Gaussian process model based predictive control

Gaussian process models provide a probabilistic non-parametric modelling approach for black-box identification of non-linear dynamic systems. The Gaussian processes can highlight areas of the input space where prediction quality is poor, due to the lack of data or its complexity, by indicating the higher variance around the predicted mean. Gaussian process models contain noticeably less coefficients to be optimized. This paper illustrates possible application of Gaussian process models within model-based predictive control. The extra information provided within Gaussian process model is used in predictive control, where optimization of control signal takes the variance information into account. The predictive control principle is demonstrated on control of pH process benchmark.

[1]  Dale E. Seborg,et al.  Adaptive nonlinear control of a pH neutralization process , 1994, IEEE Trans. Control. Syst. Technol..

[2]  Tor Arne Johansen,et al.  Non-linear predictive control using local models-applied to a batch fermentation process , 1995 .

[3]  M. Morari,et al.  Stability of model predictive control with mixed constraints , 1995, IEEE Trans. Autom. Control..

[4]  Katarina Kavsˇek-Biasizzo,et al.  Fuzzy predictive control of highly nonlinear pH process , 1997 .

[5]  Geoffrey E. Hinton,et al.  Evaluation of Gaussian processes and other methods for non-linear regression , 1997 .

[6]  T. A. Badgwell,et al.  An Overview of Industrial Model Predictive Control Technology , 1997 .

[7]  Christopher K. I. Williams.  Prediction with Gaussian Processes: From Linear Regression to Linear Prediction and Beyond , 1999, Learning in Graphical Models.

[8]  T. Johansen,et al.  On transient dynamics, off-equilibrium behaviour and identification in blended multiple model structures , 1999, 1999 European Control Conference (ECC).

[9]  Paul M. Frank,et al.  Advances in control : highlights of ECC '99 , 1999 .

[10]  G. Martin,et al.  Nonlinear model predictive control , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[11]  Stephen J. Wright,et al.  Nonlinear Predictive Control and Moving Horizon Estimation — An Introductory Overview , 1999 .

[12]  J. Maciejowski,et al.  Soft constraints and exact penalty functions in model predictive control , 2000 .

[13]  S. Joe Qin,et al.  An Overview of Nonlinear Model Predictive Control Applications , 2000 .

[14]  Basil Kouvaritakis,et al.  Nonlinear predictive control : theory and practice , 2001 .

[15]  Roderick Murray-Smith,et al.  Gaussian process priors with ARMA noise models , 2001 .

[16]  Daniel Sbarbaro,et al.  Nonlinear adaptive control using non-parametric Gaussian Process prior models , 2002 .

[17]  Jan M. Maciejowski,et al.  Predictive control : with constraints , 2002 .

[18]  Carl E. Rasmussen,et al.  Derivative Observations in Gaussian Process Models of Dynamic Systems , 2002, NIPS.

[19]  Robert E. Young,et al.  Evolution of an Industrial Nonlinear Model Predictive Controller , 2002 .

[20]  C. Rasmussen,et al.  Gaussian Process Priors with Uncertain Inputs - Application to Multiple-Step Ahead Time Series Forecasting , 2002, NIPS.

[21]  Agathe Girard,et al.  A case based comparison of identification with neural network and Gaussian process models. , 2003 .

[22]  Gregor Gregorcic,et al.  Internal model control based on a Gaussian process prior model , 2003, Proceedings of the 2003 American Control Conference, 2003..

[23]  J. Sjöberg.  Neural networks for modelling and control of dynamic systems: M. Nørgaard, O. Ravn, N. K. Poulsen and L. K. Hansen. Springer-Verlag, London Berlin Heidelberg, 2000, pp. xiv+246 , 2004 .

[24]  Agathe Girard,et al.  Dynamic systems identification with Gaussian processes , 2005 .