Ідентифікація та керування складними системами на основі моделей імпульсних процесів когнітивних карт

У дисертаційній роботі запропоновано системний підхід до проблеми динамічного прийняття рішень у складних системах, що описуються моделями імпульсних процесів когнітивних карт. А саме, розроблено принципи, підходи та методи ідентифікації та керування цими системами на основі застосування та адаптації методів теорії ідентифікації систем та теорії автоматичного керування. При цьому тестові сигнали або керування подаються безпосередньо на деякі вершини когнітивної карти, або, у разі недостатності таких вершин, в ролі керувань можуть виступати змінні ваги ребер карти. У випадку, коли кількість вершин і/або вагові коефіцієнти ребер когнітивної карти невідомі, запропоновано методи ідентифікації розмірності та параметричної ідентифікації системи. Для стабілізації нестійкої когнітивної карти запропоновано ряд методів на основі методів модального керування та керування по еталонних моделях, інші методи пропонуються для приведення координат вершин когнітивної карти на задані рівні. Практичне значення отриманих результатів проілюстровано на численних прикладах когнітивних карт реальних систем – ІТ компанії, комерційного банку, ринку криптовалюти тощо. Результати впроваджено у компанії “Noosphere” та можуть бути застосовані в подальшому для інших складних систем, представлених за допомогою когнітивних карт.In the thesis the system approach to a problem of dynamic decision - making in the complex systems described by models of impulse processes in cognitive maps is suggested. Cognitive maps are a popular and convenient tool for describing, modelling, and analyzing complex multidimensional multiconnected systems of different origin. From a mathematical point of view, a cognitive map is a weighted directed graph, the nodes of which represent the main components (concepts) of a complex system, and the edges are the relationships between them. The dynamics of a complex system described by a cognitive map can be represented as a so-called impulse process, which (in the form of Roberts) is a first-order vector difference equation. To date, many studies are known on the construction and analysis of cognitive maps, but there is almost no work that would systematically address the problems of identification (evaluation) and control of systems represented by cognitive maps. Here the principles, approaches and methods of identification and control of these systems based on the application and adaptation of methods of the theory of system identification and the theory of automatic control are developed. In this case, test signals or controls are fed directly to some nodes of the cognitive map, or, in case of insufficiency of such nodes, the variable weights of the map edges can act as controls. In the case when the number of nodes and /or weight coefficients of the cognitive map edges are unknown, methods for dimension identification and parametric identification of systems based on data from the measured cognitive map nodes are proposed, with measurement errors considered. To stabilize the unstable cognitive map, a number of methods are proposed based on the methods of modal control and control using reference models; other methods are suggested to set the nodes coordinates of the cognitive map to a given level. Cases of multirate impulse process in the cognitive map, of the presence of unmeasured constrained disturbances of arbitrary nature, of the presence of delays, of the need to control the ratios etc. are considered separately. For control of complex systems, the dynamics of which is presented in the form of impulse processes in cognitive maps, in this thesis the adaptation of methods of the automatic control theory is suggested. The dynamics of the controlled system is written by introducing a control vector that acts directly on the nodes of the cognitive map through the variation of its resources. In simpler cases, it is recommended to use methods based on reference models (if you can vary all nodes) or modal control. Also in the case of stable impulse processes, methods based on minimizing the quadratic optimality criterion can be used. But controls by varying the resources of cognitive map nodes may not be sufficient, because in practice there are often few nodes that a decision maker can actually vary. For this case, the paper first proposes a method of control by varying the weights of the edges of the cognitive map, i.e., essentially by changing the degree of influence of some nodes on others. Then the control vector is the vector of increments of weights of some edges of the cognitive map. The design of a discrete controller for such a controlled impulse process is based on the quadratic optimality criterion for this vector. We also consider the case when a decision maker can use both types of control, i.e. variation of nodes resources, and the degree of their influence on each other. For this purpose the method of combined control is developed. Particular attention is paid to the disclosure of uncertainties that arise in the presence of unmeasurable disturbances of arbitrary nature, acting on the coordinates of the nodes of the cognitive map. These can be both external perturbations (including the influence of unmeasured nodes) and internal perturbations caused by inaccurate identification or timevarying weights of the map edges. It is assumed that nothing is known about these disturbances, except that they are limited. From the control theory point of view, this is the problem of robust control. In this research, two methods of robust control of impulse processes of the cognitive map are developed and investigated - on the basis of the method of invariant ellipsoids and on the basis of the H theory. The practical significance of the obtained results is illustrated by numerous examples of cognitive maps of real systems - an IT company, its human resources department, a commercial bank, a cryptocurrency market, a socio-educational student’s process. The results have been implemented by the IT company “Noosphere”, by the Department of dynamic systems control of Space Research Institute of NASU, in the educational process of Igor Sikorsky KPI and can be used in the future for many complex systems represented by cognitive maps

Ідентифікація та керування складними системами на основі моделей імпульсних процесів когнітивних карт

