On analyzing the vulnerabilities of a railway network with Petri nets

Petri nets are used in this paper to estimate the indirect consequences of accidents in a railway network, which belongs to the class of the so-called transportation Critical Infrastructures (CIs), that is, those assets consisting of systems, resources and/or processes whose total or partial destruction, or even temporarily unavailability, has the effect of significantly weakening the functioning of the system. In the proposed methodology, a timed Petri ne<t represents the railway network and the trains travelling over the rail lines; such a net also includes some places and some stochastically-timed transitions that are used to model the occurrence of unexpected events (accidents, disruptions, and so on) that make some resources of the network (tracks, blocks, crossovers, overhead line, electric power supply, etc.) temporarily unavailable. The overall Petri net is a live and bounded Generalized Stochastic Petri Net (GSPN) that can be analyzed by exploiting the steady-state probabilities of a continuous-time Markov chain (CTMC) that can be derived from the reachability graph of the GSPN. The final target of such an analysis is to determine and rank the levels of criticality of transportation facilities and assess the vulnerability of the whole railway network

Topics in perturbation analysis for stochastic hybrid systems

Control and optimization of Stochastic Hybrid Systems (SHS) constitute increasingly active fields of research. However, the size and complexity of SHS frequently render the use of exhaustive verification techniques prohibitive. In this context, Perturbation Analysis techniques, and in particular Infinitesimal Perturbation Analysis (IPA), have proven to be particularly useful for this class of systems. This work focuses on applying IPA to two different problems: Traffic Light Control (TLC) and control of cancer progression, both of which are viewed as dynamic optimization problems in an SHS environment. The first part of this thesis addresses the TLC problem for a single intersection modeled as a SHS. A quasi-dynamic control policy is proposed based on partial state information defined by detecting whether vehicle backlogs are above or below certain controllable threshold values. At first, the threshold parameters are controlled while assuming fixed cycle lengths and online gradient estimates of a cost metric with respect to these controllable parameters are derived using IPA techniques. These estimators are subsequently used to iteratively adjust the threshold values so as to improve overall system performance. This quasi-dynamic analysis of the TLC\ problem is subsequently extended to parameterize the control policy by green and red cycle lengths as well as queue content thresholds. IPA estimators necessary to simultaneously control the light cycles and thresholds are rederived and thereafter incorporated into a standard gradient based scheme in order to further ameliorate system performance. In the second part of this thesis, the problem of controlling cancer progression is formulated within a Stochastic Hybrid Automaton (SHA) framework. Leveraging the fact that cell-biologic changes necessary for cancer development may be schematized as a series of discrete steps, an integrative closed-loop framework is proposed for describing the progressive development of cancer and determining optimal personalized therapies. First, the problem of cancer heterogeneity is addressed through a novel Mixed Integer Linear Programming (MILP) formulation that integrates somatic mutation and gene expression data to infer the temporal sequence of events from cross-sectional data. This formulation is tested using both simulated data and real breast cancer data with matched somatic mutation and gene expression measurements from The Cancer Genome Atlas (TCGA). Second, the use of basic IPA techniques for optimal personalized cancer therapy design is introduced and a methodology applicable to stochastic models of cancer progression is developed. A case study of optimal therapy design for advanced prostate cancer is performed. Given the importance of accurate modeling in conjunction with optimal therapy design, an ensuing analysis is performed in which sensitivity estimates with respect to several model parameters are evaluated and critical parameters are identified. Finally, the tradeoff between system optimality and robustness (or, equivalently, fragility) is explored so as to generate valuable insights on modeling and control of cancer progression

Use of Petri Nets to Manage Civil Engineering Infrastructures

Over the last years there has been a shift, in the most developed countries, in investment and efforts within the construction sector. On the one hand, these countries have built infrastructures able to respond to current needs over the last decades, reducing the need for investments in new infrastructures now and in the near future. On the other hand, most of the infrastructures present clear signs of deterioration, making it fundamental to invest correctly in their recovery. The ageing of infrastructure together with the scarce budgets available for maintenance and rehabilitation are the main reasons for the development of decision support tools, as a mean to maximize the impact of investments. The objective of the present work is to develop a methodology for optimizing maintenance strategies, considering the available information on infrastructure degradation and the impact of maintenance in economic terms and loss of functionality, making possible the implementation of a management system transversal to different types of civil engineering infrastructures. The methodology used in the deterioration model is based on the concept of timed Petri nets. The maintenance model was built from the deterioration model, including the inspection, maintenance and renewal processes. The optimization of maintenance is performed through genetic algorithms. The deterioration and maintenance model was applied to components of two types of infrastructure: bridges (pre-stressed concrete decks and bearings) and buildings (ceramic claddings). The complete management system was used to analyse a section of a road network. All examples are based on Portuguese data

Switching Control Strategy for Greenhouse Temperature-Humidity System Based on Prediction Modeling: A Simulation Study

It is difficult to achieve coordination control of multiple facilities that are driven by on-off actuators in a greenhouse, especially when there is more than one indoor environmental factor to consider at the same time. With the consideration of indoor air temperature and relative humidity, we propose a switching control strategy based on prediction modeling. The operation of the greenhouse system was divided into several modes according to the on-off control characteristics of the available facilities. Then, a switching diagram was designed according to the relationship between the indoor air temperature and humidity and their setting ranges. When the two indoor environmental factors reach their upper or lower limits, IARX models are used to predict them over a specified horizon for each optional mode respectively. Mode switching is carried out based on prediction results. The switching control strategy was simulated based on a mechanistic model of the greenhouse microclimate. The results show that the facilities can be coordinated very well by the proposed control strategy and it is easy to implement. The control strategy is still applicative when more facilities or more indoor environmental factors need to be taken into account