PhD position on Analysis and control of max-min-plus-scaling systems in a discrete-event framework

Updated: about 1 month ago
Deadline: 01 Jun 2022

Discrete-event systems form a large class of dynamic systems in which the evolution of the system is driven by the occurrence of certain discrete events. This in contrast to discrete-time systems where the evolution depends on the clock.

Discrete-event systems with only synchronization and no concurrency can be modeled by a max-plus linear model. This is a model in which the system equation consists of max and plus operations (e.g. paper flow in a printer or predictive scheduling for container terminals).

When competition plays a role (e.g. first-come-first-serve mechanisms) we obtain a max-min-plus system. This is a model in which the system equation consists of max, min, and plus operations (e.g. product flow in a production system with competition).

Occasionally the processing times in a system will depend on external parameters or previous values of the state and input. Such a system can written as a max-plus linear-parameter-varying system, or equivalently as a max-min-plus-scaling (MMPS) system  (e.g. traffic management on an urban railway line).

A disadvantage of  MMPS systems is that the model structure is fixed, whereby changes in the structure of the system (change of route, different order of operations) cannot be modeled. By allowing the system to switch between different modes of operation we arrive at the switching MMPS systems where in each mode the system is described by an  MMPS system description (e.g. optimal gait switching in legged locomotion). Max-plus linear systems are sometimes referred to as lattice piecewise-affine systems.

The PhD project will focus on one or more of the following important open challenges in the field of analysis and control of max-min-plus-scaling systems in a discrete-event framework:

  • Model systems in transport and logistics using discrete-event MMPS system descriptions with and without switching.
  • Analyze stability and stabilizability of MMPS systems in the discrete-event framework.
  • Develop stabilizing model predictive control algorithms for MMPS systems in the discrete-event framework.
  • Study the relations between various classes of MMPS systems (canonical forms, time/quota variables, switching).

Within our Optimzation and Learning for Control of Networks research group, we are looking for an enthusiastic and ambitious PhD candidate with a strong background in mathematics and System theory. The group itself has a strong history in analysis and control of discrete-event systems and hybrid systems, with a strong emphasis on max-plus linear systems.

Do the following techniques resonate excitement with you? Then you might be the right candidate for this position. Please do not hesitate to get in touch with us for more information. A short description of your motivation and an up-to-date curriculum vitae is required to apply for this position.

The data-driven control research group is part of the department of Delft Center for Systems and Control (DCSC) of the faculty Mechanical, Maritime and Materials Engineering. The DCSC department coordinates the education and research activities in systems and control at Delft University of Technology (TU Delft). The Centers' research mission is to conduct fundamental research in systems dynamics and control, involving dynamic modeling, advanced control theory, and optimization. The research is motivated by advanced technology development in physical imaging systems, renewable energy, robotics, and transportation systems.

We are looking for two candidates with an MSc degree in Systems and Control (Control engineering), Applied Mathematics, or a related field.

  • A strong background and genuine interest in working with mathematical tools and techniques is required, in particular numerical optimization and linear algebra.
  • While background in discrete-event systems is not required, a genuine interest for it is necessary.
  • Proficiency in expressing yourself verbally and in writing in English is required.
  • Good programming skills are a plus: MATLAB, Python.

Doing a PhD at TU Delft requires English proficiency at a certain level to ensure that the candidate is able to communicate and interact well, participate in English-taught Doctoral Education courses, and write scientific articles and a final thesis. For more details please check the Graduate Schools Admission Requirements .

Doctoral candidates will be offered a 4-year period of employment in principle, but in the form of 2 employment contracts. An initial 1,5 year contract with an official go/no go progress assessment within 15 months. Followed by an additional contract for the remaining 2,5 years assuming everything goes well and performance requirements are met.

Salary and benefits are in accordance with the Collective Labour Agreement for Dutch Universities, increasing from € 2443 per month in the first year to € 3122 in the fourth year. As a PhD candidate you will be enrolled in the TU Delft Graduate School. The TU Delft Graduate School provides an inspiring research environment with an excellent team of supervisors, academic staff and a mentor. The Doctoral Education Programme is aimed at developing your transferable, discipline-related and research skills.

The TU Delft offers a customisable compensation package, discounts on health insurance and sport memberships, and a monthly work costs contribution. Flexible work schedules can be arranged. For international applicants we offer the Coming to Delft Service and Partner Career Advice to assist you with your relocation.

