PhD: Safe Machine Learning for Nonlinear Control from Theory to Experiment

PhD: Safe Machine Learning for Nonlinear Control from Theory to Experiment

Quick Decision

Strong but verify fit. This is a specific 3.5-year EPSRC Doctoral Landscape Award project at the University of Sheffield that joins learned nonlinear-system models to stability and safety analysis, then compares them with established control routes in simulation and on a Furuta pendulum. It suits research interests at the intersection of nonlinear control, system identification, machine learning, optimization and formal verification. The University listing describes tuition, a UKRI-rate stipend and a project research grant. The important condition is that international recruitment is tightly limited across the DLA: Home-fee applicants are assessed first, and the University anticipates at most ten international places across the competition. Before investing heavily in the application, contact Dr Anton Selivanov and Dr Morgan Jones to confirm whether an overseas applicant can be considered for this particular project, and ask what hardware access and award terms are planned.

Research Problem and Doctoral Work

Advanced nonlinear controllers can manage uncertainty and disturbances, but they often rely on sufficiently accurate models. Real systems may include friction, delays, actuator limits and nonlinear interactions that are expensive to capture. Machine learning could reduce this modelling burden by extracting dynamics from operating data, but prediction quality on observed data is not a safety guarantee, especially in sparsely sampled parts of the state space. The project asks when learning can reduce control-design effort while preserving defensible stability and safety guarantees. The exact listing is available in the University project directory official project listing.

The advertised work has four connected parts:

1. Learn nonlinear dynamics and quantify uncertainty. Build models from operational data and characterise model error. Koopman-based models and neural networks are candidates, not predetermined choices.
2. Synthesize constrained controllers. Incorporate uncertainty into Control Lyapunov Functions (CLFs) and Control Barrier Functions (CBFs) to target stability and safety guarantees.
3. Verify and compare. Investigate neural-network verification, reachability analysis and mathematical error bounds. Assess data requirements, computational cost and the operating region where a guarantee holds. Compare against classical system identification followed by model-predictive control (MPC) or adaptive control across performance, data, computation, adaptability and safety. The project explicitly does not assume that ML is always better.
4. Validate in virtual and physical systems. Start with Quanser Interactive Labs digital-twin experiments, then test promising methods on physical systems such as a Furuta rotational inverted pendulum. The listing names friction, actuator nonlinearities, sensor noise, processing delays and disturbances as realistic effects to consider.

The progression from data to proof-oriented analysis to hardware is a strength, but it is also a broad research agenda. A feasible thesis will need to define one or two model classes, the assumptions used to bound error, the state/input domain covered by formal guarantees, and a manageable set of baselines. A successful pendulum demonstration would validate a defined experimental setup; it would not by itself prove safety for aircraft, autonomous robots or energy systems.

School, Programme and Field Context

The degree-awarding institution is the University of Sheffield, with the project based in its School of Electrical and Electronic Engineering. No external employer, joint award or separate host institution is specified. The University's REF 2021 Faculty of Engineering submission was ranked eighth for research quality and reported 96% of its research in the top two quality categories. This submission combined six engineering departments and the Advanced Manufacturing Research Centre, so it is a dated Faculty-level signal rather than an EEE-specific ranking (REF results).

The School's Control and Systems Engineering research theme describes work in robust and nonlinear control, MPC and dynamic optimization, model identification, learning-based control and safety/stability certificates. The School also documents a Control, Monitoring and Systems Engineering University Technology Centre established with Rolls-Royce, with research in control architecture, control-law design, monitoring and diagnostics. The Diamond Electronics and Control teaching lab lists Quanser servo systems and instrumentation. These pages show relevant surrounding expertise and infrastructure; they do not confirm a project placement, industrial collaboration, or access to a specific instrument (control research theme, Rolls-Royce Centre, Electronics and Control Lab).

The advertisement specifies a 3.5-year funded award and an October 2027 start. Sheffield's general research-degree rules say most full-time PhDs have a 3–4-year fee-paying period and the offer letter determines the exact registration period. The project notice does not separately set out mode of study or a detailed training schedule. The University's EEE research-degree English table lists IELTS 6.5 overall with at least 6.0 in each component, or an accepted equivalent; confirm applicable waiver and evidence rules with admissions (registration guidance; EEE English requirements).