У дисертаційній роботі запропоновано системний підхід до проблеми динамічного прийняття рішень у складних системах, що описуються моделями імпульсних процесів когнітивних карт. А саме, розроблено принципи, підходи та методи ідентифікації та керування цими системами на основі застосування та адаптації методів теорії ідентифікації систем та теорії автоматичного керування. При цьому тестові сигнали або керування подаються безпосередньо на деякі вершини когнітивної карти, або, у разі недостатності таких вершин, в ролі керувань можуть виступати змінні ваги ребер карти. У випадку, коли кількість вершин і/або вагові коефіцієнти ребер когнітивної карти невідомі, запропоновано методи ідентифікації розмірності та параметричної ідентифікації системи. Для стабілізації нестійкої когнітивної карти запропоновано ряд методів на основі методів модального керування та керування по еталонних моделях, інші методи пропонуються для приведення координат вершин когнітивної карти на задані рівні. Практичне значення отриманих результатів проілюстровано на численних прикладах когнітивних карт реальних систем – ІТ компанії, комерційного банку, ринку криптовалюти тощо. Результати впроваджено у компанії “Noosphere” та можуть бути застосовані в подальшому для інших складних систем, представлених за допомогою когнітивних карт.In the thesis the system approach to a problem of dynamic decision - making in the complex systems described by models of impulse processes in cognitive maps is suggested. Cognitive maps are a popular and convenient tool for describing, modelling, and analyzing complex multidimensional multiconnected systems of different origin. From a mathematical point of view, a cognitive map is a weighted directed graph, the nodes of which represent the main components (concepts) of a complex system, and the edges are the relationships between them. The dynamics of a complex system described by a cognitive map can be represented as a so-called impulse process, which (in the form of Roberts) is a first-order vector difference equation. To date, many studies are known on the construction and analysis of cognitive maps, but there is almost no work that would systematically address the problems of identification (evaluation) and control of systems represented by cognitive maps. Here the principles, approaches and methods of identification and control of these systems based on the application and adaptation of methods of the theory of system identification and the theory of automatic control are developed. In this case, test signals or controls are fed directly to some nodes of the cognitive map, or, in case of insufficiency of such nodes, the variable weights of the map edges can act as controls. In the case when the number of nodes and /or weight coefficients of the cognitive map edges are unknown, methods for dimension identification and parametric identification of systems based on data from the measured cognitive map nodes are proposed, with measurement errors considered. To stabilize the unstable cognitive map, a number of methods are proposed based on the methods of modal control and control using reference models; other methods are suggested to set the nodes coordinates of the cognitive map to a given level. Cases of multirate impulse process in the cognitive map, of the presence of unmeasured constrained disturbances of arbitrary nature, of the presence of delays, of the need to control the ratios etc. are considered separately. For control of complex systems, the dynamics of which is presented in the form of impulse processes in cognitive maps, in this thesis the adaptation of methods of the automatic control theory is suggested. The dynamics of the controlled system is written by introducing a control vector that acts directly on the nodes of the cognitive map through the variation of its resources. In simpler cases, it is recommended to use methods based on reference models (if you can vary all nodes) or modal control. Also in the case of stable impulse processes, methods based on minimizing the quadratic optimality criterion can be used. But controls by varying the resources of cognitive map nodes may not be sufficient, because in practice there are often few nodes that a decision maker can actually vary. For this case, the paper first proposes a method of control by varying the weights of the edges of the cognitive map, i.e., essentially by changing the degree of influence of some nodes on others. Then the control vector is the vector of increments of weights of some edges of the cognitive map. The design of a discrete controller for such a controlled impulse process is based on the quadratic optimality criterion for this vector. We also consider the case when a decision maker can use both types of control, i.e. variation of nodes resources, and the degree of their influence on each other. For this purpose the method of combined control is developed. Particular attention is paid to the disclosure of uncertainties that arise in the presence of unmeasurable disturbances of arbitrary nature, acting on the coordinates of the nodes of the cognitive map. These can be both external perturbations (including the influence of unmeasured nodes) and internal perturbations caused by inaccurate identification or timevarying weights of the map edges. It is assumed that nothing is known about these disturbances, except that they are limited. From the control theory point of view, this is the problem of robust control. In this research, two methods of robust control of impulse processes of the cognitive map are developed and investigated - on the basis of the method of invariant ellipsoids and on the basis of the H theory. The practical significance of the obtained results is illustrated by numerous examples of cognitive maps of real systems - an IT company, its human resources department, a commercial bank, a cryptocurrency market, a socio-educational student’s process. The results have been implemented by the IT company “Noosphere”, by the Department of dynamic systems control of Space Research Institute of NASU, in the educational process of Igor Sikorsky KPI and can be used in the future for many complex systems represented by cognitive maps

Algorithms and architectures for the multirate additive synthesis of musical tones

