Geometric Fault Detection and Isolation of Infinite Dimensional Systems

A broad class of dynamical systems from chemical processes to flexible mechanical structures, heat transfer and compression processes in gas turbine engines are represented by a set of partial differential equations (PDE). These systems are known as infinite dimensional (Inf-D) systems. Most of Inf-D systems, including PDEs and time-delayed systems can be represented by a differential equation in an appropriate Hilbert space. These Hilbert spaces are essentially Inf-D vector spaces, and therefore, they are utilized to represent Inf-D dynamical systems. Inf-D systems have been investigated by invoking two schemes, namely approximate and exact methods. Both approaches extend the control theory of ordinary differential equation (ODE) systems to Inf-D systems, however by utilizing two different methodologies. In the former approach, one needs to first approximate the original Inf-D system by an ODE system (e.g. by using finite element or finite difference methods) and then apply the established control theory of ODEs to the approximated model. On the other hand, in the exact approach, one investigates the Inf-D system without using any approximation. In other words, one first represents the system as an Inf-D system and then investigates it in the corresponding Inf-D Hilbert space by extending and generalizing the available results of finite-dimensional (Fin-D) control theory. It is well-known that one of the challenging issues in control theory is development of algorithms such that the controlled system can maintain the required performance even in presence of faults. In the literature, this property is known as fault tolerant control. The fault detection and isolation (FDI) analysis is the first step in order to achieve this goal. For Inf-D systems, the currently available results on the FDI problem are quite limited and restricted. This thesis is mainly concerned with the FDI problem of the linear Inf-D systems by using both approximate and exact approaches based on the geometric control theory of Fin-D and Inf-D systems. This thesis addresses this problem by developing a geometric FDI framework for Inf-D systems. Moreover, we implement and demonstrate a methodology for applying our results to mathematical models of a heat transfer and a two-component reaction-diffusion processes. In this thesis, we first investigate the development of an FDI scheme for discrete-time multi-dimensional (nD) systems that represent approximate models for Inf-D systems. The basic invariant subspaces including unobservable and unobservability subspaces of one-dimensional (1D) systems are extended to nD models. Sufficient conditions for solvability of the FDI problem are provided, where an LMI-based approach is also derived for the observer design. The capability of our proposed FDI methodology is demonstrated through numerical simulation results to an approximation of a hyperbolic partial differential equation system of a heat exchanger that is represented as a two-dimensional (2D) system. In the second part, an FDI methodology for the Riesz spectral (RS) system is investigated. RS systems represent a large class of parabolic and hyperbolic PDE in Inf-D systems framework. This part is mainly concerned with the equivalence of different types of invariant subspaces as defined for RS systems. Necessary and sufficient conditions for solvability of the FDI problem are developed. Moreover, for a subclass of RS systems, we first provide algorithms (for computing the invariant subspaces) that converge in a finite and known number of steps and then derive the necessary and sufficient conditions for solvability of the FDI problem. Finally, by generalizing the results that are developed for RS systems necessary and sufficient conditions for solvability of the FDI problem in a general Inf-D system are derived. Particularly, we first address invariant subspaces of Fin-D systems from a new point of view by invoking resolvent operators. This approach enables one to extend the previous Fin-D results to Inf-D systems. Particularly, necessary and sufficient conditions for equivalence of various types of conditioned and controlled invariant subspaces of Inf-D systems are obtained. Duality properties of Inf-D systems are then investigated. By introducing unobservability subspaces for Inf-D systems the FDI problem is formally formulated, and necessary and sufficient conditions for solvability of the FDI problem are provided

Збірник наукових праць 9-ї Міжнародної конференції з моніторингу, моделювання та управління емерджентною економікою (M3E2-MLPEED 2021). Одеса, Україна, 26-28 травня 2021 р.

Збірник наукових праць 9-ї Міжнародної конференції з моніторингу, моделювання та управління емерджентною економікою (M3E2-MLPEED 2021). Одеса, Україна, 26-28 травня 2021 р.Proceedings of the Selected and Revised Papers of 9th International Conference on Monitoring, Modeling & Management of Emergent Economy (M3E2-MLPEED 2021). Odessa, Ukraine, May 26-28, 2021

Third International Conference on Inverse Design Concepts and Optimization in Engineering Sciences (ICIDES-3)

Papers from the Third International Conference on Inverse Design Concepts and Optimization in Engineering Sciences (ICIDES) are presented. The papers discuss current research in the general field of inverse, semi-inverse, and direct design and optimization in engineering sciences. The rapid growth of this relatively new field is due to the availability of faster and larger computing machines

