Coefficient Matrix Decomposition Method and BIBO Stabilization of Stochastic Systems with Time Delays

The mean square BIBO stabilization is investigated for the stochastic control systems with time delays and nonlinear perturbations. A class of suitable Lyapunov functional is constructed, combined with the descriptor model transformation and the decomposition technique of coefficient matrix; thus some novel delay-dependent mean square BIBO stabilization conditions are derived. These conditions are expressed in the forms of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. Finally, three numerical examples are given to demonstrate that the derived conditions are effective and much less conservative than those given in the literature

BIBO stability analysis for delay switched systems with nonlinear perturbation

Extent: 8p.The problem of bounded-input bounded-output (BIBO) stability is investigated for a class of delay switched systems with mixed time-varying discrete and constant neutral delays and nonlinear perturbation. Based on the Lyapunov-Krasovskii functional theory, new BIBO stabilization criteria are established in terms of delay-dependent linear matrix inequalities. The numerical simulation is carried out to demonstrate the effectiveness of the results obtained in the paper.Jincheng Wei, Peng Shi, Hamid Reza Karimi, and Bo Wan

Comparative evaluation of approaches in T.4.1-4.3 and working definition of adaptive module

The goal of this deliverable is two-fold: (1) to present and compare different approaches towards learning and encoding movements us- ing dynamical systems that have been developed by the AMARSi partners (in the past during the first 6 months of the project), and (2) to analyze their suitability to be used as adaptive modules, i.e. as building blocks for the complete architecture that will be devel- oped in the project. The document presents a total of eight approaches, in two groups: modules for discrete movements (i.e. with a clear goal where the movement stops) and for rhythmic movements (i.e. which exhibit periodicity). The basic formulation of each approach is presented together with some illustrative simulation results. Key character- istics such as the type of dynamical behavior, learning algorithm, generalization properties, stability analysis are then discussed for each approach. We then make a comparative analysis of the different approaches by comparing these characteristics and discussing their suitability for the AMARSi project

Spectrum analysis of LTI continuous-time systems with constant delays: A literature overview of some recent results

In recent decades, increasingly intensive research attention has been given to dynamical systems containing delays and those affected by the after-effect phenomenon. Such research covers a wide range of human activities and the solutions of related engineering problems often require interdisciplinary cooperation. The knowledge of the spectrum of these so-called time-delay systems (TDSs) is very crucial for the analysis of their dynamical properties, especially stability, periodicity, and dumping effect. A great volume of mathematical methods and techniques to analyze the spectrum of the TDSs have been developed and further applied in the most recent times. Although a broad family of nonlinear, stochastic, sampled-data, time-variant or time-varying-delay systems has been considered, the study of the most fundamental continuous linear time-invariant (LTI) TDSs with fixed delays is still the dominant research direction with ever-increasing new results and novel applications. This paper is primarily aimed at a (systematic) literature overview of recent (mostly published between 2013 to 2017) advances regarding the spectrum analysis of the LTI-TDSs. Specifically, a total of 137 collected articles-which are most closely related to the research area-are eventually reviewed. There are two main objectives of this review paper: First, to provide the reader with a detailed literature survey on the selected recent results on the topic and Second, to suggest possible future research directions to be tackled by scientists and engineers in the field. © 2013 IEEE.MSMT-7778/2014, FEDER, European Regional Development Fund; LO1303, FEDER, European Regional Development Fund; CZ.1.05/2.1.00/19.0376, FEDER, European Regional Development FundEuropean Regional Development Fund through the Project CEBIA-Tech Instrumentation [CZ.1.05/2.1.00/19.0376]; National Sustainability Program Project [LO1303 (MSMT-7778/2014)

Robust load frequency control of interconnected grids with electric vehicles

This thesis presents new load frequency controls of interconnected grids, using electric vehicles to assist power plants in providing stability, which fluctuates with load demands and renewable powers. New robust control schemes for comprehensive power systems with electric vehicles, diverse transmission links, network-induced time delays and uncertainties are investigated.<br /

Decentralized Robust Capacity Control of Job Shop Systems with Reconfigurable Machine Tools

Manufacturing companies are confronted with various challenges from the perspective of customers individual requirements concerning variations of types of products, quantities and delivery dates. This renders the manufacturing process to be more dynamic and complex, which may result in bottlenecks and unbalanced capacity distributions. To cope with these problems, capacity adjustment is an effective approach to balance capacity and load for short or medium term fluctuations on the operational layer. Particularly, new technologies and algorithms need to be developed for the implementation of capacity adjustment. Reconfigurable machine tools (RMTs) and operator-based robust right coprime factorization (RRCF) provide an opportunity for a new capacity control strategy. Therefore, the main purpose of the research is to develop an effective machinery-oriented capacity control strategy by incorporating RMTs and RRCF for a job shop system to deal with volatile customer demands

