Adaptive Control Solution for a Class of MIMO Uncertain Underactuated Systems with Saturating Inputs
Yıl 2016,
Cilt: 4 Sayı: 4, 135 - 144, 06.12.2016
Ajay Kulkarni
,
Abhay Kumar
Öz
This paper addresses the issue of controller design for a
class of multi-input multi-output (MIMO) uncertain underactuated
systems with saturating inputs. A systematic controller framework,
composed of a hierarchically generated control term, meant to
ensure the stabilization of a particular portion of system dynamics
and some dedicated control terms designed to solve the tracking
problem of the remaining system dynamics is presented. Wavelet
neural networks are used as adaptive tuners to approximate the
system uncertainties also to reshape the control terms so as to deal
with the saturation nonlinearity in an antiwindup paradigm.
Gradient based tuning laws are developed for the online tuning of
adjustable parameters of the wavelet network. A Lyapunov based
stability analysis is carried out to ensure the uniformly ultimately
bounded (UUB) stability of the closed loop system. Finally, a
simulation is carried out which supports the theoretical
development.
Kaynakça
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- R. Olfati-Saber, “Normal Forms for Underactuated Mechanical Systems with Symmetry,” IEEE Trans on Automatic Control, vol.47, pp.305-308, 2002.
- W. Wang, J. Yi, D. Zhao and D. Liu, “Design of a Stable Sliding-Mode Controller for a Class of Second-Order Underactuated Systems,” IEE Proc.- Control Theory Appl., vol. 151, No. 6,pp.683-690, November 2004.
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- D.Qian and J.Yi, “Fuzzy Aggregated Hierarchical Sliding Mode Control for Underactuated Systems”, IEEE Conference on Mechatronics and Automation, Xi'an, China, pp. 196-201, 2010.
- H.Chyau and C.Y.Feng, “Adaptive Control for a Class of Underactuated Systems with Mismatched Uncertainties”, Proceedings of the 29th Chinese Control Conference, Beijing, China, pp. 2053-2059, 2010.
- D.Qian, J.Yi and D.Zhao, “Control of Overhead Crane Systems by Combining Sliding Mode with Fuzzy regulator,” 18th IFAC World
- Congress, Milano, pp. 9320—9325, 2011.
- D.Qian, X.Liu and J.Yi, “Adaptive Control Based on Hierarchical Sliding Mode for Under-Actuated Systems”, IEEE Conference on Mechatronics and Automation, Chengdu, China, pp. 1050-1055, 2012.
- D.Qian, S.Tong and J.Yi, “Adaptive Control Based on Incremental Hierarchical Sliding Mode for Overhead Crane Systems,”
- Appl.Math.Inf.Sci. , vol.7, no. 4, pp.1359-1364, 2013.
- C.C. Chiang and Y.W.Yah, “Hierarchical Fuzzy Sliding Mode Control for Uncertain Nonlinear Underactuated Systems”, IEEE Conference on Fuzzy Systems, Beijing, China, pp. 662-669, 2014.
- C.L.Hwang,C.C.Chiang and Y.W.Yah, “Adaptive Fuzzy Hierarchical Sliding Mode Control for the Trajectory Tracking of Uncertain Underactuated Nonlinear Dynamic Systems”, IEEE Trans on Fuzzy Systems, vol.22, pp.286-299, 2014.
- S.Aloui, O.Pages, A.Elhajjaji, A.Chaari and Y.Koubaa, “Robust adaptive fuzzy sliding mode control design for a class of MIMO underactuated system,” IFAC World Congress, Milano, Italy, pp.11127-11132, September 2011.
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- J.E. Slotin, W. Li, Applied Nonlinear Control, Prentice-Hall International, Englewood Cliffs, NJ, 1991.
- K.J.Astrom and B.Wittenmark, Adaptive Control, New York: Addison Wesley, 1995.
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- Q. Zhang, A. Benveniste, “Wavelet networks”, IEEE Transactions on Neural Networks, vol. 3 ,pp.889—898, 1992.