Supervisor and Lab Assessment

Dr Morgan Jones is a Lecturer in Machine Learning and Control Theory. His profile lists dynamic programming, reinforcement learning, Hamilton–Jacobi–Bellman (HJB) equations, nonlinear-system analysis, reachable and invariant sets, and sum-of-squares methods. Dr Anton Selivanov's profile focuses on robust control for systems with delays and distributed-parameter dynamics, with attention to disturbances, sensor noise and uncertainty. This is a plausible complement for the project's learning-plus-guarantee objective: one strand concerns approximation, identification and nonlinear optimization; the other emphasizes robustness and proof (Morgan Jones profile; Anton Selivanov profile).

Recent work gives concrete points for a supervisor discussion:

• Jones and Peet show how an approximate HJB value-function error measured in a Sobolev norm can yield a bound on feedback-controller suboptimality. The bound is conditional on the paper's finite-horizon assumptions, may be loose and can grow with horizon; it is a performance result, not a safety certificate (paper).
• Jin, Nie and Jones handle state constraints using state augmentation and switching feedback linearisation. This connects to constraint-handling and implementation questions, but it does not certify a controller built from uncertain learned dynamics (paper).
• Machado and Jones's SINDy-SI work incorporates structural side information into sparse nonlinear-system identification. It is relevant to combining data and known physical structure, while also highlighting the limits of scarce or underdetermined data. The reported examples do not establish transfer to this project's physical plant (paper).
• Jones, Nie and Peet's approximate-value-function MPC work offers a recent model-based comparison route. Selivanov, Wang and Fridman's guaranteed-cost heat-equation paper illustrates rigorous robust-control analysis, although its PDE plant differs from the advertised pendulum system (MPC paper; robust-control paper).

The project itself promises virtual tests followed by physical validation. Quanser describes its Interactive Labs as virtual experiments based on physical-system models. Sheffield's public facility pages list general Quanser teaching equipment. Neither establishes the exact QLabs license, Furuta apparatus, technical support, computing allocation or student access schedule (Quanser product information). Confirm who will provide hardware supervision and what proportion of the research is expected to be mathematical, computational and experimental.

Research Direction and Field Outlook

Recent research is moving beyond training a controller that performs well on sampled trajectories. Neural control-barrier certificates are being learned for unknown systems; differentiable barriers are being combined with robot-control networks; and researchers are developing exact or sound verification and reachability methods for neural barriers (verified neural certificates; BarrierNet; neural reachability; exact ReLU verification). These lines support the project's central tension: expressive models can fit complex dynamics, while a useful guarantee must account for model error outside training points and remain computationally tractable.

This creates several defensible research questions for discussion: how to estimate uncertainty from operational data; how to incorporate physical side information; whether a Koopman representation or neural model is easier to bound; how CLF/CBF conditions change under input limits and delays; and how verification cost scales with the system and network size. These are possible angles implied by the advertised tasks, not promised thesis chapters. A strong evaluation should report assumptions, data coverage, operating domain, guarantee type, compute cost and failure cases, alongside conventional performance metrics.

UK labour-market evidence is broad. The Government's Digital and Technologies Jobs Plan reports that about 637,000 people worked for companies in frontier technologies in 2024, within a 1.33-million-person digital and technologies sector. EngineeringUK reports engineering and technology roles made up about 19% of UK jobs in 2025. These figures indicate an extensive engineering/AI ecosystem, not demand for this narrow specialty, a salary premium, or an employment outcome for this PhD (UK Government plan; EngineeringUK workforce analysis). Transferable capabilities may be relevant to control engineering, automation, robotics, aerospace, energy, applied machine learning and research, but career direction will depend on the student's work and wider experience.

Funding, Application and Living Cost

The project directory describes a fully funded award for 3.5 years, covering tuition fees, a maintenance stipend at the UKRI rate and a research grant for project-related costs. The current UKRI baseline for 2026/27 is £21,805 per year for a full-time stipend and £5,238 for the standard fee level. These are not confirmed 2027/28 award values; ask for the figures and the duration written in the offer. The project page does not give the research-grant amount or itemized eligible expenses (project listing; UKRI stipend and fee levels).

The international position needs careful reading. Sheffield's DLA application page says EPSRC permits at most 30% of awards to go to international candidates, Home candidates are considered in the first phase, and the University anticipates at most ten international places across the competition. It also says the University will pay the difference between Home and International fees for successful overseas candidates. This is scheme-level information and does not establish whether this particular project has an overseas slot or whether an individual will meet Home-fee criteria. The official project label saying students worldwide should therefore be read alongside the more detailed scheme rules (DLA application guidance).

