Model Predictive Control PhD | Adapting Optimization Effort to System Uncertainty

Model Predictive Control PhD | Adapting Optimization Effort to System Uncertainty

Quick Decision

Promising with material uncertainties. The project has a well-defined control problem: estimate uncertainty that may be hidden in system parameters, equipment behaviour or model mismatch, then adapt the computational effort used by repeated model predictive control (MPC) calculations while preserving feasibility and stability. The subject match is strong: both named supervisors work on predictive control, dynamic optimisation and aerospace systems, and Sheffield's Control Theory environment explicitly covers uncertainty-aware MPC and real-time optimisation. (Paul Trodden, Yuanbo Nie, Control and Systems Engineering)

The project funding notice describes a 3.5-year award covering full tuition, a UKRI-rate stipend and a project research grant. The current 2026/27 UKRI minimum stipend is £21,805 per year; the 2027/28 rate and the project's grant amount need confirmation. The EPSRC Doctoral Landscape Award (DLA) application deadline is 17:00 GMT on 13 January 2027, with a 1 October 2027 start date. (UKRI studentship guidance, DLA application rules)

The largest open issue is the Airbus Defence and Space collaboration. Public material names the partner, and a broader Sheffield research group lists Airbus among its industrial collaborators, but the available project information does not identify this student's partner team, workshare, placement, co-supervision, data or simulator access, or intellectual-property and publication terms. The target system, optimizer, test setup and quantitative success criteria are also not stated. Before applying, ask both supervisors for the project work package and written funding/eligibility details; do not treat the motivating rocket scenario or the potential application list as a confirmed experiment. (Sheffield research group collaborations, Airbus space equipment context)

Research Problem and Doctoral Work

The description uses a rocket landing on a floating platform to explain why a controller repeatedly updates decisions as fresh measurements arrive. Wind, changing equipment behaviour and limitations in the mathematical model can change what the controller knows. Under MPC, each update requires an online optimisation. A fixed solve frequency and accuracy setting can be poorly matched to the moment: a long solve can delay the next control action during rapidly changing conditions, while unnecessarily intensive calculations in predictable conditions consume computing power and energy.

The proposed research will develop optimisation algorithms that change their computational effort in response to uncertainty. When uncertainty is high, the controller is meant to prioritise a fast decision; when conditions are better understood, it can spend more effort seeking a higher-quality solution. The advertised tasks include estimating and quantifying uncertainty sources that are not directly measured—such as parameter changes, equipment/model mismatch and omitted physical effects—then using their likelihood and impact to set how demanding each optimisation calculation should be and what performance can safely be guaranteed. The work is intended to connect uncertainty estimation, optimisation and control decisions in one adaptive framework that keeps decisions feasible and the system stable.

This is a substantial coupled problem. Reducing solver effort may shorten feedback time but can worsen numerical solution quality or threaten constraint satisfaction. Improving numerical accuracy does not itself correct a wrong or incomplete physical model. A feasible study therefore needs to state which uncertainty is represented, which part of the computation is adapted, what “safe performance” means, and how feasibility and stability will be evaluated. The project description does not specify an estimator, uncertainty distribution, MPC architecture, optimizer, compute budget, plant/model, baseline or acceptance thresholds.

The rocket example is a motivating scenario, not a commitment to a rocket test. Spacecraft landing, hybrid-electric aircraft and urban air mobility are listed as possible application areas; none is confirmed as the project's actual test system. That distinction matters for evaluating feasibility: a mathematical/simulation study, real-time software evaluation and access to an industrial flight or spacecraft simulator are different scopes and should not be conflated.

School, Programme and Field Context

The degree-awarding institution named for this project is the University of Sheffield, and the academic home is its School of Electrical and Electronic Engineering. Its official contact page places the University in Sheffield, UK. (University contact details)

The University reports 82nd place globally and 14th in the UK in the QS World University Rankings 2027, and 104th globally and 12th in the UK in the Times Higher Education World University Rankings 2027. These are overall institutional results rather than rankings for control engineering or this project. The University's Faculty of Engineering reports 8th place for research quality in REF 2021 and a top-national rating for research environment; the REF result is faculty-level evidence and does not measure the named supervisors or this studentship individually. (University rankings, Faculty of Engineering research and REF context)

The relevant subject evidence is more specific: Sheffield's Control and Systems Engineering theme lists both Paul Trodden and Yuanbo Nie in its Control Theory group. It describes work on MPC and dynamic optimisation, robust/adaptive/learning-based control, real-time numerical optimisation, manageable computational complexity, and safety/stability under uncertainty. Aerospace is among the stated application areas. (Control and Systems Engineering)

Sheffield says full-time PhDs normally last 3–4 years, depending on funding and research scope. The project also lists training in research skills, project management, communication and career development, together with opportunities to attend international conferences and take part in public engagement. The specific modules, schedule and travel support are not stated. The project's stated 3.5 years of funding falls within this normal range, but the exact registration end date, thesis-writing period and any unfunded time must be checked in the offer. No joint degree or separate Airbus registration is stated. (Applying essentials for PhD study)

