EPSRC-funded Project:
Modern Statistical Approaches to off-equilibrium modelling
for nonlinear system control
R. Murray-Smith (PI),
D. M. Titterington, K.
J. Hunt
University of Glasgow
Publications from the project to date:
- Gray, G., R. Murray-Smith, K. Thomson and D. J. Murray-Smith (2003). Investigation
of Gaussian process modelling applied to laboratory equipment. Technical
Report TR-2003-151. University of Glasgow, Scotland, UK.
- Kamnik, R., J. Q. Shi, R. Murray-Smith and T. Bajd. Nonlinear modelling
of FES-supported standing up in paraplegia for selection of feedback sensors.
Technical Report TR-2003-150. University of Glasgow, Scotland, UK, July 2003.
pdf
- R. Murray-Smith, B. Pearlmutter, Transformations of Gaussian Process
priors, DCS
Technical Report TR-2003-149, Department of Computing Science, Glasgow University,
June, 2003.
pdf
- J. Williamson, R. Murray-Smith, Dynamics and probabilistic text entry,
DCS
Technical Report TR-2003-147, Department of Computing Science, Glasgow University,
June, 2003. pdf
- A. Girard, R. Murray-Smith, Learning a Gaussian Process prior model with
uncertain inputs,
DCS Technical Report TR-2003-144, Department of Computing Science, Glasgow
University, June, 2003. pdf
- Murray-Smith, R, Sbarbaro, D., Rasmussen,C.E., Girard, A., Adaptive,
Cautious, Predictive control with Gaussian Process priors, International
Symposium on System Identification, IFAC, Rotterdam, 2003. pdf
- D. Sbarbaro, R. Murray-Smith, Self-tuning control of non-linear systems
using Gaussian process prior models,
DCS Technical Report TR-2003-143, Department
of Computing Science, Glasgow University, May
2003. pdf
- A case based comparison of identification with neural networks and Gaussian
Process models, Kocijan,J. Banko,B. Likar,B. Girard,A. Murray-Smith,R.
Rasmussen,C.E., IFAC International Conference on Intelligent Control Systems
and Signal Processing Faro, Portugal, April 08-11, 2003, International Federation
of Automatic Control.
- Dynamic systems identification with Gaussian Processes, Kocijan,J.
Girard,A. Banko,B. Murray-Smith,R., 4th Mathmod conference, Vienna, Int. Association.
for Mathematics and Computers in Simulation, 2003.
- Murray-Smith, R., R. Shorten and D. Leith (2002). Nonparametric models
of nonlinear dynamics. In: IEE Workshop of Nonlinear and Non-Gaussian
signal processing -N2SP, Peebles (C. Cowan, Ed.).
- J. Williamson, R. Murray-Smith, Audio feedback for gesture recognition,
DCS Technical Report TR-2002-127, Department
of Computing Science, Glasgow University, Dec.
2002. pdf
- E. Solak, R. Murray-Smith, W.E. Leithead, D.J. Leith, and C.E. Rasmussen,
Derivative observations in Gaussian Process models of dynamic systems,
NIPS 15, Vancouver, Canada, MIT Press, 2003. ps
pdf
- A. Girard, C., Rasmussen, J. Quinonero Candela, and R. Murray-Smith, Gaussian
Process Priors With Uncertain Inputs – Application to Multiple-Step Ahead
Time Series Forecasting, NIPS 15, Vancouver, Canada, MIT Press, 2003.
ps pdf
- A.
Girard, C. Rasmussen and R. Murray-Smith, Multiple-step ahead prediction
for non linear dynamic systems - a Gaussian Process treatment with propagation
of the uncertainty, DCS Technical Report TR-2002-119, 2002. pdf
- J.Q Shi, R. Murray-Smith, D. M. Titterington, Bayesian
Regression and Classification Using Mixtures of Multiple Gaussian Processes,
International Journal of Adaptive Control and Signal Processing, Volume 17,
Number 2, pp1 149-161, 2003. pdf
- D.J. Leith, W.E. Leithead, E. Solak, R. Murray-Smith, Divide & Conquer
Identification: Using Gaussian Process Priors to Combine Derivative & Non-Derivative
Observations in a Consistent Manner, Conference Decision and Control,
Las Vegas, 2002.
- A.