Delft University of Technology is built on strong foundations. As creators of the world-famous Dutch waterworks and pioneers in biotech, TU Delft is a top international university combining science, engineering and design. It delivers world class results in education, research and innovation to address challenges in the areas of energy, climate, mobility, health and digital society. For generations, our engineers have proven to be entrepreneurial problem-solvers, both in business and in a social context. At TU Delft we embrace diversity and aim to be as inclusive as possible (see our Code of Conduct ). Together, we imagine, invent and create solutions using technology to have a positive impact on a global scale.

Challenge. Change. Impact!

The Faculty of 3mE carries out pioneering research, leading to new fundamental insights and challenging applications in the field of mechanical engineering. From large-scale energy storage, medical instruments, control technology and robotics to smart materials, nanoscale structures and autonomous ships. The foundations and results of this research are reflected in outstanding, contemporary education, inspiring students and PhD candidates to become socially engaged and responsible engineers and scientists. The faculty of 3mE is a dynamic and innovative faculty with an international scope and high-tech lab facilities. Research and education focus on the design, manufacture, application and modification of products, materials, processes and mechanical devices, contributing to the development and growth of a sustainable society, as well as prosperity and welfare.

Click here to go to the website of the Faculty of Mechanical, Maritime and Materials Engineering. Do you want to experience working at our faculty? This video will introduce you to some of our researchers and their work.

For more information about this vacancy, please contact Dr.ir. Ton van den Boom, a.j.j.vandenboom@tudelft.nl .   

For information about the application procedure, please contact Hilma Bleeker, HR advisor, application-3me@tudelft.nl . 

Are you interested in this vacancy? Please apply by 1 June 2022 via the application button and upload:

  • a cover letter stating your motivation,
  • detailed curriculum vitae (including a list of publications (if any)),
  • names of up to three professional referees,
  • a summary of your MSc thesis,
  • lists of courses and grades at Master and Bachelor (in English).

The available position will be filled as soon as possible (i.e. once a suitable candidate is found). This means that the selection of candidates will already start before the application deadline.

A pre-employment screening can be part of the selection procedure.

You can apply online. We will not process applications sent by email and/or post.

Acquisition in response to this vacancy is not appreciated.    


Discrete-event systems form a large class of dynamic systems in which the evolution of the system is driven by the occurrence of certain discrete events. This in contrast to discrete-time systems where the evolution depends on the clock.

Discrete-event systems with only synchronization and no concurrency can be modeled by a max-plus linear model. This is a model in which the system equation consists of max and plus operations (e.g. paper flow in a printer or predictive scheduling for container terminals).

When competition plays a role (e.g. first-come-first-serve mechanisms) we obtain a max-min-plus system. This is a model in which the system equation consists of max, min, and plus operations (e.g. product flow in a production system with competition).

Occasionally the processing times in a system will depend on external parameters or previous values of the state and input. Such a system can written as a max-plus linear-parameter-varying system, or equivalently as a max-min-plus-scaling (MMPS) system  (e.g. traffic management on an urban railway line).

A disadvantage of  MMPS systems is that the model structure is fixed, whereby changes in the structure of the system (change of route, different order of operations) cannot be modeled. By allowing the system to switch between different modes of operation we arrive at the switching MMPS systems where in each mode the system is described by an  MMPS system description (e.g. optimal gait switching in legged locomotion). Max-plus linear systems are sometimes referred to as lattice piecewise-affine systems.

The PhD project will focus on one or more of the following important open challenges in the field of analysis and control of max-min-plus-scaling systems in a discrete-event framework:

  • Model systems in transport and logistics using discrete-event MMPS system descriptions with and without switching.
  • Analyze stability and stabilizability of MMPS systems in the discrete-event framework.
  • Develop stabilizing model predictive control algorithms for MMPS systems in the discrete-event framework.
  • Study the relations between various classes of MMPS systems (canonical forms, time/quota variables, switching).

Within our Optimzation and Learning for Control of Networks research group, we are looking for an enthusiastic and ambitious PhD candidate with a strong background in mathematics and System theory. The group itself has a strong history in analysis and control of discrete-event systems and hybrid systems, with a strong emphasis on max-plus linear systems.

Do the following techniques resonate excitement with you? Then you might be the right candidate for this position. Please do not hesitate to get in touch with us for more information. A short description of your motivation and an up-to-date curriculum vitae is required to apply for this position.