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- J.X.Xu and Y.Tan, “Nonlinear Adaptive Wavelet Control Using
- Constructive Wavelet Networks” IEEE Transactions on Neural Networks, vol. 18, no. 1, pp.115-127, January 2007.
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- M.Zekri, S.Sadri, F.Sheikholeslam, “Adaptive Wavelet Controller Design for Non Linear Systems”, Fuzzy Sets and Systems, vol. 159, pp.2668-2695, 2008.
- L.W.Lee and I.H.LI, “Wavelet Based Adaptive Sliding Mode Control with H Tracking Performance for Pneumatic Servo System Position Tracking Control”, IET Control Theory Applications, vol. 6, no. 11, pp.1699-1714, 2012.
- Y.Xue, J.Wen and Y.Du, “Robust Adaptive Control for Near Space Vehicles Based on Wavelet Neural Network”, Proceedings of IECON, Vienna, pp .3735-3739, November 2013.
- W.Gao and R.R. Selmic, “Neural Network Control for a Class of Nonlinear Systems with Actuator Saturation”, Proceedings of American Control Conference, Massachusetts, Boston, pp .2569-2574, 2004.
- J.Zhou, M.Joo and Y.Zhou, “Adaptive Neural Network Control of Uncertain Npnlinear Systems in Presence of Input Constraints,”
- Proceedings of the ICARCV, pp. 895-899, 2006.
- P.He and S.Jagannathan, “Reinforcement Learning Neural Network Based Controller for Nonlinear Systems with Input Constraints”, IEEE Transactions on Systems, Man and Cybernetics-Part B: Cybernetics, vol. 37, no. 2, pp.425-436, 2007.
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Yıl 2016,
Cilt: 4 Sayı: 4, 135 - 144, 06.12.2016
Ajay Kulkarni
,
Abhay Kumar
Kaynakça
- M. W. Spong, “Underactuated mechanical systems,” Control Problems in Robotics and Automation, Springer-Verlag, London, UK, 1997.
- R. Olfati-Saber, “Normal Forms for Underactuated Mechanical Systems with Symmetry,” IEEE Trans on Automatic Control, vol.47, pp.305-308, 2002.
- W. Wang, J. Yi, D. Zhao and D. Liu, “Design of a Stable Sliding-Mode Controller for a Class of Second-Order Underactuated Systems,” IEE Proc.- Control Theory Appl., vol. 151, No. 6,pp.683-690, November 2004.
- D.W.Qian, X.J.Liu and J.Q.Yi, “Robust Sliding Mode Control for a Class of Underactuated Systems with Mismatched Uncertainties,” JSCE, vol.223, pp.785-795, 2009.
- D.Qian and J.Yi, “Fuzzy Aggregated Hierarchical Sliding Mode Control for Underactuated Systems”, IEEE Conference on Mechatronics and Automation, Xi'an, China, pp. 196-201, 2010.
- H.Chyau and C.Y.Feng, “Adaptive Control for a Class of Underactuated Systems with Mismatched Uncertainties”, Proceedings of the 29th Chinese Control Conference, Beijing, China, pp. 2053-2059, 2010.
- D.Qian, J.Yi and D.Zhao, “Control of Overhead Crane Systems by Combining Sliding Mode with Fuzzy regulator,” 18th IFAC World
- Congress, Milano, pp. 9320—9325, 2011.
- D.Qian, X.Liu and J.Yi, “Adaptive Control Based on Hierarchical Sliding Mode for Under-Actuated Systems”, IEEE Conference on Mechatronics and Automation, Chengdu, China, pp. 1050-1055, 2012.
- D.Qian, S.Tong and J.Yi, “Adaptive Control Based on Incremental Hierarchical Sliding Mode for Overhead Crane Systems,”
- Appl.Math.Inf.Sci. , vol.7, no. 4, pp.1359-1364, 2013.