Girard, C. Rasmussen and R. Murray-Smith, Multiple-step ahead prediction
for non linear dynamic systems - a Gaussian Process treatment with propagation
of the uncertainty, DCS Technical Report TR-2002-119, 2002. pdf
- J.Q.
Shi, R. Murray-Smith, D.M. Titterington, Birth-death MCMC methods for mixtures
with an unknown number of components, DCS Technical Report TR-2002-117,
2002. pdf
- J.Q.
Shi, R. Murray-Smith, D.M. Titterington, Bayesian Regression and Classification
Using Mixtures of Gaussian Processes, DCS Technical Report TR-2002-114/Dept.
Statistics Tech. Report 02-8, 2002. pdf
- J.Q.
Shi, R. Murray-Smith, and D.M. Titterington, Hierarchical Gaussian process
mixtures for regression, DCS Technical Report TR-2002-107/Dept. Statistics
Tech. Report 02-7, 2002. pdf
- R. Murray-Smith, D. Sbarbaro, Nonlinear Adaptive
Control using non-parametric Gaussian Process prior models, International
Federation of Automatic Control, 15th IFAC Triennial World Congress, Barcelona,
2002. pdf
- R. Murray-Smith, A. Girard, Gaussian Process priors
with ARMA noise models, Irish Signals and Systems Conference, p147-153,
Maynooth, 2001.
Project Goals:
This project aims to develop modern statistical theory and methodology to
improve the performance and interpretability of the multiple-model approach
to modelling and control of dynamic systems in engineering. (Concentrating on
computationally-intensive methods such as Gaussian Process priors, or the use
of Markov Chain Monte Carlo samplers). The primary application will be in rehabilitation
engineering, where improved modelling and control methods are needed. Further
test cases will be provided by aerospace engineering and automotive engineering
problems. The work will link into existing research projects in the departments
of Mechanical and Aerospace
Engineering at Glasgow University, as well as the research labs of SINTEF
in Norway, and DaimlerChrysler in Germany.
The overall aims of the project are as follows:
1. To investigate statistical weaknesses in models fitted according to classical
approaches to transient (off-equilibrium) regimes in nonlinear plants, and to
develop improved methods for state-dependent estimates of uncertainty which
will lead to more robust control law development.
2. To develop new algorithms and interpretation tools based on the theoretical
developments in part 1, and to implement these algorithms in MATLAB. The basic
routines will be made available over the world-wide web.
3. To apply and validate the methods applicability to modelling and control
in the target domain of rehabilitation engineering. We expect significant performance
gains, as well as improved understanding of the physical systems under investigation.
Further results will be obtained in automotive and aeronautical examples.
This project runs from April 1st, 2000-March 31st 2003.
Project Research Staff
- Jian Qing Shi worked on
the project until August 2002 as a post-doctoral Research Fellow.
- John
Williamson is a Research Assistant on the project from August-November
2002.
- Roman Kamnik of the
University of Ljubljana has cooperated intensively with the work on modelling
and F.E.S.
- Gary Gray joined
the project from November-March.
Ongoing work
The project will be to discuss the problems of heterogeneity and the implementation
by a mixture model of Gaussian processes (Shi et al. 2001b). The main idea is
to define a hierarchical models for a dataset based on repeated experiments
involving similar objects and processes: a lower-level basic model is defined
to fit the data corresponding to each replication (i.e. within a group) separately;
and a higher-level model is defined to model the heterogeneity among different
replications (groups). We applied the mixture of Gaussian processes model to
several practical projects in system control. In one application we analyzed
the data related to functional electrical stimulation assisted standing-up manoeuvres
by paraplegic patients. In the case of standing up, the knee-joint extensor
muscles, the quadriceps group, are stimulated by two surface electrodes on each
leg. To use the supportive force information, which is considered to be a potential
cource of feedback, we need a model that relates the supportive forces and the
output trajectory. The mixtures of Gaussian processes model has been used to
build the model very successfully, compared to previous engineering approaches;
the details are presented in (Kamnik et al. 2003). (R. Kamnik is based in Slovenia,
but was a visiting scientist in Mechanical Engineering, with Prof. Hunt, when
this work started).
Please send general inquiries to:
Roderick Murray-Smith, rod@dcs.gla.ac.uk
Postal address:
Department of Computing Science,
Glasgow University
Glasgow G12 8QQ
Scotland