Rôle de deux groupes de vésicules dans la transmission synaptique

Les synapses formées par les fibres moussues (FM) sur les cellules principales de la région CA3 (FM-CA3) jouent un rôle crucial pour la formation de la mémoire spatiale dans l’hippocampe. Une caractéristique des FM est la grande quantité de zinc localisée avec le glutamate dans les vésicules synaptiques recyclées par la voie d’endocytose dépendante de l’AP3. En combinant l’imagerie calcique et l’électrophysiologie, nous avons étudié le rôle des vésicules contenant le zinc dans la neurotransmission aux synapses FM-CA3. Contrairement aux études précédentes, nous n’avons pas observé de rôle pour le zinc dans l’induction des vagues calciques. Nos expériences ont révélé que les vagues calciques sont dépendantes de l’activation des récepteurs métabotropiques et ionotropiques du glutamate. D’autre part, nos données indiquent que les vésicules dérivées de la voie dépendante de l’AP3 forment un groupe de vésicules possédant des propriétés spécifiques. Elles contribuent principalement au relâchement asynchrone du glutamate. Ainsi, les cellules principales du CA3 de souris n’exprimant pas la protéine AP3 avaient une probabilité inférieure de décharge et une réduction de la synchronie des potentiels d’action lors de la stimulation à fréquences physiologiques. Cette diminution de la synchronie n’était pas associée avec un changement des paramètres quantiques ou de la taille des groupes de vésicules. Ces résultats supportent l’hypothèse que deux groupes de vésicules sont présents dans le même bouton synaptique. Le premier groupe est composé de vésicules recyclées par la voie d’endocytose utilisant la clathrine et participe au relâchement synchrone du glutamate. Le second groupe est constitué de vésicules ayant été recyclées par la voie d’endocytose dépendante de l’AP3 et contribue au relâchement asynchrone du glutamate. Ces deux groupes de vésicules sont nécessaires pour l’encodage de l’information et pourraient être importants pour la formation de la mémoire. Ainsi, les décharges de courte durée à haute fréquence observées lorsque les animaux pénètrent dans les places fields pourraient causer le relâchement asynchrone de glutamate. Finalement, les résultats de mon projet de doctorat valident l’existence et l’importance de deux groupes de vésicules dans les MF qui sont recyclées par des voies d’endocytoses distinctes et relâchées durant différents types d’activités.Mossy fiber-CA3 pyramidal cell synapses play a crucial role in the hippocampal formation of spatial memories. These synaptic connections possess a number of unique features substantial for its role in the information processing and coding. One of these features is presence of zinc co-localized with glutamate within a subpopulation of synaptic vesicles recycling through AP3-dependent bulk endocytosis. Using Ca2+ imaging and electrophysiological recordings we investigated role of these zinc containing vesicles in the neurotransmission. In contrast to previous reports, we did not observe any significant role of vesicular zinc in the induction of large postsynaptic Ca2+ waves triggered by burst stimulation. Moreover, our experiments revealed that Ca2+ waves mediated by Ca2+ release from internal stores are dependent not only on the activation of metabotropic, but also ionotropic glutamate receptors. Nevertheless, subsequent experiments unveiled that the vesicles derived via AP3-dependent endocytosis primary contribute to the asynchronous, but not synchronous mode of glutamate release. Futhermore, knockout mice lacking adaptor protein AP3 had a reduced synchronization of postsynaptic action potentials and impaired information transfer; this was not associated with any changes in the synchronous release quantal parameters and vesicle pool size. These findings strongly support the idea that within a single presynaptic bouton two heterogeneous pools of releasable vesicles are present. One pool of readily releasable vesicles forms via clathrin mediated endocytosis and mainly participates in the synchronous release; a second pool forms through bulk endocytosis and primarily supplies asynchronous release. The existence of two specialized pools is essential for the information coding and transfer within hippocampus. It also might be important for hippocampal memory formation. In contrast to low firing rates at rest, dentate gyrus granule cells tend to fire high frequency bursts once an animal enters a place field. These burst activities, embedded in the lower gamma frequency, should be especially efficient in the triggering of substantial asynchronous glutamate release. Therefore, the results of my PhD project for the first time provide strong evidence for the presence and physiological importance of two vesicle pools with heterogeneous release and recycling properties via separate endocytic pathways within the same mossy fiber bouton