Design and Analysis of Neural Network-based controllers for unknown systems

About the Project

Mathematical systems and control theory “represents an attempt to codify, in mathematical terms, the principles and techniques used in the analysis and design of control systems” [1]. It concerns itself with “the basic theoretical principles underlying the analysis of feedback and the design of control systems [and] differs from the more classical study of dynamical systems in its emphasis on inputs (or controls) and outputs (or measurements)” [2].

Control systems and feedback loops are ubiquitous in science and engineering, and arise in traditional areas from aerospace control, manufacturing and process control, through to robotics, electrical power systems, systems biology, and therapeutics. The modern study of control systems traces its roots back to the industrial revolution and the principles of feedback control are at the heart of the flyball governor which was used regulate pressure in steam engines and facilitate their safe operation. The design and deployment of control systems has been fantastically successful [3]. Novel and emerging applications where control systems play an essential role range from the control of autonomous vehicles, smart grids and devices, through to epidemiology [4].

The present project seeks to combine classical model-based control theory with the emerging field of data-driven and machine-learning techniques. The project is motivated by other recent developments in the field, such [5-7]. Indeed, to quote [7]: “Recent progress in learning-based control has underscored the need to integrate formal control-theoretic guarantees—such as stability, robustness, safety, and planning—into nonlinear dynamical systems, particularly in high-dimensional, uncertain, or data-driven regimes. This need has prompted increasing interest in the intersection of machine learning and control, where rigorous methods can enhance the reliability and safety of autonomous systems, robotics, and reinforcement learning algorithms. Nonlinear control theory provides a unique design framework to ensure that controlled dynamical systems exhibit desired properties of interest.”

The present project will focus on the design and analysis of a suite of data-driven controllers for unknown nonlinear systems, blending state-of-the-art tools from nonlinear control theory with those from the field of machine learning. The project is mathematical, although there is scope for more theoretical or more applications-focused projects, which may contain a large numerical/computational component, depending on applicant and the overall direction of the research. Potential applications include to renewable energy conversion, biological systems including the spread of infectious diseases, or battery management. Please also note that prior experience of mathematical control theory is not a requirement --- strong mathematics knowledge and experience is essential, however. Perspective applicants are encouraged to contact the Supervisor before submitting their applications.

Academic qualifications

First degree (minimum 2:1 classification) in Mathematics or another cognate discipline, including Computer Science, Engineering, or Physics

English language requirement

IELTS score must be at least 6.5 (with not less than 6.0 in each of the four components). Other, equivalent qualifications will be accepted. Full details of the University’s policy are available online.

Essential attributes:

• Fundamental knowledge of Core applied mathematics (modelling, analysis, dynamical systems such as differential equations, linear algebra, numerical analysis and/or optimization)
• Confident and competent in learning new mathematical material
• Good written and oral communication skills
• Effective time management
• Strong motivation for further academic study
• Confidence and ability to work independently on an individual research project

Desirable attributes:

• Some knowledge and experience of:
  1. methods in machine learning/data science
  2. programming (Matlab/Python/C/C++/Fortran)
  3. mathematical systems and control theory.

APPLICATION CHECKLIST

• Completed application form
• CV
• 2 academic references, using the Postgraduate Educational Reference Form (download)
• Research project outline of 2 pages (list of references excluded). The outline may provide details about
  1. Background and motivation of the project. The motivation, explaining the importance of the project, should be supported also by relevant literature. You can also discuss the applications you expect for the project results.
  2. Research questions or objectives.
  3. Methodology: types of data to be used, approach to data collection, and data analysis methods.
  4. List of references.

The outline must be created solely by the applicant. Supervisors can only offer general discussions about the project idea without providing any additional support.

• Statement no longer than 1 page describing your motivations and fit with the project.
• Evidence of proficiency in English (if appropriate)

To be considered, the application must use

• the advertised title as project title

For informal enquiries about this PhD project, please contact c.guiver@napier.ac.uk

PhD Start Date: October 2026

Funding Notes

International applicants should note that visa application costs and the NHS health surcharge are additional costs to be taken into consideration, and successful applicants will need to cover these expenses themselves.