RHONN identifier-control scheme for nonlinear discrete-time systems with unknown time-delays

Abstract This work presents a neural identifier-control scheme for uncertain nonlinear discrete-time systems with unknown time-delays. This scheme is based on a neural identifier to get a model of the system and a discrete-time block control technique based on sliding modes to generate the control law. The neural identifier is based on a Recurrent High Order Neural Network (RHONN) trained with an Extended Kalman Filter (EKF) based algorithm. Applicability is shown using real-time test results for linear induction motors. Also, a Lyapunov analysis is added in order to prove the semi-globally uniformly ultimately boundedness (SGUUB) of the proposed neural identifier-control scheme.

[1]  Jianbin Qiu,et al.  New approach to delay-dependent H ∞ filtering for discrete-time Markovian jump systems with time-varying delay and incomplete transition descriptions , 2013 .

[2]  S. Haykin.  Kalman Filtering and Neural Networks , 2001 .

[3]  Sepp Hochreiter,et al.  The Vanishing Gradient Problem During Learning Recurrent Neural Nets and Problem Solutions , 1998, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[4]  Hamid Reza Karimi,et al.  New results on H∞ dynamic output feedback control for Markovian jump systems with time‐varying delay and defective mode information , 2014 .

[5]  J. Grizzle,et al.  The Extended Kalman Filter as a Local Asymptotic Observer for Nonlinear Discrete-Time Systems , 1992, 1992 American Control Conference.

[6]  Jose Egidio Azzaro,et al.  Sliding Mode Controller with Neural Network Identification , 2015, IEEE Latin America Transactions.

[7]  Simon Haykin,et al.  Neural Networks and Learning Machines , 2010 .

[8]  H. Karimi,et al.  Quantized ℋ∞ Filtering for Continuous‐Time Markovian Jump Systems with Deficient Mode Information , 2015 .

[9]  Alma Y. Alanis,et al.  Discrete-time neural identifier for electrically driven nonholonomic mobile robots , 2011, The 2011 International Joint Conference on Neural Networks.

[10]  El-Kebir Boukas,et al.  Deterministic and Stochastic Time-Delay Systems , 2002 .

[11]  Hamid A. Toliyat,et al.  Handbook of Electric Motors , 2004 .

[12]  Martin T. Hagan,et al.  Neural network design , 1995 .

[13]  Peng Shi,et al.  Output tracking control for fuzzy delta operator systems with time-varying delays , 2015, J. Frankl. Inst..

[14]  Katsuhiko Ogata,et al.  Discrete-time control systems , 1987 .

[15]  Hamid Reza Karimi,et al.  Filtering design for two-dimensional Markovian jump systems with state-delays and deficient mode information , 2014, Inf. Sci..

[16]  Wen Yu,et al.  Discrete-Time Sliding-Mode Control Based on Neural Networks , 2006, ISNN.

[17]  Edgar N. Sánchez,et al.  Decentralized neural block control for an industrial PA10-7CE robot arm , 2011, The 2011 International Joint Conference on Neural Networks.

[18]  George N. Saridis.  Advances in automation and robotics , 1985 .

[19]  Stefano Di Gennaro,et al.  Discrete time sliding mode control with application to induction motors , 2008, Autom..

[20]  Vladimir Kvrgic,et al.  Robust control of singular systems with time delay. Part I: Continuous time case , 2013, 2013 European Control Conference (ECC).

[21]  Magdi S. Mahmoud.  Switched Time-Delay Systems: Stability and Control , 2010 .

[22]  Eduardo A. B. da Silva,et al.  Digital Signal Processing: System Analysis and Design , 2002 .

[23]  Shumin Fei,et al.  Output tracking for nonlinear discrete-time systems via fuzzy control approach , 2015, J. Frankl. Inst..

[24]  Manolis A. Christodoulou,et al.  Adaptive Control with Recurrent High-order Neural Networks , 2000, Advances in Industrial Control.

[25]  Tsung-Chih Lin,et al.  Uncertain nonlinear time-delay system adaptive fuzzy PI sliding tracking control , 2014, 2014 CACS International Automatic Control Conference (CACS 2014).

[26]  Alexander G. Loukianov,et al.  Discrete-time neural block control for a doubly fed induction generator , 2011, The 2011 International Joint Conference on Neural Networks.

[27]  Hamid Reza Karimi,et al.  Model approximation for two-dimensional Markovian jump systems with state-delays and imperfect mode information , 2015, Multidimens. Syst. Signal Process..

[28]  Li Fu,et al.  The Research Survey of System Identification Method , 2013, 2013 5th International Conference on Intelligent Human-Machine Systems and Cybernetics.

[29]  Alexander G. Loukianov,et al.  Discrete-Time High Order Neural Control - Trained with Kaiman Filtering , 2010, Studies in Computational Intelligence.

[30]  Chih-Lyang Hwang,et al.  Fuzzy Neural-Based Control for Nonlinear Time-Varying Delay Systems , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[31]  Edgar N. Sanchez,et al.  Neural identification and control of a linear induction motor using an /spl alpha/ - /spl beta/ model , 2003, Proceedings of the 2003 American Control Conference, 2003..

[32]  Alexander G. Loukianov,et al.  Real-time implementation of a neural block control using sliding modes for induction motors , 2014, 2014 World Automation Congress (WAC).

[33]  Hao Xu,et al.  Neural Network-Based Finite Horizon Stochastic Optimal Control Design for Nonlinear Networked Control Systems , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[34]  Rolf Isermann,et al.  Identification of Dynamic Systems: An Introduction with Applications , 2010 .

[35]  Jian Li,et al.  Delay-dependent stability control for power system with multiple time-delays , 2016 .

[36]  钟 庆昌.  Robust Control of Time-delay Systems , 2006 .

[37]  Alma Y. Alanis,et al.  RHONN identifier for unknown nonlinear discrete-time delay systems , 2015, 2015 IEEE International Autumn Meeting on Power, Electronics and Computing (ROPEC).

[38]  Niels Kjølstad Poulsen,et al.  Neural Networks for Modelling and Control of Dynamic Systems: A Practitioner’s Handbook , 2000 .

[39]  Yoshua Bengio,et al.  Learning long-term dependencies with gradient descent is difficult , 1994, IEEE Trans. Neural Networks.

[40]  Sun Yi,et al.  Time-Delay Systems: Analysis and Control Using the Lambert W Function , 2010 .

[41]  Karel J. Keesman,et al.  System Identification: An Introduction , 2011 .

[42]  Jorge Rivera,et al.  DISCRETE-TIME SLIDING MODE CONTROL OF AN INDUCTION MOTOR , 2002 .

[43]  Yusheng Zhou,et al.  A robust optimal trajectory tracking control for systems with an input delay , 2016, J. Frankl. Inst..

[44]  Alma Y. Alanis,et al.  Neural identifier for unknown discrete-time nonlinear delayed systems , 2015, Neural Computing and Applications.

[45]  Jacek F. Gieras,et al.  Linear induction drives , 1993 .