Skip to main content
SpringerLink
Log in

Design of an amplitude-bounded output feedback adaptive neural control with guaranteed componentwise performance

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

This paper proposes a methodology for the design of a mixed output feedback linear and adaptive neural controller that guarantees componentwise boundedness of the tracking error within an a priori specified compact polyhedron for an uncertain nonlinear system. The approach is based on the design of a robust invariant ellipsoidal set where the adaptive neural network (NN) control is modeled as an amplitude-bounded signal. A linear error observer is employed to recover the unmeasured states, and a linear gain controller is used to enforce the containment of the ellipsoidal set within the performance polyhedron. The analysis and design of the observer and linear controller is set up as an LMI problem. The linear observer/controller scheme is then augmented with a general adaptive NN element having the purpose of approximating and compensating for the unknown nonlinearities thus providing performance improvement. The only requirement for the adaptive control signals is that their amplitudes must be confined within pre-specified limits. For this purpose, a novel mechanism called adaptive control redistribution is introduced to manage the adaptive NN control confinement during the online operation. A numerical example is used to illustrate the design methodology.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Narendra KS, Annaswamy AM (1989) Stable adaptive systems. Prentice-Hall, Englewood Cliffs, NJ

    MATH  Google Scholar 

  2. Lewis FL, Yegildirek A, Liu K (1996) Multilayer neural-net robot controller with guaranteed tracking performance. IEEE Trans Neural Netw 7:388–399

    Article  Google Scholar 

  3. Sanner RM, Slotine JJ (1992) Gaussian networks for direct adaptive control. IEEE Trans Neural Netw 3:837–864

    Article  Google Scholar 

  4. Polycarpou MM (1996) Stable adaptive neural control scheme for nonlinear systems. IEEE Trans Automat Contr 41:447–451

    Article  MathSciNet  MATH  Google Scholar 

  5. Campa G, Fravolini ML, Seanor B, Napolitano MR, Del Gobbo D, Yu G, Gururajan S (2002) On-line learning neural networks for sensor validation for the flight control system of a B777 research scale model. Int J Robust Nonlinear Control 12(11):987–1007

    Article  MATH  Google Scholar 

  6. Cao C, Hovakimyan N (2007) Novel L1 neural network adaptive control architecture with guaranteed transient performance. IEEE Trans Neural Netw 18:1160–1171

    Article  Google Scholar 

  7. Tseng CS, Chen BS (2001) Multiobjective PID control design in uncertain robotic systems using neural network elimination scheme. IEEE Trans Syst Man Cybern Part A 31:632–644

    Article  Google Scholar 

  8. Yanga YS, Wang XF (2007) Adaptive H ∞ tracking control for a class of uncertain nonlinear systems using radial-basis-function neural networks. Neurocomputing 70:932–941

    Article  Google Scholar 

  9. Li HY, Wong YK, Chan WL, Tsang KM (2010) Synchronization of Ghostburster neurons under external electrical stimulation via adaptive neural network H ∞ control. Neurocomputing 74:230–238

    Article  Google Scholar 

  10. Campa G, Fravolini ML, Mammarella M, Napolitano MR (2011) Bounding set calculation for neural network based output feedback adaptive control systems. Neural Comput Appl 20:373–387

    Article  Google Scholar 

  11. Zhu Q, Fei S, Zhang T, Li T (2008) Adaptive RBF neural-networks control for a class of time-delay nonlinear systems. Neurocomputing 71:3617–3624

    Article  Google Scholar 

  12. Bechlioulis CP, Rovithakis GA (2008) Robust adaptive control of feedback linearizable MIMO nonlinear systems with prescribed performance. IEEE Trans Automat Contr 53:2090–2099

    Article  MathSciNet  Google Scholar 

  13. Herrmann G, Turner MC, Postlethwaite I (2007) Performance-oriented antiwindup for a class of linear control systems with augmented neural network controller. IEEE Trans Neural Netw 18:449–465

    Article  Google Scholar 

  14. Lian KY, Tu HW (2008) LMI-based adaptive tracking control for parametric strict-feedback systems. IEEE Trans Fuzzy Syst 16:1245–1258

    Article  Google Scholar 

  15. Patre PM, Mac Kunis W, Kaiser K, Dixon WE (2008) Asymptotic tracking for uncertain dynamic systems via a multilayer neural network feed forward and RISE feedback control structure. IEEE Trans Automat Contr 53:2180–2185

    Article  MathSciNet  Google Scholar 

  16. Xu H, Ioannou PA (2003) Robust adaptive control for a class of MIMO nonlinear systems with guaranteed error bounds. IEEE Trans Automat Contr 48:728–742

    Article  MathSciNet  Google Scholar 

  17. Kostarigka AK, Rovithakis GA (2011) Prescribed performance output feedback/observer-free robust adaptive control of uncertain systems using neural networks. Trans Syst Man Cybern Part B 41:1483–1494

    Article  Google Scholar 

  18. Ren B, Ge SS, Tee KP, Lee TH (2010) Adaptive neural control for output feedback nonlinear systems using a barrier Lyapunov function. IEEE Trans Neural Netw 21:1339–1345

    Article  Google Scholar 

  19. Fravolini ML, Campa G (2011) Design of a neural network adaptive controller via a constrained invariant ellipsoids technique. IEEE Trans Neural Netw 22:627–638

    Article  Google Scholar 

  20. Blanchini F (1999) Set invariance in control. Automatica 35:1747–1767

    Article  MathSciNet  MATH  Google Scholar 

  21. Boyd HS, Ghaoui E, Feron L, Balakrishnan V (1979) Linear matrix inequality in system and control theory. http://www.stanford.edu/~boyd/lmibook/lmibook.pdf

