Abstract
This paper proposes a neural-networks(NN)-based adaptive controller for an uncertain nonlinear system with asymptotic stability. While the satisfactory performance of the NN-based adaptive controller is validated well in various uncertain nonlinear systems, the stability is commonly restricted to the uniformly ultimate boundedness(UUB). To improve the UUB of the NN-based adaptive control to the asymptotically stability(AS) with continuous control, the existing NN-based adaptive controller is augmented with a robust-integral-signum-error (RISE) feedback term, and overall closed-loop stability is rigorously analyzed by modifying the typical stability analysis for the RISE feedback control. To demonstrate the effectiveness of the proposed controller, numerical simulations for a fault tolerant flight control with a nonlinear F-16 aircraft model are performed.
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K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximator,” Neural Networks, vol. 2, no. 5, pp. 359–366, 1989.
K. S. Narendra and K. Parthasarathy, “Identification and control of dynamical systems using neural networks,” IEEE Transactions on Neural Networks, vol. 1, no. 1, pp. 4–27, 1990.
M. M. Polycarpou and P. A. Ioannou, “Identification and control of nonlinear systems using neural networks models: Design and stability analysis,” Univ. Southern California, Los Angeles, CA, Tech. Rep. 91-09-01, 1991.
R. Fierro and F. L. Lewis, “Control of nonholonomic mobile robot using neural networks,” IEEE Transactions on Neural Networks, vol. 9, no. 4, pp. 589–600, 1998.
F. Chen and H. Khalil, “Adaptive control of a class of nonlinear discrete-time systems using neural networks,” IEEE Transactions on Automatic Control, vol. 40, no. 5, pp. 791–801, 1995.
B. Kim and A. J. Calise, “Nonlinear flight control using neural networks,” AIAA Journal of Guidance, Control, and Dynamics, vol. 20, no. 1, pp. 26–33, 1997.
D. Shin and Y. Kim, “Reconfigurable flight control system design using adaptive neural networks,” IEEE Transactions on Control Systems Technology, vol. 12, no. 1, pp. 87–100, 2004.
S. Yoo, J. Park, and Y. Choi, “Adaptive output feedback control of flexible-joint robots using neural networks: Dynamic surface design approach,” IEEE Transactions on Neural Networks, vol. 19, no. 10, pp. 1712–1726, 2008.
Z. Hou, L. Cheng, and M. Tan, “Decentralized robust adaptive control for the multiagent system consensus problem using neural networks,” IEEE Transactions on Systems, Man, and Cybernetics-Part B:Cybernetics, vol. 39, no. 3, pp. 636–647, 2009.
H. Li, L. Wang, H. Du, and A. Boulkroune, “Adaptive fuzzy backstepping tracking control for strict-feedback systems with input delay,” IEEE Transactions on Fuzzy Systems, vol. 25, no. 3, pp. 642–652, 2017.
L. Wang, H. Li, Q. Zhou, and R. Lu, “Adaptive fuzzy control for nonstrict feedback systems with unmodeled dynamics and fuzzy dead zone via output feedback,” IEEE Transactions on Cybernetics, vol. 47, no. 9, pp. 2400–2412, 2017.
Y. Li and S. Tong, “Adaptive neural networks decentralized FTC design for nonstrict-feedback nonlinear interconnected large-scale systems against actuator faults,” IEEE Transactions on Neural Networks and Learning Systems, vol. 28, no. 11, pp. 2541–2554, 2017.
Y. Li and S. Tong, “Adaptive neural networks prescribed performance control design for switched interconnected uncertain nonlinear systems,” IEEE Transactions on Neural Networks and Learning Systems, vol. PP, no. 99, pp. 1–10. DOI:10.1109/TNNLS.2017.2712698.
B. Xian, D. M. Dawson, M. S. de Qeuiroz, and J. Chen, “A continuous asymptotic tracking control strategy for uncertain nonlinear systems,” IEEE Transactions on Automatic Control, vol. 49, no. 7, pp. 1206–1211, 2004.
J. Shin, J. Huh, and Y. Park, “Asymptotically stable path tracking for lateral motion of an unmanned ground vehicle,” Control Engineering Practice, vol. 40, pp. 102–112, 2015.
P. M. Patre, W. MacKunis, K. Kaiser, and W. E. Dixon, “Asymptotic tracking for uncertain dynamic systems via a multilayer neural network feedforward and RISE feedback control structure,” IEEE Transactions on Automatic Control, vol. 53, no. 9, pp. 2180–2185, 2008.
