Discrete-time positive periodic systems with state and control constraints

The aim of this paper is to provide an efficient control design technique for discrete-time positive periodic systems. In particular, stability, positivity and periodic invariance of such systems are studied. Moreover, the concept of periodic invariance with respect to a collection of boxes is introduced and investigated with connection to stability. It is shown how such concept can be used for deriving a stabilizing state-feedback control that maintains the positivity of the closed-loop system and respects states and control signals constraints. In addition, all the proposed results can be efficiently solved in terms of linear programming.

Control design for multicast-aware class-based networks

The expectations of citizens from the Information Technologies (ITs) are increasing as the ITs have become integral part of our society, serving all kinds of activities whether professional, leisure, safety-critical applications or business. Hence, the limitations of the traditional network designs to provide innovative and enhanced services and applications motivated a consensus to integrate all services over packet switching infrastructures, using the Internet Protocol, so as to leverage flexible control and economical benefits in the Next Generation Networks (NGNs). However, the Internet is not capable of treating services differently while each service has its own requirements (e.g., Quality of Service - QoS). Therefore, the need for more evolved forms of communications has driven to radical changes of architectural and layering designs which demand appropriate solutions for service admission and network resources control. This Thesis addresses QoS and network control issues, aiming to improve overall control performance in current and future networks which classify services into classes. The Thesis is divided into three parts. In the first part, we propose two resource over-reservation algorithms, a Class-based bandwidth Over-Reservation (COR) and an Enhanced COR (ECOR). The over-reservation means reserving more bandwidth than a Class of Service (CoS) needs, so the QoS reservation signalling rate is reduced. COR and ECOR allow for dynamically defining over-reservation parameters for CoSs based on network interfaces resource conditions; they aim to reduce QoS signalling and related overhead without incurring CoS starvation or waste of bandwidth. ECOR differs from COR by allowing for optimizing control overhead minimization. Further, we propose a centralized control mechanism called Advanced Centralization Architecture (ACA), that uses a single state-full Control Decision Point (CDP) which maintains a good view of its underlying network topology and the related links resource statistics on real-time basis to control the overall network. It is very important to mention that, in this Thesis, we use multicast trees as the basis for session transport, not only for group communication purposes, but mainly to pin packets of a session mapped to a tree to follow the desired tree. Our simulation results prove a drastic reduction of QoS control signalling and the related overhead without QoS violation or waste of resources. Besides, we provide a generic-purpose analytical model to assess the impact of various parameters (e.g., link capacity, session dynamics, etc.) that generally challenge resource overprovisioning control. In the second part of this Thesis, we propose a decentralization control mechanism called Advanced Class-based resource OverpRovisioning (ACOR), that aims to achieve better scalability than the ACA approach. ACOR enables multiple CDPs, distributed at network edge, to cooperate and exchange appropriate control data (e.g., trees and bandwidth usage information) such that each CDP is able to maintain a good knowledge of the network topology and the related links resource statistics on real-time basis. From scalability perspective, ACOR cooperation is selective, meaning that control information is exchanged dynamically among only the CDPs which are concerned (correlated). Moreover, the synchronization is carried out through our proposed concept of Virtual Over-Provisioned Resource (VOPR), which is a share of over-reservations of each interface to each tree that uses the interface. Thus, each CDP can process several session requests over a tree without requiring synchronization between the correlated CDPs as long as the VOPR of the tree is not exhausted. Analytical and simulation results demonstrate that aggregate over-reservation control in decentralized scenarios keep low signalling without QoS violations or waste of resources. We also introduced a control signalling protocol called ACOR Protocol (ACOR-P) to support the centralization and decentralization designs in this Thesis. Further, we propose an Extended ACOR (E-ACOR) which aggregates the VOPR of all trees that originate at the same CDP, and more session requests can be processed without synchronization when compared with ACOR. In addition, E-ACOR introduces a mechanism to efficiently track network congestion information to prevent unnecessary synchronization during congestion time when VOPRs would exhaust upon every session request. The performance evaluation through analytical and simulation results proves the superiority of E-ACOR in minimizing overall control signalling overhead while keeping all advantages of ACOR, that is, without incurring QoS violations or waste of resources. The last part of this Thesis includes the Survivable ACOR (SACOR) proposal to support stable operations of the QoS and network control mechanisms in case of failures and recoveries (e.g., of links and nodes). The performance results show flexible survivability characterized by fast convergence time and differentiation of traffic re-routing under efficient resource utilization i.e. without wasting bandwidth. In summary, the QoS and architectural control mechanisms proposed in this Thesis provide efficient and scalable support for network control key sub-systems (e.g., QoS and resource control, traffic engineering, multicasting, etc.), and thus allow for optimizing network overall control performance.

Dissecting signaling pathways that control glia migration in the developing Drosophila retina

The function of a complex nervous system relies on an intricate interaction between neurons and glial cells. However, as glial cells are generally born distant from the place where they settle, molecular cues are important to direct their migration. Glial cell migration is important in both normal development and disease, thus current research in the laboratory has been focused on dissecting regulatory events underlying that crucial process. With this purpose, the Drosophila eye imaginal disc has been used as a model. In response to neuronal photoreceptor differentiation, glial cells migrate from the CNS into the eye disc where they act to correctly wrap axons. To ensure proper development, attractive and repulsive signals must coordinate glial cell migration. Importantly, one of these signals is Bnl, a Fibroblast Growth Factor (FGF) ligand expressed by retinal progenitor cells that was suggested to act as a non-autonomous negative regulator of excessive glial cell migration (overmigration) by binding and activating the Btl receptor expressed by glial cells. Through the experimental results described in chapter 3 we gained a detailed insight into the function of bnl in eye disc growth, photoreceptor development, and glia migration. Interestingly, we did not find a direct correlation between the defects on the ongoing photoreceptors and the glia overmigration phenotype; however, bnl knockdown caused apoptosis of eye progenitor cells what was strongly correlated with glia migration defects. Glia overmigration due to Bnl down-regulation in eye progenitor cells was rescued by inhibiting the pro-apoptotic genes or caspases activity, as well as, by depleting JNK or Dp53 function in retinal progenitor cells. Thus, we suggest a cross-talk between those developmental signals in the control of glia migration at a distance. Importantly, these results suggest that Bnl does not control glial migration in the eye disc exclusively through its ability to bind and activate its receptor Btl in glial cells. We also discuss possible biological roles for the glia overmigration in the bnl knockdown background. Previous results in the lab showed an interaction between dMyc, a master regulator of tissue growth, and Dpp, a Transforming Growth Factor-β important for retinal patterning and for accurate glia migration into the eye disc. Thus, we became interested in understanding putative relationships between Bnl and dMyc. In chapter 4, we show that they positively cooperate in order to ensure proper development of the eye disc. This work highlights the importance of the FGF signaling in eye disc development and reveals a signaling network where a range of extra- and intra-cellular signals cooperate to non-autonomously control glial cell migration. Therefore, such inter-relations could be important in other Drosophila cellular contexts, as well as in vertebrate tissue development.