Abstract
System states are often required to solve control-theory problems. Unfortunately, there are situations in which some or even all variables are not available from measurements, requiring them to be estimated a priori. Here, we used the paraconsistent annotated logic by 2-value annotations (PAL2v) to investigate the state estimation problem applied in the control of a Furuta pendulum. The PAL2v code blocks, labeled as paraconsistent artificial neural cells (PANC), allow designing models to handle contradictions and ambiguities. This study proposes to build estimators with a specific PAL2v cell, labeled PANC of learning by contradiction extraction (\(\mathrm {PANCL_{CTX}}\)), which derives or asymptotically integrates values depending on the selected output. Through \(\mathrm {PANCL_{CTX}}\), we built PAL2v estimators and filters, requiring low complexity mathematics, with good results when compared to standard methods.
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References
Bol’shev LN. Statistical estimator, in Hazewinkel. Encyclopedia of mathematics. Michiel: Springer; 2001.
Fan Y, Liu X. Two-stage auxiliary model gradient-based iterative algorithm for the input nonlinear controlled autoregressive system with variable-gain nonlinearity. Int J Robust Nonlinear Control. 2020;30:5492–509.
Deka B, Baishnab D. A noncausal linear prediction based switching median filter for the removal of salt and pepper noise. In: 2012 International conference on signal processing and communications (SPCOM), pp. 1–5. 2012.
Aravkin A, et al. Generalized Kalman smoothing: modeling and algorithms. Automatica. 2017;86:63–86.
Matsubara T, Moshnyaga VG, Hashimoto K. A low-complexity noise removal technique and its hardware implementation. In: TENCON 2010—2010 IEEE Region 10 conference, pp. 716–719. 2010.
Carvalho Junior A, et al. Rotary inverted pendulum identification for control by paraconsistent neural network. IEEE Access. 2021;9:74155–67.
Abe JM. Paraconsistent artificial neural networks: an introduction. Including sub-series lecture notes in artificial intelligence and lecture notes in bioinformatics, vol. 214, no. 1, pp. 942–8 (2004).
Silva Filho JI. Treatment of uncertainties with algorithms of the paraconsistent annotated logic. J Intell Learn Syst Appl. 2012;4(2):144–53.
Sarkar TT, Dewan L, Mahanta C. Real time swing up and stabilization of rotary inverted pendulum system. In: 2020 International conference on computational performance evaluation (ComPE), pp. 517–522 (2020).
Zabihifar SH, Yushchenko AS, Navvabi H. Robust control based on adaptive neural network for rotary inverted pendulum with oscillation compensation. Neural Comput Appl. 2020;32:14667–79.
Hazem ZB, Fotuhi MJ, Bingül Z. A comparative study of the joint neuro-fuzzy friction models for a triple link rotary inverted pendulum. IEEE Access. 2020;8:9066–49078.
Abe JM, Souza S. Paraconsistent artificial neural networks and aspects of pattern recognition. Abe J. (eds). Paraconsistent Intell Based Syst. 2015;94(1):207–31.
Abe JM, Nakamatsu K, Silva Filho JI. The decades of paraconsistent annotated logics: a review paper on some applications. Procedia Comput Sci. 2019;159(1):1175–81.
Akama S, Costa NCA. Why paraconsistent logics? Intell Syst Ref Libr. 2016;110(1):7–24.
Silva Filho JI, Lambert-Torres G, Abe JM. Uncertainty treatment using paraconsistent logic: introducing paraconsistent artificial neural networks. Front Artif Intell Appl 311 (2010)
Coelho MS, et al. Hybrid pi controller constructed with paraconsistent annotated logic. Control Eng Pract. 2019;84(1):112–4.
Garcia DV, et al. Analysis of Raman spectroscopy data with algorithms based on paraconsistent logic for characterization of skin cancer lesions. Vib Spectrosc. 2019;103(1):1–10.
Silva Filho JI, et al. Paraconsistent artificial neural network for structuring statistical process control in electrical engineering. Intell Syst Ref Libr. 2016;110:77–102.
Cruz C., et al. Application of paraconsistent artificial neural network in statistical process control acting on voltage level monitoring in electrical power systems. In: 18th International conference on intelligent system application to power systems (ISAP 2015), pp. 1–6 (2015)
Carvalho Junior A, et al. A study of paraconsistent artificial NEURALT cell of learning applied as PAL2V filter. IEEE Latin Am Trans. 2018;16(1):202–9.
Carvalho Junior A, et al. Paraconsistent logic approach for active noise reduction. J Mechatron Eng. 2020;3(1):2–8.
Ribeiro JC, et al. Paraconsistent analysis network for uncertainties treatment in electric power system fault section estimation. Int J Electr Power Energy Syst. 2021;134(107317):1–11.
Matlab, Kalman filter design, Mathworks Doc., The Mathworks Inc. 2019. https://www.mathworks.com/help/control/examples/kalman-filter-design.html.
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Carvalho, A., Justo, J.F., Angélico, B.A. et al. Paraconsistent State Estimator for a Furuta Pendulum Control. SN COMPUT. SCI. 4, 29 (2023). https://doi.org/10.1007/s42979-022-01427-z
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DOI: https://doi.org/10.1007/s42979-022-01427-z