Soft Computing

, Volume 19, Issue 12, pp 3665–3676 | Cite as

Adaptive least square control in discrete time of robotic arms

  • José de Jesús RubioEmail author


In this paper, the trajectory tracking problem of robotic arms in discrete time is considered. To solve this problem, an adaptive least square controller is proposed. The uniform stability of the tracking error and parameters error for the aforementioned controller is guaranteed by means of a Lyapunov-like analysis. The effectiveness of the proposed controller is verified by on-line simulations.


State-feedback control Adaptive least square Robotic arm Uniform stability 



The author is grateful with the editors and the reviewers for their valuable comments and insightful suggestions, which helped to improve this research significantly. The author thanks the Secretaría de Investigación y Posgrado, Comisión de Operación y Fomento de Actividades Academicas del IPN, and Consejo Nacional de Ciencia y Tecnología for their help in this research.


  1. Balaguer-Ballester E, Bouchachia H, Lapish CC (2013) Identifying sources of non-stationary neural ensemble dynamics. BMC Neurosci 14(Suppl 1):15Google Scholar
  2. Blazic S, Skrjanc I, Matko D (2003) Globally stable direct fuzzy model reference adaptive control. Fuzzy Sets Syst 139:3–33zbMATHMathSciNetCrossRefGoogle Scholar
  3. Bordignon F, Gomide F (2014) Uninorm based evolving neural networks and approximation capabilities. Neurocomputing 127:13–20CrossRefGoogle Scholar
  4. Brodka P, Saganowski S, Kazienko P (2013) Ged: the method for group evolution discovery in social networks. Soc Netw Anal Min 3:1–14CrossRefGoogle Scholar
  5. Buchachia A (2012) Dynamic clustering. Evolv Syst 3(3):133–134CrossRefGoogle Scholar
  6. Chen Z, Jagannathan S (2008) Generalized hamilton–jacobi–bellman formulation-based neural network control of affine nonlinear discrete-time systems. IEEE Trans Neural Netw 19(1):90–106CrossRefGoogle Scholar
  7. Dotschel T, Auer E, Rauh A, Aschemann H (2013) Thermal behavior of high-temperature fuel cells: reliable parameter identification and interval-based sliding mode control. Soft Comput 17:1329–1343CrossRefGoogle Scholar
  8. García-Cuesta E, Iglesias JA (2012) User modeling: through statistical analysis and subspace learning. Expert Syst Appl 39(5):5243–5250CrossRefGoogle Scholar
  9. Jagannathan S (2001) Control of a class of nonlinear discrete-time systems using multilayer neural networks. IEEE Trans Neural Netw 12(5):1113–1120MathSciNetCrossRefGoogle Scholar
  10. Jahed M, Farrokhi M (2013) Robust adaptive fuzzy control of twin rotor mimo system. Soft Comput 17:1847–1860CrossRefGoogle Scholar
  11. Lee M, Choi HS (2000) A robust neural controller for underwater robot manipulators. IEEE Trans Neural Netw 11(6):1465–1469CrossRefGoogle Scholar
  12. Lewis FL, Dawson DM, Abdallah CT (2004) Robot manipulator control theory and practice. ISBN: 0- 8247-4072-6Google Scholar
  13. Lughofer E (2012) Sigle pass active learning with conflict and ignorance. Evolv Syst 3:251–271CrossRefGoogle Scholar
  14. Lughofer E, Trawinski B, Trawinski K, Kempa O, Lasota T (2011) On employing fuzzy modeling algorithms for the valuation of residential premises. Inf Sci 181:5123–5142CrossRefGoogle Scholar
  15. Lughofer E (2011) Evolving fuzzy systems: methodologies. Advanced concepts and applications. Springer, BerlinCrossRefGoogle Scholar
  16. Maciel L, Lemos A, Gomide F, Ballini R (2012) Evolving fuzzy systems for pricing fixed income options. Evolv Syst 3:5–18CrossRefGoogle Scholar
  17. Marques Silva A, Caminhas W, Lemos A, Gomide F (2014) A fast learning algorithm for evolving neo-fuzzy neuron. Appl Soft Comput 14(B):194–209CrossRefGoogle Scholar
  18. Musial K, Kazienko P (2013) Social networks on the internet. World Wide Web 16:31–72CrossRefGoogle Scholar
  19. Perez-Cruz JH, Rubio JJ, Pacheco J, Soriano E (2014a) State estimation in MIMO nonlinear systems subject to unknown deadzones using recurrent neural networks. Neural Comput Appl. doi: 10.1007/s00521-013-1533-5
