Stability for Discrete Event Max-Min-Plus (MMP) and Max-Min-Plus-Scaling (MMPS) Systems: Max-Plus Lyapunov Functions for Stability Analysis and Control

This research presents a framework for analysing the stability and control of discrete-event systems, specifically emphasising max-min-plus (MMP) and max-min-min-plus-scaling (MMPS) systems. These systems are valuable modelling tools for various applications, including production systems and urban railway traffic management, respectively....

Max-plus-algebraic hybrid automata: Beyond synchronisation and linearity

Man-made systems, such as manufacturing and transportation networks, and their interactions with the environment are driven by human-designed operational rules. These rules are most often based on the asynchronous occurrence of discrete events over time, such as the arrival and departure of trains at a station. The modelling, analysis, and...

Model Predictive Control on Max-min-plus-scaling Systems: Control procedure and stability conditions

Max-plus-linear (MPL) systems are systems that are linear in max-plus algebra. A generalization of these systems are Max-Min-Plus-Scaling (MMPS) systems. Next to maximization and addition (plus), MMPS systems use the operations minimization and scaling. They are discrete-event (DE) systems, which means that the changing of the states is...

Modeling and scheduling an autonomous sorting system using a switching max-plus linear model

Sorting systems form an example of event driven systems. These types of systems are referred to as discrete event systems (DES), and they consist of jobs that need to be performed at available resources. In an autonomous sorting system, jobs consist of robots receiving and delivering parcels at the correct locations. With scheduling, optimal...

Data-driven Abstractions with Probabilistic Guarantees for Linear PETC Systems

We employ the scenario approach to compute probably approximately correct (PAC) bounds on the average inter-sample time (AIST) generated by an unknown PETC system, based on a finite number of samples. We extend the scenario optimisation to multiclass SVM algorithms in order to construct a PAC map between the concrete state-space and the inter...

Modelling the hybrid dynamics of a hexapedal robot: Predicting the Zebro's path using an identified leg-ground slippage model

Legged locomotion is a discrete event system (DES) due to the ever changing contact states of each leg. As such, it requires a nonlinear modelling method to predict the trajectory of a legged robot. One such robot has been focused on throughout this thesis; the six legged "Zebro''. With its half-circular legs, the Zebro is well suited for...

Structural Controllability of Switching Max-Plus Linear Systems

We introduce a framework for studying controllability properties of discrete-event systems modelled as switching max-plus linear systems. In this framework, we generalise the notion of structural controllability to include the switching phenomenon. Such models provide an additional discrete input to change the synchronisation and/or ordering...

Framework for Studying Stability of Switching Max-Plus Linear Systems

We propose a framework for studying the stability of discrete-event systems modelled as switching max-plus linear systems. In this framework, we propose a set of notions of stability for generic discrete-event systems in the max-plus algebra. Then we show the loss of equivalence of these notions for switching max-plus linear systems due to the...

Analysis and control of max-plus linear discrete-event systems: An introduction

The objective of this paper is to provide a concise introduction to the max-plus algebra and to max-plus linear discrete-event systems. We present the basic concepts of the max-plus algebra and explain how it can be used to model a specific class of discrete-event systems with synchronization but no concurrency. Such systems are called max...

VirtualCrowd: A Simulation Platform for Microtask Crowdsourcing Campaigns

This demo presents VirtualCrowd, a simulation platform for crowdsourcing campaigns. The platform allows the design, configuration, step-by-step execution, and analysis of customized tasks, worker profiles, and crowdsourcing strategies. The platform will be demonstrated through a crowd-mapping example in two cities, which will highlight the...

Adaptive Gait Switching Control Structure using Max Plus in Legged Locomotion

The ZeBRo (Dutch abbreviation: Zesbenige Robot, six-legged robot), is a walking robot designed by the TU Delft, with its foundations on the RHex. The current version of the ZeBRo project, the DeciZebro, is made for the research to swarming in robotics, and is about the size of an A4-paper. <br/>To counter these shortcomings of CPG (a method to...

Multi-resolution modeling based on quotient space and DEVS

As simulation systems get more and more complex, the study of multi-resolution modeling (MRM) remains an exciting and fertile area of research. Contrasting its abundant successful use cases, a rigorous mathematical foundation is still lacking in MRM. In this paper, we propose a quotient space based multi-resolution modeling (QMRM) theory...

Language Equations for Maximal Decompositions in Coordination Control

The problem considered is to construct all solutions of an equation for a tuple of languages. The tuple in synchronous composition should equal a considered language. Of special interest are the maximal solutions with respect to a partial order relation on the set of solutions. The motivation of the problem is coordination control. The approach...

Modeling and control of switching max-plus-linear systems with random and deterministic switching

Switching max-plus-linear (SMPL) systems are discrete-event systems that can switch between different modes of operation. In each mode the system is described by a max-plus-linear state equation and a max-plus-linear output equation, with different system matrices for each mode. The switching may depend on the inputs and the states, or it may be...

Supervisory hybrid model predictive control for voltage stability of power networks

Emergency voltage control problems in electric power networks have stimulated the interest for the implementation of online optimal control techniques. Briefly stated, voltage instability stems from the attempt of load dynamics to restore power consumption beyond the capability of the transmission and generation system. Typically, this situation...

Stable model predictive control for constrained max-plus-linear systems

Model predictive control for Max-Plus-Linear and piecewise affine systems

This Ph.D. thesis considers the development of new analysis and control techniques for special classes of hybrid systems and discrete event systems. Two particular classes of hybrid systems (piecewise affine systems and max-min-plus-scaling systems), and two particular classes of discrete event systems (max-plus-linear systems and switching max...

Algorithms and Applications in Timed Discrete Event Systems