- C.C. Chiang and Y.W.Yah, “Hierarchical Fuzzy Sliding Mode Control for Uncertain Nonlinear Underactuated Systems”, IEEE Conference on Fuzzy Systems, Beijing, China, pp. 662-669, 2014.
- C.L.Hwang,C.C.Chiang and Y.W.Yah, “Adaptive Fuzzy Hierarchical Sliding Mode Control for the Trajectory Tracking of Uncertain Underactuated Nonlinear Dynamic Systems”, IEEE Trans on Fuzzy Systems, vol.22, pp.286-299, 2014.
- S.Aloui, O.Pages, A.Elhajjaji, A.Chaari and Y.Koubaa, “Robust adaptive fuzzy sliding mode control design for a class of MIMO underactuated system,” IFAC World Congress, Milano, Italy, pp.11127-11132, September 2011.
- H.K. Khalil, Nonlinear Systems .Upper Saddle River, NJ: Prentice Hall, 2002.
- J.E. Slotin, W. Li, Applied Nonlinear Control, Prentice-Hall International, Englewood Cliffs, NJ, 1991.
- K.J.Astrom and B.Wittenmark, Adaptive Control, New York: Addison Wesley, 1995.
- 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.
- Q. Zhang, A. Benveniste, “Wavelet networks”, IEEE Transactions on Neural Networks, vol. 3 ,pp.889—898, 1992.
- J. Zhang, G. G. Walter, Y. Miao, and W. N. W. Lee, “Wavelet Neural Networks for Function Learning,” IEEE Transactions on Signal Processing, vol. 43, no. 6, pp.1485-1497, June 1995.
- J.X.Xu and Y.Tan, “Nonlinear Adaptive Wavelet Control Using
- Constructive Wavelet Networks” IEEE Transactions on Neural Networks, vol. 18, no. 1, pp.115-127, January 2007.
- S.A.Billings and H.L.Wei, “A New Class of Wavelet Networks for Nonlinear System Identification,” IEEE Transactions on Neural Networks, vol. 16, pp.862—874, 2005.
- C.F. Hsu, C.M. Lin, T.-T. Lee, “ Wavelet Adaptive Backstepping Control for a Class of Nonlinear Systems” IEEE Transactions on Neural Networks, vol. 17, no. 5,pp.1175-1183, September 2006.
- M.Zekri, S.Sadri, F.Sheikholeslam, “Adaptive Wavelet Controller Design for Non Linear Systems”, Fuzzy Sets and Systems, vol. 159, pp.2668-2695, 2008.
- L.W.Lee and I.H.LI, “Wavelet Based Adaptive Sliding Mode Control with H Tracking Performance for Pneumatic Servo System Position Tracking Control”, IET Control Theory Applications, vol. 6, no. 11, pp.1699-1714, 2012.
- Y.Xue, J.Wen and Y.Du, “Robust Adaptive Control for Near Space Vehicles Based on Wavelet Neural Network”, Proceedings of IECON, Vienna, pp .3735-3739, November 2013.
- W.Gao and R.R. Selmic, “Neural Network Control for a Class of Nonlinear Systems with Actuator Saturation”, Proceedings of American Control Conference, Massachusetts, Boston, pp .2569-2574, 2004.
- J.Zhou, M.Joo and Y.Zhou, “Adaptive Neural Network Control of Uncertain Npnlinear Systems in Presence of Input Constraints,”
- Proceedings of the ICARCV, pp. 895-899, 2006.
- P.He and S.Jagannathan, “Reinforcement Learning Neural Network Based Controller for Nonlinear Systems with Input Constraints”, IEEE Transactions on Systems, Man and Cybernetics-Part B: Cybernetics, vol. 37, no. 2, pp.425-436, 2007.
- S.Laboid and T.M.Guerra, “Adaptive fuzzy control of a class of SISO nonaffine nonlinear systems,” Fuzzy Sets and Systems, vol. 158, pp.1126- 1137, 2007.