The fixed deadline is 17:00 UK time on Wednesday 13 January 2027 for a 1 October 2027 start. Only the dedicated EPSRC DLA form is accepted. The form asks three DLA-specific questions, each with a 300-word maximum, and lets applicants select up to two projects in preference order. Sheffield strongly encourages discussion with project supervisors before submission. The page also directs applicants to read the DLA's recruitment statement on AI use and notes that the form asks candidates to disclose and explain any AI use in the application. Check the current instructions and disclose accurately if applicable.

For a present-day budget reference, Sheffield lists postgraduate shared-bathroom accommodation at £155.68–£173.32 per week on a 51-week contract, with utilities, contents insurance and internet included. The University's monthly guide items outside rent are groceries £155, transport £73, going out £60, eating out £45, clothes/shopping £33, mobile £15 and subscriptions £14 (a listed sum of £395). Compared with the 2026/27 stipend baseline of about £1,817 a month, these figures provide a rough planning view, not a promise of buying power. They are 2026/27 rates and may change before the start; private housing, visa and immigration health surcharge, travel and individual spending require separate estimates (2026/27 rent rates; University living-cost guide).

Applicant Fit and Preparation

No project-specific degree classification, mandatory software package or minimum years of experience is stated in the advertisement. The methods listed—nonlinear system identification, Koopman models, neural networks, CLFs/CBFs, reachability and MPC—describe the research, not formal entry prerequisites. Sheffield makes its academic admission assessment separately; obtain the School's view of degree equivalence and any English-language evidence required for the candidate's circumstances (DLA application guidance).

Useful application evidence would connect prior work to the actual research: a control or dynamical-systems problem; a model learned or identified from data; an optimization or verification task; coding and reproducibility; or an experiment where noise, mismatch or constraints mattered. The point is to explain the question, methods, decisions, results and limitations, not to claim mastery of every advertised method. The DLA form specifically asks why the research degree and topic are of interest, how previous knowledge and skills support doctoral work, and for an example of addressing a research question.

Next Actions and Questions to Verify

Before Applying

• Ask the supervisors whether this project will consider international candidates after the Home-fee phase and whether a project-level overseas allocation is available.
• Confirm the correct DLA form, project preference rules, the AI-use disclosure statement and current deadline instructions.
• Ask admissions what academic-equivalence and English-language evidence is required.
• Request written detail on 2027/28 stipend, tuition coverage, funding duration and research-grant scope.

At Interview

• Which model classes, uncertainty bounds and operating regions will be prioritized?
• How will neural/Koopman approaches be compared fairly with system identification plus MPC or adaptive control?
• Which Furuta system, QLabs license, physical-lab time, computing and technical support are planned?
• How will the theory, formal verification, baselines and experiments be prioritised within 3.5 funded years?

Before Accepting

• Confirm fee status, full fee-gap cover if applicable, award end date, registration period and progress milestones in writing.
• Clarify guaranteed hardware/software access, supervisor roles, training support and which costs the research grant may cover.

Evidence and Sources

Project and DLA application

• PhD project directory | The University of Sheffield
• How to apply for the EPSRC DLA | The University of Sheffield
• Fully funded EPSRC PhDs | The University of Sheffield

School, programme and research environment

• Registration and fees for research degrees | The University of Sheffield
• English language requirements for research degrees | The University of Sheffield
• Research Excellence Framework 2021 | Faculty of Engineering, The University of Sheffield
• Control and Systems Engineering | The University of Sheffield
• Rolls-Royce Control, Monitoring and Systems Engineering University Technology Centre | The University of Sheffield
• Electronics and Control Lab | The University of Sheffield
• Quanser Interactive Labs | Quanser
• Contact the University of Sheffield

Supervisors and recent original research

• Dr Morgan Jones | The University of Sheffield
• Dr Anton Selivanov | The University of Sheffield
• Bounding the Error of Value Functions in Sobolev Norm Yields Bounds on Suboptimality of Controller Performance
• Feedback Linearisation with State Constraints
• Sparse Identification of Nonlinear Dynamics with Side Information (SINDy-SI)
• Model Predictive Bang-Bang Controller Synthesis via Approximate Value Functions
• Guaranteed Cost Boundary Control of the Semilinear Heat Equation

Field frontier

• Formally Verified Neural Network Control Barrier Certificates for Unknown Systems
• BarrierNet: Differentiable Control Barrier Functions for Learning of Safe Robot Control
• Safe Reach Set Computation via Neural Barrier Certificates
• Exact Verification of ReLU Neural Control Barrier Functions

Funding and living costs

• Guidance for training grant holders | UKRI
• Living costs | The University of Sheffield
• Rents 2026/27 | The University of Sheffield

Career context

• Digital and Technologies Jobs Plan | UK Government
• Engineering and technology workforce | EngineeringUK