## Problem description

System identification is concerned with estimating a dynamical model from paired input and output data. In particular, we are considering an electro-mechanical positioning system (EMPS), where a motor drives a small platform on a track between two points (a prismatic joint) [1]. These are ubiquitous in robotics and machine tool applications, but can be challenging to control when non-linearities such as friction are involved. Our goal is to estimate the inverse dynamical model (torque/force as a function of position, velocity and acceleration), outperforming the current least-squares baseline approach. More information on the electro-mechanical positioning system, including baseline, data and code, can be found at http://nonlinearbenchmark.org/.

The Bayesian Intelligent Autonomous Systems lab (BIASlab) is working on intelligent agents that perceive and act through Bayesian machine learning. We work with a principled technique for approximate inference, called variational free energy minimization, and apply it to discrete-time dynamical systems. For an introduction to this framework, see our toolbox ForneyLab. Currently, we are interested in system identification and would like to tackle the EMPS benchmark using our techniques.

## Student task description

We expect the student to familiarize him/her self with variational free
energy minimization and system identification. Your job will be to
program an agent to infer the dynamical parameters of the system from
given input-output data, and compare the agent to baseline methods. We
hope to include an *optimal design / active inference* experiment as
well, where the agent infers which inputs it should test to infer the
dynamics as fast as possible.

### Tasks:

Literature search over the intersection between Bayesian machine learning and nonlinear system identification.

Familiarize yourself with the difficulties of nonlinear system identification.

Understand the challenges of applying variational free energy minimization to nonlinear system identification.

Collaborate and discuss with researchers in BIASlab and the Control Systems group.

Implement an agent that infers dynamics in the system.

Experiment with the implementation and compare to baselines.

Analyze results and reflect on what has been achieved.

Write a report detailing the advantages and limitations of this approach.

### Supervision:

Weekly progress meetings with Maarten Schoukens and Wouter Kouw.

The student is expected to be prepared for meetings, preferably by writing reports that can be used to track progress.

All developed code and reports should be accessible via git to achieve efficient collaboration.

## Information

For more information go to the project page at TU/e Master Marketplace.

## References

[1]: Alexandre Janot, Maxime Gautier, and Mathieu Brunot. Data set and reference models of EMPS. In *2019 Workshop on Nonlinear System Identification Benchmarks, Eindhoven, The Netherlands, April 10-12, 2019*.