  20. Perez-Cruz JH, Chairez I, Rubio JJ, Pacheco J (2014b) Identification and control of a class of nonlinear systems with nonsymmetric deadzone using recurrent neural networks. IET Control Theory Appl 8(3):183–192MathSciNetCrossRefGoogle Scholar
  21. Perng J-W (2013) Limit-cycle analysis of dynamic fuzzy control systems. Soft Comput 17:1553–1561CrossRefGoogle Scholar
  22. Precup R-E, David R-C, Petriu EM, Preitl S, Radac M-B (2014) Novel adaptive charged system search algorithm for optimal tuning of fuzzy controllers. Expert Syst Appl 41:1168–1175CrossRefGoogle Scholar
  23. Pratama M, Anavatti SG, Angelov PP, Lughofer E (2014) Panfis: a novel incremental learning machine. IEEE Trans Neural Netw Learn Syst 25(1):55–68CrossRefGoogle Scholar
  24. Pratama M, Anavatti SG, Lughofer E (2014) GENEFIS: Towards An Effective Localist Network. IEEE Trans Fuzzy Syst. doi: 10.1109/TFUZZ.2013.2264938
  25. Rubio JJ (2014) Stable and optimal controls of a proton exchange membrane fuel cell. Int J Control. doi: 10.1080/00207179.2014.913201
  26. Rubio JJ, Angelov P, Pacheco J (2011) An uniformly stable backpropagation algorithm to train a feedforward neural network. IEEE Trans Neural Netw 22(3):356–366CrossRefGoogle Scholar
  27. Rubio JJ (2012) Modified optimal control with a backpropagation network for robotic arms. IET Control Theory Appl 6(14):2216–2225Google Scholar
  28. Rubio JJ, Zamudio Z, Pacheco J (2013) Proportional derivative control with inverse dead-zone for pendulum systems. Math Probl Eng 2013:1–9MathSciNetGoogle Scholar
  29. Rubio JJ (2014) Evolving intelligent algorithms for the modelling of brain and eye signals. Appl Soft Comput 14(B):259–268Google Scholar
  30. Rubio JJ, Perez-Cruz JH (2014) Evolving intelligent system for the modelling of nonlinear systems with dead-zone input. Appl Soft Comput 14(B):289–304Google Scholar
  31. Song R, Xiao W, Wei Q (2013) Multi-objective optimal control for a class of nonlinear time-delay systems via adaptive dynamic programming. Soft Comput 17:2109–2115CrossRefGoogle Scholar
  32. Skrjanc I, Blazic S, Matko D (2003) Model-reference fuzzy adaptive control as a framework for nonlinear system control. J Intell Robot Syst 36:331–347CrossRefGoogle Scholar
  33. Spong MW, Vidyasagar M (1989) Robot dynamics and control. Wiley, New YorkGoogle Scholar
  34. Sun F, Sun Z, Woo PY (2001) Neural network-based adaptive controller design of robotic manipulators with an observer. IEEE Trans Neural Netw 12(1):54–66CrossRefGoogle Scholar
  35. Tar JK, Rudas IJ, Bito JF, Preitl S, Precup RE (2010) Convergence stabilization by parameter tuning in robust fixed point transformation based adaptive control of underactuated MIMO systems, International joint conference on computational cybernetics and technical informatics, pp 407–412Google Scholar
  36. Trawinski B (2013) Evolutionary fuzzy system ensemble approach to model real estate market based on data stream exploration. J Univ Comput Sci 19(4):539–562 Google Scholar
  37. Wai RJ, Chen PC (2004) Intelligent tracking control for robot manipulator including actuator dynamics via tsk-type fuzzy neural network. IEEE Trans Fuzzy Syst 12(4):552–558CrossRefGoogle Scholar
  38. Yang F, Yuan R, Yi J, Fan G, Tan X (2013) Direct adaptive type-2 fuzzy neural network control for a generic hypersonic flight vehicle. Soft Comput 17:2053–2064CrossRefGoogle Scholar
  39. Yu W, Rubio JJ (2009) Recurrent neural networks training with stable bounding ellipsoid algorithm. IEEE Trans Neural Netw 20(6):983–991CrossRefGoogle Scholar
  40. Zhao D, Wang B, Liu D (2013) A supervised actor–critic approach for adaptive cruise control. Soft Comput 17:2089–2099CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Sección de Estudios de Posgrado e Investigación, ESIME AzcapotzalcoInstituto Politécnico NacionalMéxico D.F.México

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