Fundamental Carrier-Envelope Phase Noise Limitations during Pulse Formation and Detection

The difference between the positions of the maximum peak of the carrier wave of a laser pulse and the maximum of its intensity envelope is termed carrier-envelope phase (CEP). In the last decades, the control and stabilization of this parameter has greatly improved, which enables many applications in research fields that rely on CEP-stable pulses such as attosecond science and optical frequency metrology. Further progress in these fields depends strongly on minimizing the CEP noise that restricts stabilization performance. While the CEP of most high repetition-rate low-energy laser oscillators has been stabilized to a remarkable precision, some types of oscillators show extensive noise that inhibits precise stabilization. The CEP stabilization performance of low repetition-rate high peak-power amplified laser systems also remains limited by noise, which is believed to stem mainly from the CEP detection process. In this thesis, the origins of the CEP noise within four oscillators as well as the noise induced by the measurement of the CEP of amplified pulses are investigated. In the first part, the properties of the CEP noise of one Ti:sapphire oscillator and three different fiber oscillators are extracted by analyzing the unstabilized CEP traces by means of time-resolved correlation analysis of carrier-envelope amplitude and phase noise as well as by methods that reveal the underlying statistical noise properties. In the second part, investigations into the origin of CEP noise induced by the measurement of the CEP of amplified pulses are conducted by comparing several different CEP detection designs that are based on f -2 f interferometry. These detection setups differ in the employed sources of spectral broadening as well as frequency doubling media, both necessary steps to measure the CEP. The results in both parts of this thesis show that white quantum noise dominates most CEP measurements. In one particular fiber oscillator, the strong white noise is found to be a result of a correlating mechanism within the employed SESAM. During amplifier CEP detection, the CEP noise is found to be originating only to a marginal degree from the number of photons that are detected during the measurement, which excludes shot noise as a limiting source. Instead, the analysis reveals that the origin of the observed strong white noise can be interpreted as a loss of coherence during detection. This type of coherence is termed here intra-pulse coherence and describes the phase transfer within f -2 f interferometry. Its degradation is a result of amplitude-to-phase coupling during the spectral broadening process that leads to pulse-to-pulse fluctuations of the phases at the edges of the extended spectrum. Numerical simulations support the concept of intra-pulse coherence degradation and show that the degradation is substantially stronger during plasma-driven spectral broadening as compared to self-phase modulation-dominated spectral broadening. This difference in degradation also explains the much stronger CEP noise typically observed in amplified systems as compared to oscillators, as the former typically rely on filamentation-based and hence plasma-dominated spectral broadening for CEP detection. The concept of intra-pulse coherence constitutes a novel measure to assess the suitability of a spectral broadening mechanism for application in active as well as in passive CEP stabilization schemes and provides new strategies to reduce the impact of the CEP detection on the overall stabilization performance of most lasers.Diese Arbeit beschäftigt sich mit der Identifizierung und Minimierung fundamentaler Rauschquellen, die zu einer Limitierung des erreichbaren Carrier-Envelope Phasen (CEP) Jitters führen. Die Carrier-Envelope Phase beschreibt die Differenz zwischen dem Maximum der Trägerwelle und dem Scheitelpunkt der Intensitätseinhüllenden. In den letzten Jahrzehnten hat sich die Kontrolle und Stabilisierung der CEP deutlich verbessert, was zu einem schnellen Fortschritt in Forschungsfeldern geführt hat, bei denen CEP-stabile Pulse notwendig sind. Diese Forschungsfelder umfassen die Attosekundenforschung und optische Frequenzmetrologie. Weitere Entwicklungen in diesen Feldern hängt stark von der Minimierung von CEP Rauschen ab, welches die CEP Stabilisierung stark beeinträchtigt. Obwohl die CEP der Pulse der meisten Laseroszillatoren mit hohen Repetitionsraten äußerst genau stabilisiert werden kann, existieren einige Laseroszillatoren bei denen starke Rauschquellen eine Stabilisierung verhindern oder stark einschränken. Des Weiteren zeigen vor Allem verstärkte System mit niedrigen Repetitionsraten und hohen Spitzenleistungen eine Beschränkung der CEP Stabilisierung aufgrund von Rauschen, dass vermutlich zum großen Teil durch den Detektionsprozess entsteht. In dieser Arbeit ist der Ursprung von CEP Rauschen in vier unterschiedlichen Laseroszillatoren sowie während der Detektion der CEP von verstärkten Systemen untersucht worden. Im ersten Teil wurden die Eigenschaften des CEP Rauschens eines Ti:Saphir-basierten Oszillators und drei verschiedener Faserlaser analysiert. Hierzu wurde das Rauschen unter anderem mittels zeitaufgelöster Korrelationsanalyse von Carrier-Envelope Amplituden- und Phasenrauschen sowie mittels Methoden, die die statistischen Eigenschaften des Rauschens offenlegen, analysiert. Im zweiten Teil der Arbeit wurde das Rauschen untersucht, welches durch den Messprozess der CEP von verstärkten Pulsen mittels f -2 f Interferometrie entsteht. Experimentell wurden hierzu vier unterschiedliche Detektionsanordnungen verwendet, die sich durch die Nutzung unterschiedlicher nichtlinearer Prozesse zum Erzeugen der spektralen Verbreiterung sowie zur Erzeugung der zweiten Harmonischen unterscheiden. Die Ergebnisse in beiden Teilen der Arbeit zeigen dominierendes weißes Quantenrauschen in den meisten CEP Messungen. In einem bestimmten Faserlaser, in dem besonders starkes weißes Rauschen vorlag, konnte der Ursprung einerWechselwirkung innerhalb des verwendeten halbleiterbasierten sättigbaren Absorbers zugeordnet werden. Bei der Detektion der CEP bei verstärkten Systemen wurde hingegen gezeigt, dass niedrige Photonenzahlen und damit Schrotrauschen nur zum kleinen Teil für die starken weißen Rauschanteile verantwortlich gemacht werden kann. Stattdessen kann die Ursache des starken Rauschens einem Verlust von Kohärenz zugeordnet werden. Diese Art von Kohärenz ist hier mit intra-Puls Kohärenz bezeichnet und beschreibt den Phasentransfer innerhalb der Detektion mittels f -2 f Interferometrie. Der Verlust von intra-Puls Kohärenz ist eine Folge von Amplituden-zu-Phasen Koppelung während der spektralen Verbreiterung. Von Puls zu Puls führt dies zu Fluktuationen der Phase an beiden Rändern der erzeugten spektralen Verbreiterung. Numerische Simulationen unterstützen das Konzept der intra-Puls Kohärenz und zeigen auf, dass die Degradation bedeutend stärker bei plasmadominierten Prozessen ausfällt als im Vergleich zu spektraler Verbreiterung mittels Selbstphasenmodulation. Dieser unterschiedlich starke Verlust der intra-Puls Kohärenz erklärt das deutlich höhere Rauschniveau in verstärkten Systemen im Vergleich zu Oszillatoren, da verstärkte Systeme plasmadominierte Prozesse zur spektralen Verbreiterung nutzen. Das Konzept der intra-Puls Kohärenz stellt ein neues Maß zur Einschätzung einer Methode zur spektralen Verbreiterung für eine bestimmte Anwendung dar, die sowohl in aktiven sowie passiven CEP Stabilisierungen von Lasern eine Rolle spielt. Es ermöglicht somit neue Strategien, um den Einfluss der Detektion auf die CEP Stabilisierung der meisten Laser zu senken