The data-driven control research group is part of the department of Delft Center for Systems and Control (DCSC) of the faculty Mechanical, Maritime and Materials Engineering. The DCSC department coordinates the education and research activities in systems and control at Delft University of Technology (TU Delft). The Centers' research mission is to conduct fundamental research in systems dynamics and control, involving dynamic modeling, advanced control theory, and optimization. The research is motivated by advanced technology development in physical imaging systems, renewable energy, robotics, and transportation systems.

We are looking for two candidates with an MSc degree in Systems and Control (Control engineering), Applied Mathematics, or a related field.

  • A strong background and genuine interest in working with mathematical tools and techniques is required, in particular numerical optimization and linear algebra.
  • While background in discrete-event systems is not required, a genuine interest for it is necessary.
  • Proficiency in expressing yourself verbally and in writing in English is required.
  • Good programming skills are a plus: MATLAB, Python.

Doing a PhD at TU Delft requires English proficiency at a certain level to ensure that the candidate is able to communicate and interact well, participate in English-taught Doctoral Education courses, and write scientific articles and a final thesis. For more details please check the Graduate Schools Admission Requirements .

Doctoral candidates will be offered a 4-year period of employment in principle, but in the form of 2 employment contracts. An initial 1,5 year contract with an official go/no go progress assessment within 15 months. Followed by an additional contract for the remaining 2,5 years assuming everything goes well and performance requirements are met.

Salary and benefits are in accordance with the Collective Labour Agreement for Dutch Universities, increasing from € 2443 per month in the first year to € 3122 in the fourth year. As a PhD candidate you will be enrolled in the TU Delft Graduate School. The TU Delft Graduate School provides an inspiring research environment with an excellent team of supervisors, academic staff and a mentor. The Doctoral Education Programme is aimed at developing your transferable, discipline-related and research skills.

The TU Delft offers a customisable compensation package, discounts on health insurance and sport memberships, and a monthly work costs contribution. Flexible work schedules can be arranged. For international applicants we offer the Coming to Delft Service and Partner Career Advice to assist you with your relocation.

Delft University of Technology is built on strong foundations. As creators of the world-famous Dutch waterworks and pioneers in biotech, TU Delft is a top international university combining science, engineering and design. It delivers world class results in education, research and innovation to address challenges in the areas of energy, climate, mobility, health and digital society. For generations, our engineers have proven to be entrepreneurial problem-solvers, both in business and in a social context. At TU Delft we embrace diversity and aim to be as inclusive as possible (see our Code of Conduct ). Together, we imagine, invent and create solutions using technology to have a positive impact on a global scale.

Challenge. Change. Impact!

The Faculty of 3mE carries out pioneering research, leading to new fundamental insights and challenging applications in the field of mechanical engineering. From large-scale energy storage, medical instruments, control technology and robotics to smart materials, nanoscale structures and autonomous ships. The foundations and results of this research are reflected in outstanding, contemporary education, inspiring students and PhD candidates to become socially engaged and responsible engineers and scientists. The faculty of 3mE is a dynamic and innovative faculty with an international scope and high-tech lab facilities. Research and education focus on the design, manufacture, application and modification of products, materials, processes and mechanical devices, contributing to the development and growth of a sustainable society, as well as prosperity and welfare.

Click here to go to the website of the Faculty of Mechanical, Maritime and Materials Engineering. Do you want to experience working at our faculty? This video will introduce you to some of our researchers and their work.

For more information about this vacancy, please contact Dr.ir. Ton van den Boom, a.j.j.vandenboom@tudelft.nl .   

For information about the application procedure, please contact Hilma Bleeker, HR advisor, application-3me@tudelft.nl . 

Are you interested in this vacancy? Please apply by 1 June 2022 via the application button and upload:

  • a cover letter stating your motivation,
  • detailed curriculum vitae (including a list of publications (if any)),
  • names of up to three professional referees,
  • a summary of your MSc thesis,
  • lists of courses and grades at Master and Bachelor (in English).

The available position will be filled as soon as possible (i.e. once a suitable candidate is found). This means that the selection of candidates will already start before the application deadline.

A pre-employment screening can be part of the selection procedure.

You can apply online. We will not process applications sent by email and/or post.

Acquisition in response to this vacancy is not appreciated.    


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