Supervisor and Lab Assessment

Dr Paul Trodden is a Senior Lecturer and Control Theme Lead. His profile describes research on constrained MPC, robust and adaptive MPC for uncertain or time-varying systems, computational tractability, stability and constraint-satisfaction guarantees, invariant sets and aerospace control including spacecraft trajectory optimisation, rendezvous and docking. (Paul Trodden profile)

Dr Yuanbo Nie works on numerical methods for dynamic optimisation, direct transcription and integrated-residual methods, optimisation-based control including MPC, solution guarantees and feasibility in nonlinear or uncertain systems, and aerospace control and simulation. His training and research experience span aerospace engineering and computational methods. (Yuanbo Nie profile)

Five recent original papers help show the technical environment while setting limits on what can be inferred:

• Li and Trodden's 2026 paper studies constrained output-feedback MPC under bounded disturbances and random actuator-channel packet loss. It develops conditions for bounded state-estimation error and compares MPC formulations with different feasibility properties. This is close to the project's estimation/feasibility concern, but its setting is linear and packet-loss based; it does not demonstrate uncertainty-conditioned solver-budget allocation. (Paper record)
• Trodden, Maestre and Ishii's 2026 paper gives sufficient conditions under which robust constraint or reachability guarantees cannot be achieved for certain constrained linear systems with bounded disturbances. It is a useful reminder that safety guarantees depend on disturbance assumptions and constraint geometry; it is not an adaptive controller or an uncertainty estimator. (Paper record)
• Nie and Kerrigan's 2025 paper introduces integrated-residual regularized direct collocation to improve solution reliability in challenging dynamic optimisation problems. It informs the numerical accuracy side of the trade-off, but does not establish online MPC latency or an adaptive stopping policy. (Paper record)
• Jones, Nie and Peet's 2024 paper combines approximate value functions with a receding-horizon strategy for a specialised input-affine, bang-bang optimal-control problem. It is an example of approximating optimisation within predictive control, not evidence that this project will use the same method. (Paper record)
• Ramesh, Kerrigan and Nie's 2024 paper studies numerical optimal-control formulations for tracking within a tolerance range, including regularisation for nonsmooth objectives. It shows how formulation choices can affect numerical solvers, but does not study uncertainty-aware computation allocation. (Paper record)

Together these papers provide relevant experience in estimation, constrained MPC, feasibility, numerical solution accuracy and optimisation formulations. They do not establish the proposed thesis method, a specific Airbus application or guaranteed outputs.

Sheffield's Control Theory theme is the clearest group-level fit. A separate Intelligent Systems, Decision and Control page lists Airbus among general industrial collaborators, and Airbus's own site describes its space-equipment work involving avionics, control, sensors, actuators and mission data. These sources make the named collaboration plausible in context but do not verify the role of Airbus Defence and Space in this studentship. The formal partner identity, technical team, student contact, work package, site visits or secondment, access to data/simulator, and IP/security/publication conditions remain questions for the supervisors. (Control Theory theme, broader group collaborations, Airbus space-equipment context)

For computational research, Sheffield's Research Software Engineering information says staff and students can use university HPC systems, with research students needing a supervisor to request access. This is evidence of a potential institutional route to computing; it is not a promise of access for this project or proof that batch HPC is suitable for real-time/embedded testing. Ask whether the research will use simulation, a hardware-in-the-loop platform, a flight/spacecraft simulator, a dedicated computer or only numerical benchmarks. (Research Software Engineering resources)

Funding, Application, and Living Cost

The project funding notice states that the award covers full tuition, a stipend at the UKRI rate, and a research grant for 3.5 years. UKRI's published minimum for 2026/27 is £21,805 per year (about £1,817 per month); this is a current benchmark, not a confirmed rate for the October 2027 start. The grant amount and eligible spending have not been published in the reviewed material. (UKRI training-grant guidance, UKRI doctoral training framework)

This is an EPSRC DLA competition, not a routine standalone PhD application. Sheffield requires its dedicated DLA form; standard PhD applications cannot substitute for it. The form asks three questions of up to 300 words each about motivation, relevant knowledge and skills, and a research example. Applicants can choose up to two relevant projects, are encouraged to contact supervisors, and should select the 1 October 2027 start date. Collaborative-project applications may be shared with the partner. The page also requires applicants to read the DLA AI-use statement and disclose/explain AI use in the application. The deadline is 17:00 UK time on Wednesday 13 January 2027. (How to apply for the EPSRC DLA)

International applicants face a real selection constraint: EPSRC limits international awards to 30% of DLA places; Sheffield anticipates at most 10 international places, considers Home candidates first, and says it will cover the Home/International fee difference for successful international candidates. This does not establish that this individual project will remain available to international applicants after the first phase. The applicant's Home fee status and final fee treatment need confirmation. (DLA international-applicant rules, UKRI training-grant eligibility guidance)

