Closed loop stability of measure-driven impulsive control systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Studies on the Effect of Randomness on the Synchronization of Coupled Systems and on the Dynamics of Intermittently driven systems

Nonlinear dynamics has emerged into a prominent area of research in the past few Decades.Turbulence, Pattern formation,Multistability etc are some of the important areas of research in nonlinear dynamics apart from the study of chaos.Chaos refers to the complex evolution of a deterministic system, which is highly sensitive to initial conditions. The study of chaos theory started in the modern sense with the investigations of Edward Lorentz in mid 60's. Later developments in this subject provided systematic development of chaos theory as a science of deterministic but complex and unpredictable dynamical systems. This thesis deals with the effect of random fluctuations with its associated characteristic timescales on chaos and synchronization. Here we introduce the concept of noise, and two familiar types of noise are discussed. The classifications and representation of white and colored noise are introduced. Based on this we introduce the concept of randomness that we deal with as a variant of the familiar concept of noise. The dynamical systems introduced are the Rossler system, directly modulated semiconductor lasers and the Harmonic oscillator. The directly modulated semiconductor laser being not a much familiar dynamical system, we have included a detailed introduction to its relevance in Chaotic encryption based cryptography in communication. We show that the effect of a fluctuating parameter mismatch on synchronization is to destroy the synchronization. Further we show that the relation between synchronization error and timescales can be found empirically but there are also cases where this is not possible. Studies show that under the variation of the parameters, the system becomes chaotic, which appears to be the period doubling route to chaos.

Studies on the effect of randoniness on the synchronization of coupled systems and on the dynamics of intermittently driven systems

It has been shown recently that systems driven with random pulses show the signature of chaos ,even without non linear dynamics.This shows that the relation between randomness and chaos is much closer than it was understood earlier .The effect of random perturbations on synchronization can be also different. In some cases identical random perturbations acting on two different chaotic systems induce synchronizations. However most commonly ,the effect of random fluctuations on the synchronizations of chaotic system is to destroy synchronization. This thesis deals with the effect of random fluctuations with its associated characteristic timescales on chaos and synchronization. The author tries to unearth yet another manifestation of randomness on chaos and sychroniztion. This thesis is organized into six chapters.

Analysis of slow- and fast-alpha band asymmetry during performance of a saccadic eye movement task: Dissociation between memory- and attention-driven systems

This study aimed at analyzing the relationship between slow- and fast-alpha asymmetry within frontal cortex and the planning, execution and voluntary control of saccadic eye movements (SEM), and quantitative electroencephalography (qEEG) was recorded using a 20-channel EEG system in 12 healthy participants performing a fixed (i.e., memory-driven) and a random SEM (i.e., stimulus-driven) condition. We find main effects for SEM condition in slow- and fast-alpha asymmetry at electrodes F3-F4, which are located over premotor cortex, specifically a negative asymmetry between conditions. When analyzing electrodes F7-F8, which are located over prefrontal cortex, we found a main effect for condition in slow-alpha asymmetry, particularly a positive asymmetry between conditions. In conclusion, the present approach supports the association of slow- and fast-alpha bands with the planning and preparation of SEM, and the specific role of these sub-bands for both, the attention network and the coordination and integration of sensory information with a (oculo)-motor response. (C) 2011 Elsevier B.V. All rights reserved.

Incremental model transformation for the evolution of model-driven systems

Model transformations are an integral part of model-driven development. Incremental updates are a key execution scenario for transformations in model-based systems, and are especially important for the evolution of such systems. This paper presents a strategy for the incremental maintenance of declarative, rule-based transformation executions. The strategy involves recording dependencies of the transformation execution on information from source models and from the transformation definition. Changes to the source models or the transformation itself can then be directly mapped to their effects on transformation execution, allowing changes to target models to be computed efficiently. This particular approach has many benefits. It supports changes to both source models and transformation definitions, it can be applied to incomplete transformation executions, and a priori knowledge of volatility can be used to further increase the efficiency of change propagation.

Architecture of Extensible Computations Driven Systems

Никола Вълчанов, Тодорка Терзиева, Владимир Шкуртов, Антон Илиев - Една от основните области на приложения на компютърната информатика е автоматизирането на математическите изчисления. Информационните системи покриват различни области като счетоводство, електронно обучение/тестване, симулационни среди и т. н. Те работят с изчислителни библиотеки, които са специфични за обхвата на системата. Въпреки, че такива системи са перфектни и работят безпогрешно, ако не се поддържат остаряват. В тази работа описваме механизъм, който използва динамично библиотеките за изчисления и взема решение по време на изпълнение (интелигентно или интерактивно) за това как и кога те да се използват. Целта на тази статия е представяне на архитектура за системи, управлявани от изчисления. Тя се фокусира върху ползите от използването на правилните шаблони за дизайн с цел да се осигури разширяемост и намаляване на сложността.

Stability for impulsive control systems

In this paper we extend the notion of the control Lyapounov pair of functions and derive a stability theory for impulsive control systems. The control system is a measure driven differential inclusion that is partly absolutely continuous and partly singular. Some examples illustrating the features of Lyapounov stability are provided.

Lyapounov stability for impulsive dynamical systems

This article addresses the problem of stability of impulsive control systems whose dynamics are given by measure driven differential inclusions. One important feature concerns the adopted solution which allows the consideration of systems whose singular dynamics do not satisfy the so-called Frobenius condition. After extending the conventional notion of control Lyapounov pair for impulsive systems, some stability conditions of the Lyapounov type are given. Some conclusions follow the outline of the proof of the main result.

