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

Updated: about 2 months ago
Deadline: 02 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.

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