Sheffield's current student budget page lists monthly examples of £155 for groceries, £73 for transport, £60 for going out, £45 for takeaways/eating out, £33 for clothes/shopping, £15 for a mobile phone and £14 for subscriptions. Those listed categories total £395 and do not include housing or every possible cost. The University's 2026/27 postgraduate accommodation table lists shared-bathroom rooms on 51-week contracts at £155.68–£173.32 per week (£7,939.68–£8,839.32 total) and a studio at £240.38 per week (£12,259.38 total). Utilities, contents insurance and internet are included; the page says these prices were correct as of February 2026. Annualizing the 51-week contract totals across 12 months gives about £662–£1,022 per month. Adding that to the £395 example spending gives an illustrative subtotal of about £1,057–£1,417, leaving about £400–£760 of the current £1,817 monthly stipend before visa/travel costs, deposits and personal variation. A separate University guide gives groceries at £30–£45 per week; this is an alternative estimate, not an extra amount to add to the £155 monthly grocery line. 2027/28 accommodation prices are not yet confirmed. (Sheffield living-cost examples, 2026/27 postgraduate accommodation rents, grocery estimates)

Applicant Fit and Preparation

The public project description does not give a minimum degree classification, required discipline, programming language or prior MPC experience. Sheffield says academic entry requirements vary by School and project. The technical tasks suggest that applicants could strengthen an application by showing preparation in control systems, dynamic modelling, MPC/optimal control, numerical optimisation and programming-based evaluation. These are suggested areas to evidence, not advertised formal prerequisites. An aerospace background could help contextualise an application but is not listed as mandatory. (PhD applying essentials, Paul Trodden profile, Yuanbo Nie profile)

For EEE/Automatic Control research degrees, Sheffield lists IELTS 6.5 overall with at least 6.0 in each component, or equivalent. The DLA application needs a clear research example with question, approach, result and challenge; it should connect the applicant's quantitative or computational experience to the project's actual problem without presenting a speculative method as an agreed work plan. (Research-degree English requirements, DLA application questions)

Potential careers include control-systems engineering, systems engineering and control/optimisation research and development, including adjacent aerospace, defence, space, mobility, energy and manufacturing work. Skills England's occupational map describes control-systems roles across sectors and reports an occupation-wide median salary of £44,134; this is not a predicted salary for a PhD graduate. EngineeringUK reports 6.3 million engineering and technology roles, about 19% of UK jobs, using 2025 Labour Force Survey data. ADS reports 468,500 direct jobs across the combined aerospace, defence, security and space sectors. Both workforce indicators are broad and should not be read as forecasts for MPC vacancies. (Skills England control-systems occupation map, EngineeringUK workforce briefing, ADS industry facts and figures)

Next Actions and Questions to Verify

Before Applying

1. Email both supervisors to confirm which Airbus Defence and Space team/site is involved, what work package the student will undertake, and whether co-supervision, partner meetings, visits or a secondment are committed.
2. Ask what academic background and grade the School expects for this project, whether a separate proposal or technical portfolio is needed, and how Home fee status and international availability will be handled.
3. Request written confirmation of the 3.5-year funding package: fee treatment for the applicant's status, 2027/28 stipend, the research-grant amount and purpose, and any costs not covered.
4. Use the dedicated DLA application form by 17:00 GMT on 13 January 2027 and review the word limits, two-project selection option and AI-use disclosure rules.

At Interview

1. Ask which system/model, uncertainty sources and estimation approach are in scope; which MPC formulation and solver will be compared; and what changes in response to uncertainty.
2. Ask how the team will define and validate computation time, solution accuracy/optimality, feasible operation, stability and safe performance bounds.
3. Confirm the baseline, simulation/data/hardware platform, available compute and software, and whether project-specific Airbus data, simulators or test access are already arranged.
4. Clarify supervision division, industrial milestones, authorship, IP/security review and publication permissions.

Before Accepting an Offer

1. Check the written offer for registration and funding end dates, thesis-writing arrangements, stipend, tuition coverage, research support and any visa/travel exclusions.
2. Confirm any Airbus security, confidentiality, data-use or publication constraints before relying on the project as an open, publishable academic thesis.

Evidence and Sources

University, Programme and DLA

• Fully funded EPSRC PhDs | University of Sheffield
• How to apply for the EPSRC DLA
• UKRI doctoral training investment framework
• University contact details
• Applying essentials for PhD study
• Research-degree English requirements
• University rankings
• Faculty of Engineering research and REF context

Supervisors, Research Environment and Publications

• Paul Trodden profile
• Yuanbo Nie profile
• Control and Systems Engineering theme
• Intelligent Systems, Decision and Control group
• Research Software Engineering resources
• Output-feedback MPC under lossy actuation via dual constrained full-information estimation (2026)
• On the limits of robust control under adversarial disturbances (2026)
• Reliable solution to dynamic optimization using integrated residual regularized direct collocation (2025)
• Model predictive bang-bang controller synthesis via approximate value functions (2024)
• Tracking-in-range formulations for numerical optimal control (2024)

Funding, Living Costs, Career and Industry Context

• UKRI guidance for training-grant holders
• Sheffield living-cost examples
• Rent and grocery estimates for international students
• GOV.UK Student visa financial requirement
• Skills England control-systems occupation map
• EngineeringUK engineering and technology workforce briefing
• ADS industry facts and figures
• Airbus space-equipment context