  22. Fravolini ML, Campa G, Napolitano MR (2011) Performance-oriented adaptive neural augmentation of an existing flight control system. IET Control Theory Appl 5:1819–1828

    Article  MathSciNet  Google Scholar 

  23. Zhanga H, Liao X (2005) LMI-based robust stability analysis of neural networks with time-varying delay. Neurocomputing 67:306–312

    Article  Google Scholar 

  24. Huang H, Feng G, Cao J (2008) An LMI approach to delay-dependent state estimation for delayed neural networks. Neurocomputing 71:2857–2867

    Article  Google Scholar 

  25. Shen Y, Li C (2008) LMI-based finite-time boundedness analysis of neural networks with parametric uncertainties. Neurocomputing 71:502–507

    Article  Google Scholar 

  26. Hovakimyan N, Nardi F, Calise AJ (2002) A novel error observer-based adaptive output feedback approach for control of uncertain systems. IEEE Trans Automat Contr 47:1310–1314

    Article  MathSciNet  Google Scholar 

  27. The MathWorks Inc., Robust Control Toolbox Users’s Guide (2009). http://www.mathworks.com/access/helpdesk/help/toolbox/

  28. Wang J, Patel V, Cao C, Hovakimyan N, Lavretsky E (2008) L1 adaptive neural network controller for autonomous aerial refueling with guaranteed transient performance. J Guid Control Dyn 31:182–193

    Article  Google Scholar 

  29. Lavretsky E (2009) Combined/composite model reference adaptive control. IEEE Trans Automat Contr 54:2692–2697

    Article  MathSciNet  Google Scholar 

  30. Patel V, Cao C, Hovakimyan N, Wise KA, Lavretsky E (2009) L1 adaptive controller for tailless unstable aircraft in the presence of unknown actuator failures. Int J Control 82:705–720

    Article  MathSciNet  MATH  Google Scholar 

  31. Herrmann G, Ge SS, Guo G (2005) Practical Implementation of a neural network controller in a hard disk drive. IEEE Trans Control Syst Technol 13:146–154

    Article  Google Scholar 

  32. Cao C, Hovakimyan N (2007) Guaranteed transient performance with L1 adaptive controller for systems with unknown time-varying parameters and bounded disturbances: Part I. In: Proceedings of American Control Conference, pp 3925–3930

  33. Kofman E (2005) Non conservative ultimate bound estimation in LTI perturbed systems. Automatica 41:1835–1838

    Article  MathSciNet  MATH  Google Scholar 

  34. Hao F, Chu T, Wang L, Huang L (2003) An LMI approach to persistent bounded disturbance rejection for uncertain impulsive. In: Proceedings of IEEE conference decision and control, pp 4068–4073

  35. Fravolini ML, Campa G (2011) Integrated design of a linear/neuro-adaptive controller in the presence of norm-bounded uncertainties. Int J Control 84:1664–1677

    Article  MathSciNet  MATH  Google Scholar 

  36. Valmorbida G, Tarbouriech S, Garcia G (2010) State feedback design for input-saturating quadratic systems. Automatica 46:1196–1202

    Article  MathSciNet  MATH  Google Scholar 

  37. Zhanga XM, Wu M, She JH, He Y (2005) Delay-dependent stabilization of linear systems with time-varying state and input delays. Automatica 41:1405–1412

    Article  Google Scholar 

  38. Park J, Sandberg IW (1991) Universal approximation using radial-basis-function networks. Neural Comput 3:246–257

    Article  Google Scholar 

  39. Lavretsky E, Hovakimyan N, Calise AJ (2003) Upper bounds for approximation of continuous-time dynamics using delayed outputs and feedforward neural networks. IEEE Trans Automat Contr 48:1606–1610

    Article  MathSciNet  Google Scholar 

  40. Liang Y, Huang GB, Saratchandran P, Sundararajan N (2006) A fast and accurate online sequential learning algorithm for feedforward networks. IEEE Trans Neural Netw 17:1411–1422

    Article  Google Scholar 

  41. He P, Jagannathan S (2007) Reinforcement learning neural-network-based controller for nonlinear discrete-time systems with input constraints. IEEE Trans Syst Man Cybern Part B 37:425–436

    Article  Google Scholar 

  42. Kawato M, Furukawa K, Suzuki R (1987) A hierarchical neural-network model for control and learning of voluntary movements. Biol Cybern 57:169–185

    Article  MATH  Google Scholar 

  43. Calise AJ, Hovakimyan N, Idan M (2001) Adaptive output feedback control of nonlinear systems using neural networks. Automatica 37:1201–1211

    Article  MathSciNet  MATH  Google Scholar 

  44. Chang YC, Yen HM (2005) Adaptive output feedback tracking control for a class of uncertain nonlinear systems using neural networks. IEEE Trans Syst Man Cybern Part B 35:1311–1316

    Article  Google Scholar 

  45. Selmic RR, Lewis FL (2002) Neural-network approximation of piecewise continuous functions: application to friction compensation. IEEE Trans Neural Netw 13:745–751

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Engineering, University of Perugia, Via G. Duranti No 93, 06125, Perugia, Italy

    Mario Luca Fravolini

  2. The Mathworks, 400 Continental Blvd, Suite, El Segundo, CA, 600-028, USA

    Giampiero Campa

Authors
  1. Mario Luca Fravolini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Giampiero Campa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mario Luca Fravolini.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fravolini, M.L., Campa, G. Design of an amplitude-bounded output feedback adaptive neural control with guaranteed componentwise performance. Neural Comput & Applic 25, 1313–1328 (2014). https://doi.org/10.1007/s00521-014-1612-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-014-1612-2

Keywords

Search

Navigation