., in press, doi: 10.1109/TCYB.2020.2979614
[25]	H. Zhang, Y. Cai, Y. Wang, and H. Su, "Adaptive bipartite event-triggered output consensus of heterogeneous linear multiagent systems under fixed and switching topologies, " IEEE Trans. Neural Netw. Learn. Syst., in press, doi: 10.1109/TNNLS.2019.2958107
[26]	Q. Wei, L. Wang, Y. Liu, and M. M. Polycarpou, "Optimal elevator group control via deep asynchronous actor-critic learning, " IEEE Trans. Neural. Netw. Learn. Syst., in press, doi: 10.1109/TNNLS.2020.2965208
[27]	Q. Wei, D. Liu, Y. Liu, and R. Song, "Optimal Constrained Self-learning Battery Sequential Management in Microgrid Via Adaptive Dynamic Programming, " IEEE/CAA J. Autom. Sinica, vol. 4, no. 2, pp. 168-176, Apr. 2017. http://en.cnki.com.cn/Article_en/CJFDTOTAL-ZDHB201702003.htm
[28]	D. Liu, Y. Xu, Q. Wei, and X. Liu, "Residential energy scheduling for variable weather solar energy based on adaptive dynamic programming, " IEEE/CAA J. Autom. Sinica, vol. 5, no. 1, pp. 36-46, Jan. 2018. http://en.cnki.com.cn/Article_en/CJFDTotal-ZDHB201801004.htm
[29]	K. G. Vamvoudakis and F. L. Lewis, "Online actorritic algorithm to solve the continuous-time infinite horizon optimal control problem, " Automatica, vol. 46, no. 5, pp. 878-808, 2010. doi: 10.1016/j.automatica.2010.02.018
[30]	T. Dierks and S. Jagannathan, "Optimal control of affine nonlinear continuous-time systems, " in Proc. Amer. Control Conf., MD, USA, Jul. 2010, pp. 1568-1573. https://www.researchgate.net/publication/224162610_Optimal_control_of_affine_nonlinear_continuous-time_systems
[31]	D. Nodland, H. Zargarzadeh, and S. Jagannathan, "Neural network-based optimal adaptive output feedback control of a helicopter UAV, " IEEE Trans. Neural. Netw. Learn. Syst., vol. 24, no. 7, pp. 1061-1073, Jul. 2013. https://pubmed.ncbi.nlm.nih.gov/24808521/
[32]	H. Zargarzadeh, T. Dierks, and S. Jagannathan, "Optimal control of nonlinear continuous-time systems in strict-feedback form, " IEEE Trans. Neural. Netw. Learn. Syst., vol. 26, no. 10, pp. 2535-2549, Oct. 2015. https://pubmed.ncbi.nlm.nih.gov/26111400/
[33]	R. Bell and K. Aström, Dynamic Models for Boliler-Turbine-Alternator Units: Data Logs and Parameter Estimation for a 160 MW Unit. Sweden: Department of Automatic Control, Lund Institute of Technology, 1987.
[34]	G. Pellegrinetti, and J. Bentsman, "Nonlinear control oriented boiler modeling-a benchmark problem for controller design, " IEEE Trans. Control Syst. Technol., vol. 4, no. 1, pp. 57-64, Jan. 1996. https://www.researchgate.net/publication/3331856_Nonlinear_control_oriented_boiler_modeling_-_A_benchmark_problem_for_controller_design
[35]	G. Wen, S. S. Ge, W. Zhou, C. L. P. Chen, F. Tu, and S. Wang, "Adaptive tracking control of surface vessel using optimized backstepping technique, " IEEE Trans. Cybern., vol. 49, no. 9, pp. 3420-3431, Sep. 2019. https://ieeexplore.ieee.org/document/8396836
[36]	W. Gao, and Z. P. Jiang, "Learning-based adaptive optimal tracking control of strict-feedback nonlinear systems, " IEEE Trans. Neural. Netw. Learn. Syst., vol. 29, no. 6, pp. 2614-2624, Jun. 2018. https://pubmed.ncbi.nlm.nih.gov/29771677/
[37]	Y. Liu, H. Zhang, R. Yu, and Z. Xing, "H_∞ Tracking control of discrete-time system with delays via data-based adaptive dynamic programming, " IEEE Trans. Syst., Man, Cybern., Syst., to be published, doi: 10.1109/TSMC.2019.2946397.
[38]	F. Li, M. Zhou, and Y. Ding, "An adaptive online co-search method with distributed samples for dynamic target tracking, " IEEE Trans. Control Syst. Technol., vol. 26, no. 2, pp. 439-451, Mar. 2018.
[39]	S. Li, M. Zhou, and X. Luo, "Modified primal-dual neural networks for motion control of redundant manipulators with dynamic rejection of harmonic noises, " IEEE Trans. Neural. Netw. Learn. Syst., vol. 29, no. 10, pp. 4791-4801, Oct. 2018. https://www.researchgate.net/publication/322093421_Modified_Primal-Dual_Neural_Networks_for_Motion_Control_of_Redundant_Manipulators_With_Dynamic_Rejection_of_Harmonic_Noises
[40]	H. Zhang, Q. Wei, and Y. Luo, "A novel infinite-time optimal tracking control scheme for a class of discrete-time nonlinear systems via the greedy HDP iteration algorithm, " IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 38, no. 4, pp. 937-942, Aug. 2008.
