Skip to main content
SpringerLink
Log in

Introduction

  • Chapter
  • First Online:
Modelling and Control of Dynamic Systems Using Gaussian Process Models

Part of the book series: Advances in Industrial Control ((AIC))

  • 4142 Accesses

Abstract

The first chapter introduces GP models and provides a simple, illustrative example of modelling of a static mapping function. Next, a brief historical overview of developments in the field of GP models for dynamic systems identification is presented. The chapter continues with a discussion about the rationale and the relevance of using GP modelling for system identification and control design.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Krige, D.G.: A statistical approach to some basic mine valuation problems on the Witwatersrand. J. Chem., Metal. Min. Soc. S. Afr. 52(6), 119–139 (1951)

    Google Scholar 

  2. O’Hagan, A.: On curve fitting and optimal design for regression (with discussion). J. R. Stat. Soc. Ser. B (Methodol.) 40(1), 1–42 (1978)

    MATH  MathSciNet  Google Scholar 

  3. Neal, R.M.: Bayesian Learning for Neural Networks. Lecture Notes in Statistics. Springer, New York, NY (1996)

    Google Scholar 

  4. Rasmussen, C.E.: Evaluation of Gaussian processes and other methods for nonlinear regression. Ph.D. thesis, University of Toronto, Toronto (1996)

    Google Scholar 

  5. Gibbs, M.N.: Bayesian Gaussian processes for regression and classification. Ph.D. thesis, Cambridge University, Cambridge (1997)

    Google Scholar 

  6. Williams, C.K.I.: Prediction with Gaussian processes: from linear regression and beyond. In: Jordan, M. (ed.) Learning in graphical models, Nato Science Series D, vol. 89, pp. 599–621. Springer, Berlin (1998)

    Chapter  Google Scholar 

  7. Rasmussen, C.E., Williams, C.K.I.: Gaussian Processes for Machine Learning. MIT Press, Cambridge, MA (2006)

    Google Scholar 

  8. Shi, J.Q., Choi, T.: Gaussian process regression analysis for functional data. Chapman and Hall/CRC, Taylor & Francis group, Boca Raton, FL (2011)

    Google Scholar 

  9. MAC Multi-Agent Control: Probabilistic reasoning, optimal coordination, stability analysis and controller design for intelligent hybrid systems (2000–2004). Research Training Network, 5th EU framework

    Google Scholar 

  10. Johnson, R.A., Miller, I., Freund, J.E.: Probability and Statistics for Engineers, 8th edn. Pearson, Boston, MA (2011)

    Google Scholar 

  11. Rohatgi, V.K.: An Introduction to Probability Theory and Mathematical Statistics. Wiley, New York, NY (1976)

    Google Scholar 

  12. Bishop, C.M.: Pattern recognition and machine learning. Springer Science \(+\) Business Media (2006)

    Google Scholar 

  13. Suykens, J.A.K., Gestel, T.V., Brabanteer, J.D., Moor, B.D., Vandewalle, J.: Least Squares Support Vector Machines. World Scientific, Singapore (2002)

    Book  MATH  Google Scholar 

  14. Peterka, V.: Bayesian approach to system identification (chapter). Trends and Progress in System Identification, pp. 239–304. Pergamon Press, Oxford (1981)

    Google Scholar 

  15. Ljung, L.: System identification—Theory for the User, 2nd edn. Prentice Hall, Upper Saddle River, NJ (1999)

    Google Scholar 

  16. Deisenroth, M.P.: Efficient reinforcement learning using Gaussian processes. Ph.D. thesis, Karlsruhe Institute of Technology, Karlsruhe (2010)

    Google Scholar 

  17. Thompson, K.: Implementation of Gaussian process models for non-linear system identification. Ph.D. thesis, University of Glasgow, Glasgow (2009)

    Google Scholar 

  18. Gevers, M.: A personal view of the development of system identification, a 30-year journey through an exciting field. IEEE Control Syst. Mag. 26(6), 93–105 (2006)

    Article  Google Scholar 

  19. Girard, A., Rasmussen, C., Murray-Smith, R.: Gaussian process priors with uncertain inputs: Multiple-step ahead prediction. Tech. Rep. DCS TR-2002-119, University of Glasgow, Glasgow (2002)

    Google Scholar 

  20. Gregorčič, G., Lightbody, G.: Gaussian processes for modelling of dynamic non-linear systems. In: Proceedings of the Irish Signals and Systems Conference, pp. 141–147. Cork (2002)

    Google Scholar 

  21. Kocijan, J., Girard, A., Banko, B., Murray-Smith, R.: Dynamic systems identification with Gaussian processes. In: Troch, I., Breitenecker, F. (eds.) Proceedings of 4th IMACS Symposium on Mathematical Modelling (MathMod), pp. 776–784. Vienna (2003)

    Google Scholar 

  22. Wang, J., Fleet, D., Hertzmann, A.: Gaussian process dynamical models. Adv. Neural Inf. Process. Syst. 18, 1441–1448 (2005)

    Google Scholar 

  23. Babovic, V., Keijzer, M.: A Gaussian process model applied to prediction of the water levels in Venice lagoon. In: Proceedings Of The XXIX Congress Of International Association For Hydraulic Research, pp. 509–513 (2001)

    Google Scholar 

  24. Grašič, B., Mlakar, P., Božnar, M.: Ozone prediction based on neural networks and Gaussian processes. Nuovo cimento Soc. ital. fis., C Geophys. space phys. 29(6), 651–661 (2006)