In classical Additive Synthesis (AS), the output signal is the sum of a large number of independently controllable sinusoidal partials. The advantages of AS for music synthesis are well known as is the high computational cost. This thesis is concerned with the computational optimisation of AS by multirate DSP techniques. In note-based music synthesis, the expected bounds of the frequency trajectory of each partial in a finite lifecycle tone determine critical time-invariant partial-specific sample rates which are lower than the conventional rate (in excess of 40kHz) resulting in computational savings. Scheduling and interpolation (to suppress quantisation noise) for many sample rates is required, leading to the concept of Multirate Additive Synthesis (MAS) where these overheads are minimised by synthesis filterbanks which quantise the set of available sample rates. Alternative AS optimisations are also appraised. It is shown that a hierarchical interpretation of the QMF filterbank preserves AS generality and permits efficient context-specific adaptation of computation to required note dynamics. Practical QMF implementation and the modifications necessary for MAS are discussed. QMF transition widths can be logically excluded from the MAS paradigm, at a cost. Therefore a novel filterbank is evaluated where transition widths are physically excluded. Benchmarking of a hypothetical orchestral synthesis application provides a tentative quantitative analysis of the performance improvement of MAS over AS. The mapping of MAS into VLSI is opened by a review of sine computation techniques. Then the functional specification and high-level design of a conceptual MAS Coprocessor (MASC) is developed which functions with high autonomy in a loosely-coupled master- slave configuration with a Host CPU which executes filterbanks in software. Standard hardware optimisation techniques are used, such as pipelining, based upon the principle of an application-specific memory hierarchy which maximises MASC throughput

Graph Signal Processing: Overview, Challenges and Applications

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing. We then summarize recent developments in developing basic GSP tools, including methods for sampling, filtering or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning. We finish by providing a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE

Analysis and resynthesis of polyphonic music

This thesis examines applications of Digital Signal Processing to the analysis, transformation, and resynthesis of musical audio. First I give an overview of the human perception of music. I then examine in detail the requirements for a system that can analyse, transcribe, process, and resynthesise monaural polyphonic music. I then describe and compare the possible hardware and software platforms. After this I describe a prototype hybrid system that attempts to carry out these tasks using a method based on additive synthesis. Next I present results from its application to a variety of musical examples, and critically assess its performance and limitations. I then address these issues in the design of a second system based on Gabor wavelets. I conclude by summarising the research and outlining suggestions for future developments

Software defined radio em FPGA

Mestrado em Engenharia Electrónica e TelecomunicaçõesEsta dissertação teve como objectivo o desenvolvimento de parte de um receptor para Digital Audio Broadcasting (DAB) recorrendo aos conceitos ditados por Software Defined Radio (SDR). O receptor de rádio inclui a conversão de digital para analógico e a subsequente desmodelação de banda- base,pelo que é possível aceder à bit stream em qualquer ponto do sistema. A dissertação foi dividida em duas fases. Na primeira, o receptor completo foi simulado em MATLAB. Na segunda, o mesmo sistema foi implementado e testado numa placa XtremeDSP Development Kit-IV, a qual contêm um Field-Programmable Gate Array (FPGA). O sistema simulado foi testado com dois tipos de amostras. As primeiras consistiram em sinais DAB gerados em MATLAB e posteriormente distorcidos por diferentes canais também simulados pelo mesmo software. Foi assim possível fazer um estudo da probabilidade de erro quando o sinal é exposto a diferentes perturbações, como ruído, desvios na frequência e no tempo. O sistema foi ainda testado com amostras DAB reais. As constelações desmodelados mostraram o correcto funcionamento do sistema. Apenas parte do receptor simulado foi implementado no FPGA. A parte já desenvolvida consiste nas funções de desmodelação: desmodelação OFDM, desmodelação diferencial, frequency deinterleaving e demapeamento QPSK. O sistema de sincronização DAB não foi implementado. O sistema já desenvolvido é assim capaz de desmodelar um sinal DAB gerado no MATLAB, desde que este não contenha qualquer distorção. ABSTRACT: The aim of this dissertation was the development of part of a Digital Audio Broadcasting (DAB) receiver by means of Software Defined Radio (SDR). This radio receiver includes the Intermediate Frequency (IF) to baseband conversion and the subsequent baseband demodulation, thus one may access the bit stream in any point of the system. This dissertation was divided in two phases. In the first one, the whole DAB system was simulated in MATLAB. In the second, the receiver was implemented and tested in an XtremeDSP Development Kit-IV platform, which includes a Field-Programmable Gate Array (FPGA). The simulated system was tested with two kinds of samples. The first ones were generated in MATLAB and subsequently distorted by different channel conditions also simulated in the same software. This well known DAB digital signal allowed us to perform a Bit Error Rate (BER) study with several channel conditions, such as noise, multipath, frequency and time offsets. Further on, real DAB samples were used for testing. The demodulated QPSK constellations showed the correct operation of the system. Only part of the simulated receiver was implemented in the FPGA. This part consists in the channel demodulation functions: OFDM demodulation, differential demodulation, frequency deinterleaving and QPSK demapper. The DAB synchronization block was not implemented. The developed system is able to recover the modulated bit stream from the digital signal produced in MATLAB, since this signal is free of noise, frequency and time offset