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


Final Project report: project report in pdf format

Publications from the project to date:


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

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