Optimal control for biomedical applications
MSc thesis students (2020)
venerdì 10 gennaio 2020

In the treatment of cancer patients, chemotherapy and radiotherapy both play fundamental roles, either as standalone modalities, or - in many cases - in combination. Modelling and optimisation of individualized treatments can help effectively kill tumor cells, while sparing healthy tissues as possible.
Methods from systems and control theory can aid the planning and optimisation of single modality radiotherapy, as well as of combined chemo-radiotherapy treatments. While some preliminary work exists in pure chemotherapy application, regarding
the optimal dosage of a set of chemotherapy drugs to control heterogeneous tumors (consisting of multiple species of cancer cells having varying drug resistance, mutation rate and spatial migration rate), application to the temporal optimization of radiotherapy or chemo-radiotherapy is a new idea. This approach could be
vital for effective treatment adaptation by choosing optimal times to switch between chemotherapy drugs, or to use radiotherapy in combination or as boosts to certain chemotherapy resistant areas, in order to achieve tumor control with minimal side effects.

Possible MSc thesis projects:

  • Optimal control of combined chemo-radiation therapy treatments for improving cancer care.

In collaboration with the group of Zoltán Perkó, TU Delft, The Netherlands (possibility to spend a period abroad).

The topic is interdisciplinary, but very well suited for systems and control engineers!

Your profile:

  • Motivated, enthusiastic and independent
  • Strong mathematical background, knowledge of linear algebra, systems and control theory, optimal control, nonlinear systems, modelling
  • Very good programming skills, for numerical simulations
  • Interest for interdisciplinary work

Suggested Readings

  • A convex optimization approach to cancer treatment to address tumor
    heterogeneity and imperfect drug penetration in physiological compartments, IEEE CDC 2016
  • Optimal duration and planning of switching treatments taking drug toxicity into account: a convex optimisation approach, IEEE CDC 2019
Structural analysis of (biological) systems
BSc or MSc thesis students (2020)
venerdì 10 gennaio 2020

Can a class of systems necessarily give rise to a particular qualitative behaviour, regardless of parameter values?
This is indeed the case for many natural and biological systems: although plagued by huge uncertainties and parameter variations, their global behaviour (arising from the complex interplay of local interactions) is often astoundingly robust to environmental changes and perturbations.
Structural analysis aims at assessing whether a class of systems always enjoys a given property, due to its structure (topology of the interaction graph) and not to specific parameter values.
The problem is formally approached by considering a system structure (associated with a graph topology) along with qualitative assumptions (such as positivity of the variables and monotonicity of the involved functions).

Possible BSc thesis projects:

  • "Verification" of structural properties: given a graph structure, generate random functions satisfying the assumptions and check that the property always holds through an extensive simulation campaign.

Possible MSc thesis projects:

  • Simulation-based and analytical study of biological systems and chemical reaction networks (but possibly also of engineering systems), to discover or verify structural properties.

The projects can be theoretical and/or numerical (computer simulations).

The topic is interdisciplinary, but very well suited for systems and control engineers!

Your profile:

  • Motivated, enthusiastic and independent
  • Strong mathematical background, knowledge of linear algebra, systems and control theory (for a theoretical project)
  • Possibly, familiar with parametric robustness, nonlinear systems, modelling
  • Very good programming skills (for a practical project based on numerical simulations)
  • Interest for interdisciplinary work

Suggested Readings

  • Computing the structural influence matrix for biological systems, Journal of Mathematical Biology 2016
  • Piecewise-linear Lyapunov functions for structural stability of biochemical networks, Automatica 2014
  • A structural classification of candidate oscillatory and multistationary
    biochemical systems, Bulletin of Mathematical Biology 2014
  • Determining the structural properties of a class of biological models, IEEE CDC 2012
Network-decentralised control, coordination and estimation
BSc or MSc thesis students (2020)
venerdì 10 gennaio 2020

Complex large-scale systems composed of a set of naturally decoupled subsystems often have to be stabilised/controlled/coordinated, to ensure the desired global behaviour, by a set of local control agents that interconnect the subsystems and thus introduce coupling.
In network-decentralised control strategies, each control agent, affecting a subset of the subsystems (local action), has access to the state of these subsystems only (local information).
In network-decentralised estimation, conversely, a group of agents exchange information about local measurements, according to a communication graph, to asymptotically estimate their own state (e.g., height/position in a 3D-localisation problem).

Possible BSc/MSc thesis projects:

  • Network-decentralised coordination of moving agents (robots) with collision avoidance.
  • Network-decentralised height/position estimation for cartography: infer a global map based on local information exchanges.
  • Network-decentralised control of flow networks in the presence of uncertainties.

The projects can be theoretical and/or practical (computer simulations or experimental realisation in the lab).

Your profile:

  • Motivated, enthusiastic and independent
  • Strong mathematical background, knowledge of linear algebra, systems and control theory (for a theoretical project aimed at developing novel strategies)
  • Possibly, familiar with robust control and networked control
  • Very good programming skills (for a practical project aimed at applying and numerically simulating the strategies, to perform assessment/comparison)
  • Very good lab skills (for an experimental project aimed at implementing the strategies in a physical setup)

Suggested Readings

  • The smallest eigenvalue of the generalized Laplacian matrix, with application to network-decentralized estimation for homogeneous systems, IEEE TNSE, 2016
  • Compartmental flow control: decentralization, robustness and optimality, Automatica, 2016
  • Network-decentralized control strategies for stabilization, IEEE TAC, 2015
  • Network-decentralized robust congestion control with node traffic splitting, IEEE CDC 2014
  • Structured-LMI conditions for stabilizing network-decentralized control, IEEE CDC 2013
Implementing COLREGS in Dynamic Obstacle Avoidance for Autonomous Boats
BSc or MSc thesis students (2020)
venerdì 10 gennaio 2020

Implementing autonomous navigation for unmanned boats (unmanned surface vehicles, USV) is challenging. To prevent accidents with human driven boats, it is crucial that the automated navigation system complies with all the regulations on maritime navigation: this enables all other ships to anticipate the behavior of the USVs and react appropriately and timely. In maritime navigation, ships have to obey the International Regulations for preventing collisions at sea, also known as COLREGS (COLlision REGulationS).

Possible BSc/MSc thesis project:

Write a comprehensive overview that surveys all the contributions in the literature proposing collision avoidance algorithms for USVs that comply with COLREGS.

The thesis is fully theoretical and literature-review based, but can be enriched with simulation of several different approaches proposed in the literature, to assess and compare them (highly recommended!).

Your profile:

  • Motivated, enthusiastic and independent
  • Very good English level
  • Very good programming skills (to numerically simulate the strategies in the literature, so as to assess/compare them)
  • Willingness to write (with supervision) a survey paper to be submitted to an international journal

Suggested Readings