Abstract
In this paper, a Long Short Term Memory (LSTM) based Self Tuning Regulator (STR) for trajectory tracking problem of nonlinear systems is proposed. In the STR, a Proportional Integral Derivative (PID) controller is used as an adaptive parametric controller. The system model is estimated at every time step since it is utilized in computing the system Jacobian, hence controller design involves an inherent system identification problem. In the proposed architecture, LSTM is employed for both system model estimation and for updating the parameters of the PID controller. Namely, the \(K_P\), \(K_I\) and \(K_D\) gains are computed at every time step by LSTM, so that a cost function which is obtained from tracking error is minimized. The performance of the proposed method has been evaluated on two different nonlinear systems by extensive simulations. Simulation results justify the success of the introduced control architecture.
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References
Bobál V, Böhm J, Fessl J, Machácek J (2005) Digital self-tunning controllers. Advanced textbooks in control and signal processing. Springer-Verlag, London, pp 5–137
Landau ID, Lozano R, M’Saad M, Karimi A (2011) Adaptive control. Algorithm, analysis and applications, 2nd edn. Springer, London, pp 193–407
Kemal U, Gülay ÖG (2017) Generalized self-tuning regulator based on online support vector regression. Neural Comput Appl 28(S1):775–801. https://doi.org/10.1007/s00521-016-2387-4
Astöm KS (1983) Theory and applications of adaptive control. Automatica (Journal of IFAC) 19(5):471–486. https://doi.org/10.1016/0005-1098(83)90002-X
Stoica P, Söderström T (1989) System identification. Prentice hall international series in systems and control engineering. Prentice Hall, Michigan
Hochreiter S, Schmidhuber J (1997) Long short-term memory. Neural Comput 9(8):1735–1780. https://doi.org/10.1162/neco.1997.9.8.1735
Zhou C, Sun C, Liu Z, Lau F (2005) A C-LSTM neural network for text classification. Cornell University, pp 1–10 arXiv:1511.08630
Liu G, Guo J (2019) Bidirectional LSTM with attention mechanism and convolutional layer for text classification. Elsever Neurocomputing 337:325–338. https://doi.org/10.1016/j.neucom.2019.01.078
Dong C, Zhang J, Zong C, Hattori M, Di H (2016) Character-based LSTM-CRF with radical-level features for chinese named entity recognition. Nat Lang Underst and Intelligent Appl, LNAI 10102:239–250. https://doi.org/10.1007/978-3-319-50496-4_20
Malhotra P, Ramakrishnan A, Anand G, Vig L, Agarwal P, Shroff G (2016) LSTM-based encoder-decoder for multi-sensor anomaly detection. Cornell University, pp 1–5 arXiv:1607.00148
Nicola F, Fujimoto Y, Oboe R (2018) A LSTM Neural network applied to mobile robots path planning, IEEE, Porto, pp 1–6, https://doi.org/10.1109/INDIN.2018.8472028
Ruslan F, Samad A, Zain Z, Adnan R (2013) Flood prediction using NARX neural network and EKF prediction technique: a comparative study. In: IEEE 3rd international conference on system engineering and technology, pp 1–6. https://doi.org/10.1109/ICSEngT.2013.6650171
KERAS library web site: (2021) https://keras.io/
Graves A (2012) Supervised sequence labelling with recurrent neural networks. Springer, Berlin, Heidelberg, pp 37–45
Analytics Vidhya web site: Pranjal Srivastava (2017) Essentials of deep learning : introduction to long short term memory, https://www.analyticsvidhya.com/blog/2017/12/fundamentals-of-deep-learning-introduction-to-lstm/
Colah github web site: Felix Gers, Fred Cummins, Santiago Fernandez, Justin Bayer, Daan Wierstra, Julian Togelius, Faustino Gomez, Matteo Gagliolo, Alex Graves (2015) Understanding LSTM Networks: http://colah.github.io/posts/2015-08-Understanding-LSTMs/