    Google Scholar 

  25. Ko, J., Fox, D.: GP-Bayesfilters: Bayesian filtering using Gaussian process prediction and observation models. Auton. Robot. 27(1), 75–90 (2009)

    Article  Google Scholar 

  26. Deisenroth, M.P., Huber, M.F., Hannebeck, U.D.: Analytic moment-based Gaussian process filtering. In: Proceedings of the 26th Annual International Conference on Machine Learning, pp. 225–232. Montreal (2009)

    Google Scholar 

  27. Gregorčič, G., Lightbody, G.: Gaussian processes for internal model control. In: Rakar, A. (ed.) Proceedings of 3rd International PhD Workshop on Advances in Supervision and Control Systems, A Young Generation Viewpoint, pp. 39–46. Strunjan (2002)

    Google Scholar 

  28. Kocijan, J.: Gaussian process model based predictive control. Tech. Rep. DP-8710, Jozef Stefan Institute, Ljubljana (2002)

    Google Scholar 

  29. Murray-Smith, R., Sbarbaro, D.: Nonlinear adaptive control using nonparametric Gaussian process prior models. In: Proceedings of IFAC 15th World Congress. Barcelona (2002)

    Google Scholar 

  30. Kocijan, J., Murray-Smith, R.: Nonlinear predictive control with a Gaussian process model. In: Murray-Smith, R., Shorten, R. (eds.) Switching and Learning in Feedback Systems, pp. 185–200. Springer, Berlin (2005). Lecture Notes in Computer Science

    Chapter  Google Scholar 

  31. Ko, J., Klein, D.J., Fox, D., Haehnel, D.: Gaussian processes and reinforcement learning for identification and control of an autonomous blimp. In: Proceedings of the International Conference on Robotics and Automation, pp. 742–747. Rome (2007)

    Google Scholar 

  32. Deisenroth, M.P., Rasmussen, C.E.: PILCO: A model-based and data-efficient approach to policy search. In: Proceedings of the 28th International Conference on Machine Learning (ICML 2011). Bellevue, WA (2011)

    Google Scholar 

  33. Deisenroth, M.P., Rasmussen, C.E., Fox, D.: Learning to control a low-cost manipulator using data-efficient reinforcement learning. In: Proceedings of the International Conference on Robotics: Science & Systems (R:SS 2011). Los Angeles, CA (2011)

    Google Scholar 

  34. Juričić, D., Kocijan, J.: Fault detection based on Gaussian process model. In: Troch, I., Breitenecker, F. (eds.) Proceedings of the 5th Vienna Symposium on Mathematical Modeling (MathMod). Vienna (2006)

    Google Scholar 

  35. Serradilla, J., Shi, J.Q., Morris, J.A.: Fault detection based on Gaussian process latent variable models. Chem. Intel. Lab. Syst. 109(1), 9–21 (2011)

    Article  Google Scholar 

  36. Osborne, M.A., Garnett, R., Swersky, K., de Freitas, N.: Prediction and fault detection of environmental signals with uncharacterised faults. In: 26th AAAI Conference on Artificial Intelligence (AAAI-12). Toronto (2012)

    Google Scholar 

  37. Deisenroth, M.P., Turner, R.D., Huber, M.F., Hanebeck, U.D., Rasmussen, C.E.: Robust filtering and smoothing with Gaussian processes. IEEE Trans. Autom. Control 57(7), 1865–1871 (2012). doi:10.1109/TAC.2011.2179426

    Article  MathSciNet  Google Scholar 

  38. Deisenroth, M.P., Mohamed, S.: Expectation propagation in Gaussian process dynamical systems. Adv. Neural Info. Process. Sys. 25, 2618–2626 (2012)

    Google Scholar 

  39. Kocijan, J., Likar, B.: Gas-liquid separator modelling and simulation with Gaussian-process models. Simul. Model. Pract. Theory 16(8), 910–922 (2008)

    Article  Google Scholar 

  40. Likar, B., Kocijan, J.: Predictive control of a gas-liquid separation plant based on a Gaussian process model. Comput. Chem. Eng. 31(3), 142–152 (2007)

    Article  Google Scholar 

  41. Faul, S., Gregorčič, G., Boylan, G., Marnane, W., Lightbody, G., Connolly, S.: Gaussian process modeling of EEG for the detection of neonatal seizures. IEEE Trans. Biomed. Eng. 54(12), 2151–2162 (2007)

    Article  Google Scholar 

  42. Ažman, K., Kocijan, J.: Application of Gaussian processes for black-box modelling of biosystems. ISA Trans. 46, 443–457 (2007)

    Article  Google Scholar 

  43. Leith, D., Heidl, M., Ringwood, J.: Gaussian process prior models for electrical load forecasting. In: International Conference on Probabilistic Methods Applied to Power Systems, pp. 112–117 (2004)

    Google Scholar 

  44. Leithead, W., Zhang, Y., Neo, K.: Wind turbine rotor acceleration: identification using Gaussian regression. In: Proceedings of International conference on informatics in control automation and robotics (ICINCO). Barcelona (2005)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Systems and Control, Jožef Stefan Institute, Ljubljana, Slovenia

    Juš Kocijan

  2. Centre for Systems and Information Technologies, University of Nova Gorica, Nova Gorica, Slovenia

    Juš Kocijan

Authors
  1. Juš Kocijan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Juš Kocijan .

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Kocijan, J. (2016). Introduction. In: Modelling and Control of Dynamic Systems Using Gaussian Process Models. Advances in Industrial Control. Springer, Cham. https://doi.org/10.1007/978-3-319-21021-6_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-21021-6_1

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21020-9

  • Online ISBN: 978-3-319-21021-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation