Discrete events: Perspectives from system theory

Systems Theory;differentiaal/ integraal-vergelijkingen

A Mathematical Framework for Agent Based Models of Complex Biological Networks

Agent-based modeling and simulation is a useful method to study biological phenomena in a wide range of fields, from molecular biology to ecology. Since there is currently no agreed-upon standard way to specify such models it is not always easy to use published models. Also, since model descriptions are not usually given in mathematical terms, it is difficult to bring mathematical analysis tools to bear, so that models are typically studied through simulation. In order to address this issue, Grimm et al. proposed a protocol for model specification, the so-called ODD protocol, which provides a standard way to describe models. This paper proposes an addition to the ODD protocol which allows the description of an agent-based model as a dynamical system, which provides access to computational and theoretical tools for its analysis. The mathematical framework is that of algebraic models, that is, time-discrete dynamical systems with algebraic structure. It is shown by way of several examples how this mathematical specification can help with model analysis.Comment: To appear in Bulletin of Mathematical Biolog

Discrete and hybrid methods for the diagnosis of distributed systems

Many important activities of modern society rely on the proper functioning of complex systems such as electricity networks, telecommunication networks, manufacturing plants and aircrafts. The supervision of such systems must include strong diagnosis capability to be able to effectively detect the occurrence of faults and ensure appropriate corrective measures can be taken in order to recover from the faults or prevent total failure. This thesis addresses issues in the diagnosis of large complex systems. Such systems are usually distributed in nature, i.e. they consist of many interconnected components each having their own local behaviour. These components interact together to produce an emergent global behaviour that is complex. As those systems increase in complexity and size, their diagnosis becomes increasingly challenging. In the first part of this thesis, a method is proposed for diagnosis on distributed systems that avoids a monolithic global computation. The method, based on converting the graph of the system into a junction tree, takes into account the topology of the system in choosing how to merge local diagnoses on the components while still obtaining a globally consistent result. The method is shown to work well for systems with tree or near-tree structures. This method is further extended to handle systems with high clustering by selectively ignoring some connections that would still allow an accurate diagnosis to be obtained. A hybrid system approach is explored in the second part of the thesis, where continuous dynamics information on the system is also retained to help better isolate or identify faults. A hybrid system framework is presented that models both continuous dynamics and discrete evolution in dynamical systems, based on detecting changes in the fundamental governing dynamics of the system rather than on residual estimation. This makes it possible to handle systems that might not be well characterised and where parameter drift is present. The discrete aspect of the hybrid system model is used to derive diagnosability conditions using indicator functions for the detection and isolation of multiple, arbitrary sequential or simultaneous events in hybrid dynamical networks. Issues with diagnosis in the presence of uncertainty in measurements due sensor or actuator noise are addressed. Faults may generate symptoms that are in the same order of magnitude as the latter. The use of statistical techniques,within a hybrid system framework, is proposed to detect these elusive fault symptoms and translate this information into probabilities for the actual operational mode and possibility of transition between modes which makes it possible to apply probabilistic analysis on the system to handle the underlying uncertainty present

Measurements, Models, Systems and Design

531 s.

Modeling and Stability Analysis of Nonlinear Sampled-Data Systems with Embedded Recovery Algorithms

Computer control systems for safety critical systems are designed to be fault tolerant and reliable, however, soft errors triggered by harsh environments can affect the performance of these control systems. The soft errors of interest which occur randomly, are nondestructive and introduce a failure that lasts a random duration. To minimize the effect of these errors, safety critical systems with error recovery mechanisms are being investigated. The main goals of this dissertation are to develop modeling and analysis tools for sampled-data control systems that are implemented with such error recovery mechanisms. First, the mathematical model and the well-posedness of the stochastic model of the sampled-data system are presented. Then this mathematical model and the recovery logic are modeled as a dynamically colored Petri net (DCPN). For stability analysis, these systems are then converted into piecewise deterministic Markov processes (PDP). Using properties of a PDP and its relationship to discrete-time Markov chains, a stability theory is developed. In particular, mean square equivalence between the sampled-data and its associated discrete-time system is proved. Also conditions are given for stability in distribution to the delta Dirac measure and mean square stability for a linear sampled-data system with recovery logic

Computational Techniques for the Structural and Dynamic Analysis of Biological Networks

The analysis of biological systems involves the study of networks from different omics such as genomics, transcriptomics, metabolomics and proteomics. In general, the computational techniques used in the analysis of biological networks can be divided into those that perform (i) structural analysis, (ii) dynamic analysis of structural prop- erties and (iii) dynamic simulation. Structural analysis is related to the study of the topology or stoichiometry of the biological network such as important nodes of the net- work, network motifs and the analysis of the flux distribution within the network. Dy- namic analysis of structural properties, generally, takes advantage from the availability of interaction and expression datasets in order to analyze the structural properties of a biological network in different conditions or time points. Dynamic simulation is useful to study those changes of the biological system in time that cannot be derived from a structural analysis because it is required to have additional information on the dynamics of the system. This thesis addresses each of these topics proposing three computational techniques useful to study different types of biological networks in which the structural and dynamic analysis is crucial to answer to specific biological questions. In particu- lar, the thesis proposes computational techniques for the analysis of the network motifs of a biological network through the design of heuristics useful to efficiently solve the subgraph isomorphism problem, the construction of a new analysis workflow able to integrate interaction and expression datasets to extract information about the chromo- somal connectivity of miRNA-mRNA interaction networks and, finally, the design of a methodology that applies techniques coming from the Electronic Design Automation (EDA) field that allows the dynamic simulation of biochemical interaction networks and the parameter estimation

On Minimum-time Control of Continuous Petri nets: Centralized and Decentralized Perspectives

Muchos sistemas artificiales, como los sistemas de manufactura, de logística, de telecomunicaciones o de tráfico, pueden ser vistos "de manera natural" como Sistemas Dinámicos de Eventos Discretos (DEDS). Desafortunadamente, cuando tienen grandes poblaciones, estos sistemas pueden sufrir del clásico problema de la explosión de estados. Con la intención de evitar este problema, se pueden aplicar técnicas de fluidificación, obteniendo una relajación fluida del modelo original discreto. Las redes de Petri continuas (CPNs) son una aproximación fluida de las redes de Petri discretas, un conocido formalismo para los DEDS. Una ventaja clave del empleo de las CPNs es que, a menudo, llevan a una substancial reducción del coste computacional. Esta tesis se centra en el control de Redes de Petri continuas temporizadas (TCPNs), donde las transiciones tienen una interpretación temporal asociada. Se asume que los sistemas siguen una semántica de servidores infinitos (velocidad variable) y que las acciones de control aplicables son la disminución de la velocidad del disparo de las transiciones. Se consideran dos interesantes problemas de control en esta tesis: 1) control del marcado objetivo, donde el objetivo es conducir el sistema (tan rápido como sea posible) desde un estado inicial a un estado final deseado, y es similar al problema de control set-point para cualquier sistema de estado continuo; 2) control del flujo óptimo, donde el objetivo es conducir el sistema a un flujo óptimo sin conocimiento a priori del estado final. En particular, estamos interesados en alcanzar el flujo máximo tan rápido como sea posible, lo cual suele ser deseable en la mayoría de sistemas prácticos. El problema de control del marcado objetivo se considera desde las perspectivas centralizada y descentralizada. Proponemos varios controladores centralizados en tiempo mínimo, y todos ellos están basados en una estrategia ON/OFF. Para algunas subclases, como las redes Choice-Free (CF), se garantiza la evolución en tiempo mínimo; mientras que para redes generales, los controladores propuestos son heurísticos. Respecto del problema de control descentralizado, proponemos en primer lugar un controlador descentralizado en tiempo mínimo para redes CF. Para redes generales, proponemos una aproximación distribuida del método Model Predictive Control (MPC); sin embargo en este método no se considera evolución en tiempo mínimo. El problema de control de flujo óptimo (en nuestro caso, flujo máximo) en tiempo mínimo se considera para redes CF. Proponemos un algoritmo heurístico en el que calculamos los "mejores" firing count vectors que llevan al sistema al flujo máximo, y aplicamos una estrategia de disparo ON/OFF. También demostramos que, debido a que las redes CF son persistentes, podemos reducir el tiempo que tarda en alcanzar el flujo máximo con algunos disparos adicionales. Los métodos de control propuestos se han implementado e integrado en una herramienta para Redes de Petri híbridas basada en Matlab, llamada SimHPN

Modeling and Simulation of Biological Systems through Electronic Design Automation techniques

Modeling and simulation of biological systems is a key requirement for integrating invitro and in-vivo experimental data. In-silico simulation allows testing different experimental conditions, thus helping in the discovery of the dynamics that regulate the system. These dynamics include errors in the cellular information processing that are responsible for diseases such as cancer, autoimmunity, and diabetes as well as drug effects to the system (Gonalves, 2013). In this context, modeling approaches can be classified into two categories: quantitative and qualitative models. Quantitative modeling allows for a natural representation of molecular and gene networks and provides the most precise prediction. Nevertheless, the lack of kinetic data (and of quantitative data in general) hampers its use for many situations (Le Novere, 2015). In contrast, qualitative models simplify the biological reality and are often able to reproduce the system behavior. They cannot describe actual concentration levels nor realistic time scales. As a consequence, they cannot be used to explain and predict the outcome of biological experiments that yield quantitative data. However, given a biological network consisting of input (e.g., receptors), intermediate, and output (e.g., transcription factors) signals, they allow studying the input-output relationships through discrete simulation (Samaga, 2013). Boolean models are gaining an increasing interest in reproducing dynamic behaviors, understanding processes, and predicting emerging properties of cellular signaling networks through in-silico experiments. They are emerging as a valid alternative to the quantitative approaches (i.e., based on ordinary differential equations) for exploratory modeling when little is known about reaction kinetics or equilibrium constants in the context of gene expression or signaling. Even though several approaches and software have been recently proposed for logic modeling of biological systems, they are limited to specific contexts and they lack of automation in analyzing biological properties such as complex attractors, and molecule vulnerability. This thesis proposes a platform based on Electronic Design Automation (EDA) technologies for qualitative modeling and simulation of Biological Systems. It aims at overtaking limitations that affect the most recent qualitative tools