[41]	H. Zhang, L. Cui, X. Zhang, and Y. Luo, "Data-driven robust approximate optimal tracking control for unknown general nonlinear systems using adaptive dynamic programming method, " IEEE Trans. Neural. Netw. Learn. Syst., vol. 22, no. 12, pp. 2226-2236, Dec. 2011. http://med.wanfangdata.com.cn/Paper/Detail/PeriodicalPaper_PM21997259
[42]	C. Mu, Z. Ni, C. Sun, and H. He, "Data-driven tracking control with adaptive dynamic programming for a class of continuous-Time Nonlinear Systems, " IEEE Trans. Cybern., vol. 47, no. 6, pp. 1460-1470, Jun. 2017. https://pubmed.ncbi.nlm.nih.gov/27116758/
[43]	Z. Cao, Q. Xiao, R. Huang, and M. Zhou, "Robust neuro-optimal control of underactuated snake robots with experience replay, " IEEE Trans. Neural. Netw. Learn. Syst., vol. 29, no. 1, pp. 208-217, Jan. 2018. https://www.researchgate.net/publication/321091006_Robust_Neuro-Optimal_Control_of_Underactuated_Snake_Robots_With_Experience_Replay
[44]	Q. Wei, H. Li, and F.-Y. Wang, "Parallel control for continuous-time linear systems: A case study, " IEEE/CAA J. Autom. Sinica, vol. 7, no. 4, pp. 919-926, Jul. 2020.
[45]	F.-Y. Wang, "Parallel control: a method for data-driven and computation control, " Acta Automatica Sinica, vol. 39, no. 4, pp. 293-302, Apr. 2013. http://en.cnki.com.cn/Article_en/CJFDTOTAL-MOTO201304002.htm
[46]	F.-Y. Wang and Q. Wei, "Intelligent control: from learning control to parallel control, " Control Theory & Applications, vol. 35, no. 7, pp. 939-948, Jul. 2018. http://en.cnki.com.cn/Article_en/CJFDTotal-KZLY201807005.htm
[47]	F. Zhu, Z. Li, S. Chen, and G. Xiong, "Parallel transportation management and control system and its applications in building smart cities, " IEEE Trans. Intell. Transp. Syst., vol. 17, no. 6, pp. 1576-1585, Jun. 2016. https://ieeexplore.ieee.org/document/7381677
[48]	B. Ning, H. Dong, D. Weng, L. Li, and C.-J. Cheng, "ACP-based control and management of urban rail transportation systems, " IEEE Intell. Syst., vol. 26, no. 2, pp. 84-88, Mar. 2011. https://ieeexplore.ieee.org/document/5751217
[49]	F.-Y. Wang and S. Tang, "Artificial societies for integrated and sustainable development of metropolitan systems, " IEEE Intell. Syst., vol. 19, no. 4, pp. 82-87, Jul. 2004. https://www.researchgate.net/publication/220628871_Artificial_Societies_for_Integrated_and_Sustainable_Development_of_Metropolitan_Systems
[50]	F.-Y. Wang, N.-N Zheng, D. Cao, C. M. Martinez, L. Li, and T. Liu, "Parallel driving in CPSS: A unified approach for transport automation and vehicle intelligence, " IEEE/CAA J. Autom. Sinica, vol. 4, no. 4, pp. 577-587, Oct. 2017. https://ieeexplore.ieee.org/document/8039015
[51]	W. Zhang, K. Wang, Y. Liu, Y. Lu, and F.-Y. Wang, "A parallel vision approach to scene-specific pedestrian detection, " Neurocomputing, vol. 394, no. 21, pp. 114-126, Jun. 2020. https://www.researchgate.net/publication/334007978_A_Parallel_Vision_Approach_to_Scene-Specific_Pedestrian_Detection
[52]	Q. Wei, L. Wang, J. Lu, and F.-Y. Wang, "Discrete-Time self-learning parallel control, " IEEE Trans. Syst., Man, Cybern., Syst., in press, doi: 10.1109/TSMC.2020.2995646.
[53]	G. Bartolini and P. Pydynowski, "An improved, chattering free, V.S.C. scheme for uncertain dynamical systems, " IEEE Trans. Autom. Control, vol. 41, no. 8, pp. 1220-1226, Aug. 1996. https://ieeexplore.ieee.org/document/533691
[54]	M. Krstic, I. Kanellakopoulos, and P. V. Kokotovic, Nonlinear and Adaptive Control Design. New York, USA: John Wiley & Sons. Inc., 1995.
[55]	F. L. Lewis, S. Jagannathan, and A. Yesildirek, Neural Network Control of Robot Manipulators and Nonlinear Systems. Philadelphia, USA: Taylor & Francis, 1999.
[56]	P. Tabuada, "Event-triggered real-time scheduling of stabilizing control tasks, " IEEE Trans. Autom. Control, vol. 52, no. 9, pp. 1680-1685, Sep. 2007. https://ieeexplore.ieee.org/document/4303247

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Parallel Control for Optimal Tracking via Adaptive Dynamic Programming

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