Invariance for Impulsive Control Systems

In this article, we provide invariance conditions for control systems whose dynamics are given by measure driven differential inclusions. The solution concept plays a critical role in the extension of the conventional conditions for the impulsive control context. A couple of examples illustrating the specific features of impulsive control systems are included.

A maximum principle for constrained infinite horizon dynamic control systems

This article presents and discusses a maximum principle for infinite horizon constrained optimal control problems with a cost functional depending on the state at the final time. The main feature of these optimality conditions is that, under reasonably weak assumptions, the multiplier is shown to satisfy a novel transversality condition at infinite time. It is also shown that these conditions can also be obtained for impulsive control problems whose dynamics are given by measure driven differential equations. © 2011 IFAC.

Disorder driven transitions in non-equilibrium quantum systems

This thesis presents studies of the role of disorder in non-equilibrium quantum systems. The quantum states relevant to dynamics in these systems are very different from the ground state of the Hamiltonian. Two distinct systems are studied, (i) periodically driven Hamiltonians in two dimensions, and (ii) electrons in a one-dimensional lattice with power-law decaying hopping amplitudes. In the first system, the novel phases that are induced from the interplay of periodic driving, topology and disorder are studied. In the second system, the Anderson transition in all the eigenstates of the Hamiltonian are studied, as a function of the power-law exponent of the hopping amplitude.

In periodically driven systems the study focuses on the effect of disorder in the nature of the topology of the steady states. First, we investigate the robustness to disorder of Floquet topological insulators (FTIs) occurring in semiconductor quantum wells. Such FTIs are generated by resonantly driving a transition between the valence and conduction band. We show that when disorder is added, the topological nature of such FTIs persists as long as there is a gap at the resonant quasienergy. For strong enough disorder, this gap closes and all the states become localized as the system undergoes a transition to a trivial insulator.

Interestingly, the effects of disorder are not necessarily adverse, disorder can also induce a transition from a trivial to a topological system, thereby establishing a Floquet Topological Anderson Insulator (FTAI). Such a state would be a dynamical realization of the topological Anderson insulator. We identify the conditions on the driving field necessary for observing such a transition. We realize such a disorder induced topological Floquet spectrum in the driven honeycomb lattice and quantum well models.

Finally, we show that two-dimensional periodically driven quantum systems with spatial disorder admit a unique topological phase, which we call the anomalous Floquet-Anderson insulator (AFAI). The AFAI is characterized by a quasienergy spectrum featuring chiral edge modes coexisting with a fully localized bulk. Such a spectrum is impossible for a time-independent, local Hamiltonian. These unique characteristics of the AFAI give rise to a new topologically protected nonequilibrium transport phenomenon: quantized, yet nonadiabatic, charge pumping. We identify the topological invariants that distinguish the AFAI from a trivial, fully localized phase, and show that the two phases are separated by a phase transition.

The thesis also present the study of disordered systems using Wegner's Flow equations. The Flow Equation Method was proposed as a technique for studying excited states in an interacting system in one dimension. We apply this method to a one-dimensional tight binding problem with power-law decaying hoppings. This model presents a transition as a function of the exponent of the decay. It is shown that the the entire phase diagram, i.e. the delocalized, critical and localized phases in these systems can be studied using this technique. Based on this technique, we develop a strong-bond renormalization group that procedure where we solve the Flow Equations iteratively. This renormalization group approach provides a new framework to study the transition in this system.

Energy Efficiency in Electrical Drive Systems: Technical potentials, barriers and policy approaches for small and medium industries in Ghana

Today industries and commerce in Ghana are facing enormous energy challenge. The pressure is on for industries to reduce energy consumption, lower carbon emissions and provide se-cured power supply. Industrial electric motor energy efficiency improvement is one of the most important tools to reduce global warming threat and reduce electricity bills. In order to develop a strategic industrial energy efficiency policy, it is therefore necessary to study the barriers that inhibit the implementation of cost – effective energy efficiency measures and the driving forces that promote the implementation. The aim of this thesis is to analyse the energy consumption pattern of electric motors, study factors that promote or inhibit energy efficiency improvements in EMDS and provide cost – effective solutions that improve energy efficiency to bridge the existing energy efficiency gap in the surveyed industries. The results from this thesis has revealed that, the existence of low energy efficiency in motor-driven systems in the surveyed industries were due to poor maintenance practices, absence of standards, power quality issues, lack of access to capital and limited awareness to the im-portance of energy efficiency improvements in EMDS. However, based on the results pre-sented in this thesis, a policy approach towards industrial SMEs should primarily include dis-counted or free energy audit in providing the industries with the necessary information on potential energy efficiency measures, practice best motor management programmes and estab-lish a minimum energy performance standard (MEPS) for motors imported into the country. The thesis has also shown that education and capacity development programmes, financial incentives and system optimization are effective means to promote energy efficiency in elec-tric motor – driven systems in industrial SMEs in Ghana

Investigating affect in algorithmic composition systems

There has been a significant amount of work implementing systems for algorithmic composition with the intention of targeting specific emotional responses in the listener, but a full review of this work is not currently available. This gap creates a shared obstacle to those entering the field. Our aim is thus to give an overview of progress in the area of these affectively driven systems for algorithmic composition. Performative and transformative systems are included and differentiated where appropriate, highlighting the challenges these systems now face if they are to be adapted to, or have already incorporated, some form of affective control. Possible real-time applications for such systems, utilizing affectively driven algorithmic composition and biophysical sensing to monitor and induce affective states in the listener are suggested.