The School of Mathematics at the University of Birmingham, in collaboration with The Modelling & Simulation group at P&G Newcastle Technical Centre is offering a PhD vacancy on developing a Multi-input Multi-output Model-Based Controller that integrates a combination of mechanistic/empirical relationships. Household Care P&G is working on developing the control operation for a complex process with formulated products. The key of objectives of the project are:

• Develop a parameter selection algorithm for automatically including the most important input variables in non-linear models of different forms.
• Develop a generic non-linear function and systematic approach that reduces lack of fit (vs. multivariate polynomial functions) when regressing large-domain multivariate empirical data in specific formulated products systems (e.g. non-linear regression, Multivariate Adaptive Regression Splines, etc), where especial care should be taken on capturing the effects of the interactions between different variables. Here, it is important that a single non-linear function can describe well the system across a large domain of inputs (one of the key current challenges when using polynomial models).
• The non-linear empirical models will be combined with mechanistic non-linear models that describe the key transformations that we are to control in our process. The parameter selection algorithm should also work in these combined models.
• Develop a Multi-input Multi-output Model Based Controller that uses a combination of fixed and real-time sensed inputs together with a set of success criteria metrics in conjunction with the final non-linear system model to deliver accurate control of a multi-output process that involves formulated products. The controller will optimize real-time approximately 10 different outputs, which are intercorrelated so that the process performance always delivers optimum performance and cost irrespective of the specific inputs. The algorithm will learn from outputs feedback so that it can automatically improve over time.

We are looking for an applied mathematics candidate with a passion for optimization/regression/control areas. The candidate will spend a large portion of the PhD based at Newcastle Technical Centre in order to access data and methods key to his/her project. This will also allow the candidate to access a broad range of technical and interpersonal skills trainings.

Funding Notes:
This project will be jointly funded by Procter and Gamble, and a School-allocated Doctoral Training Account. A first class (or predicted first class) degree or masters distinction in Mathematics or closely-related subject is essential. It would be strongly preferred if the candidate could start in January 2019, however applications to commence studies later will be considered.

In your application (via the University of Birmingham online PhD application system), please indicate that you are interested in the joint P&G-Mathematics studentship in the Research Statement.

References
https://arxiv.org/abs/1810.01692