Relaxing Fundamental Assumptions in Iterative Learning Control

Iterative learning control (ILC) is perhaps best decribed as an open loop feedforward control technique where the feedforward signal is learned through repetition of a single task. As the name suggests, given a dynamic system operating on a finite time horizon with the same desired trajectory, ILC aims to iteratively construct the inverse image (or its approximation) of the desired trajectory to improve transient tracking. In the literature, ILC is often interpreted as feedback control in the iteration domain due to the fact that learning controllers use information from past trials to drive the tracking error towards zero. However, despite the significant body of literature and powerful features, ILC is yet to reach widespread adoption by the control community, due to several assumptions that restrict its generality when compared to feedback control. In this dissertation, we relax some of these assumptions, mainly the fundamental invariance assumption, and move from the idea of learning through repetition to two dimensional systems, specifically repetitive processes, that appear in the modeling of engineering applications such as additive manufacturing, and sketch out future research directions for increased practicality: We develop an L1 adaptive feedback control based ILC architecture for increased robustness, fast convergence, and high performance under time varying uncertainties and disturbances. Simulation studies of the behavior of this combined L1-ILC scheme under iteration varying uncertainties lead us to the robust stability analysis of iteration varying systems, where we show that these systems are guaranteed to be stable when the ILC update laws are designed to be robust, which can be done using existing methods from the literature. As a next step to the signal space approach adopted in the analysis of iteration varying systems, we shift the focus of our work to repetitive processes, and show that the exponential stability of a nonlinear repetitive system is equivalent to that of its linearization, and consequently uniform stability of the corresponding state space matrix.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133232/1/altin_1.pd

Robust controller design--minimizing peak-to-peak gain

Includes bibliographical references (p. 87-92).Supported by Wright Patterson Air Force Base. F33615-90-c-3608Munther A. Dahleh