Duch W, Jankowski N (1999) Survey of neural transfer functions. Neural Comput Surv 2:163–213
Sak H, Senior A, Beaufays F (2018) Long short-term memory recurrent neural network architectures for large scale acoustic modeling. Cornell University, pp 1–5 arXiv:1402.1128
López D, Verai N, Pedraza L (2016) Analysis of multilayer neural network modeling and long short-term memory. World Acad Sci Eng Technol Int J Math Comp Sci 10(12):1–6. https://doi.org/10.5281/zenodo.1339748
Towards data science web site: Jae Duk Seo, Aidan Gomez (2018) [Back to Basics] Deriving Back Propagation on simple RNN/LSTM (feat. Aidan Gomez), https://towardsdatascience.com/back-to-basics-deriving-back-propagation-on-simple-rnn-lstm-feat-aidan-gomez-c7f286ba973d/
Golnaraghi F, Kuo B (2017) Automatic control systems, 9th edn. McGraw-Hill Education, United States of America, pp 2–223
Akhyar S, Omatu S (1993) Self-tuning PID control by neural networks. In: Proceedings of 1993 international joint conference on neural networks, IEEE, pp 2749–2752, https://doi.org/10.1109/IJCNN.1993.714292
Sung SW, Lee J, Lee IB (2009) Process identification and PID control. IEEE Press, Wiley, Singapore, pp 275–343
İplikçi S (2010) A comparative study on a novel model-based PID tuning and control mechanism for nonlinear systems. Int J Robust Nonlinear Control 20(13):1483–1501. https://doi.org/10.1002/rnc.1524
Uçak K, Günel GÖ (2019) An adaptive sliding mode controller based on online support vector regression for nonlinear systems. Soft Comput 24(6):4623–4643. https://doi.org/10.1007/s00500-019-04223-9
Borisson U, Wittenmark B (1974) An industrial application of a self tuning regulator. In: 4th IFAC/IFIP international conference on digital computer applications to process control. Lecture notes in economics and mathematical systems, Springer, Berlin, Heidelberg, Vol 93. pp 76–87, https://doi.org/10.1007/978-3-642-65796-2_7
Astöm KS, Borisson U, Ljung L, Wittenmark B (1977) Theory and applications of self-tuning regulators. Elsevier, Automatica 13(5):457–476. https://doi.org/10.1016/0005-1098(77)90067-X
Hagan MT, Demuth HB, De Jesus O (2002) An introduction to the use of neural networks in control systems. Int J Robust Nonlinear Control 12(11):959–985. https://doi.org/10.1002/rnc.727
Sanatel Ç, Günel GÖ (2020) Long short term memory based system identificationand adaptive control, Thesis (M.Sc.), İstanbul Technical University, Institute of Science and Technology, pp 63–78
Zribi A, Chtourou M, Djemel M (2015) A new PID neural network controller design for nonlinear processes. J Circuits Syst Comput 27(4):1–11. https://doi.org/10.1142/S0218126618500652
Staudemeyer RC, Morris ER (2019) Understanding LSTM a tutorial into long short-term memory recurrent neural networks. Cornell University, pp 1–42 arXiv:1909.09586
Alpaydın E (2004) Introduction to machine learning, The MIT Press Essential Knowledge series, pp 197–271
Shang W, Shengdun Z, Yajing S (2008) Adaptive PID controller based on online LSSVM identification. IEEE/ASME international conference on advanced intelligent mechatronics. pp 1–5, https://doi.org/10.1109/AIM.2008.4601744
Kravaris C, Palanki S (1988) Robust nonlinear state feedback under structured uncertainty. AIChE J 34(7):1119–1127
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Sanatel, Ç., Günel, G.Ö. Long Short Term Memory Based Self Tuning Regulator Design for Nonlinear Systems. Neural Process Lett 55, 3045–3079 (2023). https://doi.org/10.1007/s11063-022-10997-1
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DOI: https://doi.org/10.1007/s11063-022-10997-1