P. M. Patre, W. MacKunis, M. Johnson, and W. E. Dixon, “Composite adaptive control for Euler-Lagrange systems with additive disturbances,” Automatica, vol. 46, no. 1, pp. 140–147, 2010.
N. Sharma, K. Stegath, C. Gregory, and W. E. Dixon, “Nonlinear neuromuscular electrical stimulation tracking control of a human limb,” IEEE Transactions on Neural Systems and Rehabilitation Engineering, vol. 17, no. 6, pp. 576–584, 2009.
J. Shin, H. J. Kim, Y. Kim, and W. E. Dixon, “Asymptotic attitude tracking of the rotorcraft-based UAV via RISE feedback and NN feedforward terms,” Proc. of The 49th IEEE Conference on Decision and Control (CDC), Atlanta, GA, pp. 3694–3699, 2010.
J. Shin, H. J. Kim, Y. Kim, and W. E. Dixon, “Autonomous flight of the rotorcraft-based UAV using RISE feedback and NN feedforward terms,” IEEE Transactions on Control System Technology, vol. 20, no. 5, pp. 1392–1399, 2012.
Z. Wilcox, W. MacKunis, S. Bhat, R. Lind, and W. E. Dixon, “Lyapunov-based exponential tracking control of a hypersonic aircraft with aerothermoelastic effects,” Proc. of AIAA Journal of Guidance, Control and Dynamics, vol. 33, no. 4, pp. 1213–1224, 2010.
A. Filippov, “Differential equations with discontinuous right-hand side,” American Mathematical Society Translations, vol. 42, no. 2, pp. 199–231, 1964.
G. V. Smirnov, Introduction to the Theory of Differential Inclusions, American Mathematical Society, 2002.
B. Paden and S. Sastry, “A calculus for computing Filippov’s differential inclusion with application to the variable structure control of robot manipulator,” IEEE Transactions on Circuits and Systems, vol. 34, no. 1, pp. 73–82, 1987.
H. K. Khalil, Nonlinear Systems, 3rd edition, Prentice-Hall PTR, Upper Saddle River, NJ, 2002.
W. E. Dixon, A. Behal, D. M. Dawson, and S. P. Nagarkatti, Nonlinear Control of Engineering Systems: A Lyapunov-Based Approach, Birkhauser, Boston, MA, 2003.
E. A. Morelli, “Global nonlinear parametric modeling with application to F-16 aerodynamics,” Proceeding of American Control Conference, pp. 997–1001, 1998.
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Recommended by Associate Editor Hongyi Li under the direction of Editor Myo Taeg Lim. This research was supported by a grant to Bio-Mimetic Robot Research Center Funded by Defense Acquisition Program Administration, and by Agency for Defense Development (UD130070ID).
Jongho Shin received the B.S. degree in Mechanical Engineering from Soongsil University, Seoul, Korea, in 2005, and then acquired the Ph.D. degree in the Department of Mechanical and Aerospace Engineering from Seoul National University in 2011. He is currently a senior researcher in Agency for Defense Development, Daejeon, Korea. His research interests include adaptive/robust/optimal control with applications to aerial robots, autonomous ground robots, surface vessel and other mechanical systems.
Seungkeun Kim received the B.Sc. degree in mechanical and aerospace engineering from Seoul National University, Seoul, Korea, in 2002, and then acquired the Ph.D. degree from Seoul National University in 2008. He is currently an associate professor at the Department of Aerospace Engineering, Chungnam National University, Korea. Previously he was a research fellow and a lecturer at Cranfield University, United Kingdom, in 2008–2012. His research interests cover nonlinear guidance and control, estimation, sensor and information fusion, fault diagnosis, fault tolerant control, and decision making for unmanned systems.
Antonios Tsourdos obtained a MEng on Electronic, Control and Systems Engineering from the University of Sheffield (1995), an MSc on Systems Engineering from Cardiff University (1996) and a PhD on Nonlinear Robust Missile Autopilot Design and Analysis from Cranfield University (1999). He is a Professor of Control Engineering with Cranfield University. Appointed Head of the Cyber-Physical Systems in 2013. Professor Tsourdos was member of the Team Stellar, the winning team for the UK MoD Grand Challenge (2008) and the IET Innovation Award (Category Team, 2009).
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Shin, J., Kim, S. & Tsourdos, A. Neural-networks-based Adaptive Control for an Uncertain Nonlinear System with Asymptotic Stability. Int. J. Control Autom. Syst. 16, 1989–2001 (2018). https://doi.org/10.1007/s12555-017-0641-x
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DOI: https://doi.org/10.1007/s12555-017-0641-x