2,362 research outputs found
A Worst-Case Latency and Age Analysis of Coded Distributed Computing With Unreliable Workers and Periodic Tasks
Full text linkOver the past decade, the deep learning revolution has led to ever-increasing demands for computing power and working memory to support larger and larger neural networks. As this coincided with the end of Moore’s law, distributed solutions have emerged as a natural answer: in particular, the novel Coded Distributed Computing (CDC) paradigm exploits results from coding theory to divide large tasks into redundant sets of smaller subtasks to be processed across multiple workers, making the computation more robust to stragglers and malicious worker nodes. Optimizing the use of these distributed computing resources is critical, as excessive redundancy might impact on performance and energy consumption. This work considers a CDC system receiving periodic tasks, deriving the full distribution of the latency, reliability, and Peak Age of Information (PAoI) under worker diversity and random failures. The CDC system is modeled as a fork-join queue, where only K of the coded N subtasks are necessary to solve the overall task, and workers can hold up to L subtasks in their queues. Our results are useful for resource optimization, showing the relationship between system load, redundancy, and latency, as well as the trade-off between latency, reliability, and age performance
Peak Age of Information Distribution Bounds for Multi-Connectivity Transmissions
Full text linkTransmission of packets over multiple wireless interfaces is an effective method to improve reliability and reduce the delay of Internet of Things (IoT) transmissions. In this context, Age of Information (AoI) has become a useful metric for many applications, measuring the freshness of the information available on a process that is measured by a remote sensor. In this work, we study the Peak Age of Information (PAoI) of an M/M/2 fork-join system, in which a sensor sends packets simultaneously over 2 separate queuing systems. The first packet to reach the receiver is considered as delivered. We derive lower and upper bounds on the PAoI for systems with finite and infinite buffers based on a low-traffic approximation, and show that the bounds are very tight at the optimal working point, so that the best rate derived from the bounds is very close to the optimum.</p
Latency and Peak Age of Information in Non-Preemptive Multipath Communications
Full text linkMultipath communication is a critical technology to provide Quality of Service (QoS) to interactive and Internet of Things (IoT) monitoring and control applications. In this work, we model the exemplary case with two paths and consider different strategies that exploit redundancy and coding to improve the timing performance of wireless communications. We consider two disparate scenarios, in which the data blocks are generated via a Markovian and a deterministic process, respectively. We consider simple scheduling and coding schemes, considering both lossless and lossy encoding, and modeling the resulting process as a fork-join queue with different arrival processes. We analyze the full distribution of two relevant metrics for the two-path case: the packet delay and the Peak Age of Information (PAoI), which measures the freshness of the information at the receiver. The results show interesting trade-offs between the update frequency, latency, PAoI, and level of compression, with interesting implications for system designers
Latency and Peak Age of Information in Multipath Coded Communications
Full text linkThe use of parallel communication paths to provide reliable, low-latency service is a significant trend in cellular networks, as it can provide a way to satisfy the exacting Quality of Service (QoS) requirements of 5G-enabled applications. In particular, coding data across multiple paths can significantly improve reliability and reduce overall latency, compensating for stragglers and lost packets with the redundant information from other paths. However, the design trade-offs in optimizing these systems are non-trivial, particularly when considering Age of Information (AoI). In this work, we derive the latency and Peak Age of Information (PAoI) distributions for such a multipath coded system, drawing design insights on how to optimize either. While preemption is always the optimal choice to minimize AoI in a single-path, uncoded queuing system, the trade-off in this case is more complex, as dropping a late packet on one path might affect the reliability of the whole block. Our results show that the parameters to minimize the PAoI lead to poor latency performance, and optimizing both at once might require significant resource overprovisioning
Beatriz Manrique de Lara Alberro, Marchioness of García del Postigo, author of La Pensadora Gaditana under pseudonym “Beatriz Cienfuegos”
Full text linkEste artículo analiza una amplia documentación y concluye que Beatriz
Manrique de Lara Alberro, Marquesa de García del Postigo, fue la autora del periódico La Pensadora Gaditana y de la traducción de la tragedia Zaïre de Voltaire publicada con el título de Combates de amor y ley. En el primer caso, bajo el pseudónimo de «Beatriz Cienfuegos», compuesto por su propio nombre y un anagrama a partir del nombre de su hija; en el segundo, bajo otro pseudónimo formado con el nombre de su marido y su hijo, «Juan Francisco del Postigo», transformado en el anagrama Fernando Jugaccis Pilotos.This paper analyzes a large amount of data and concludes that Beatriz Manrique de Lara Alberro, Marchioness of García del Postigo, was author of the newspaper La Pensadora Gaditana and translator of the Voltaire’s tragedy Zaïre, published as Combates de amor y ley. In the first case, under the pseudonym of «Beatriz Cienfuegos», composed by her own name and an anagram from the name of her daughter; in the second, under another pseudonym formed by the names of her husband and one of her sons, «Juan Francisco del Postigo», transformed into the anagram «Fernando Jugaccis Pilotos»
The Art of Beatriz da Costa
Full text linkIn this article, the author interviews Beatriz da Costa, an interdisciplinary artist whose work combines art, science, engineering, and politics to address environmental and social issues. While in residence at Montalvo Arts Center in 2010, she developed The Endangered Species Finder, a smartphone app that guides users to the habitats of threatened species in the UK, encouraging real-world encounters beyond museum displays
Multi-Agent Deep Reinforcement Learning for Distributed Satellite Routing.
Full text linkUniversidad de Málaga. Campus de Excelencia Internacional Andalucía Tech.This paper introduces a Multi-Agent Deep Rein- forcement Learning (MA-DRL) approach for routing in Low Earth Orbit Satellite Constellations (LSatCs). Each satellite is an independent decision-making agent with a partial knowledge of the environment, and supported by feedback received from the nearby agents. Building on our previous work that introduced a Q-routing solution, the contribution of this paper is to extend it to a deep learning framework able to quickly adapt to the network and traffic changes, and based on two phases: (1) An offline exploration learning phase that relies on a global Deep Neural Network (DNN) to learn the optimal paths at each possible position and congestion level; (2) An online exploitation phase with local, on-board, pre-trained DNNs. Results show that MA- DRL efficiently learns optimal routes offline that are then loaded for an efficient distributed routing online.F. Lozano-Cuadra ([email protected]) and B. Soret are with the Telecom- munications Research Institute, University of Malaga, 29071, Malaga, Spain. This work is partially funded by ESA SatNEx V (prime contract no. 4000130962/20/NL/NL/FE), and by the Spanish Ministerio de Ciencia, Inno- vacio ́n y Universidades (PID2022-136269OB-I00)
On Age-of-Information Aware Resource Allocation for Industrial Control-Communication-Codesign
Full text linkUnter dem Überbegriff Industrie 4.0 wird in der industriellen Fertigung die zunehmende Digitalisierung und Vernetzung von industriellen Maschinen und Prozessen zusammengefasst. Die drahtlose, hoch-zuverlässige, niedrig-latente Kommunikation (engl. ultra-reliable low-latency communication, URLLC) – als Bestandteil von 5G gewährleistet höchste Dienstgüten, die mit industriellen drahtgebundenen Technologien vergleichbar sind und wird deshalb als Wegbereiter von Industrie 4.0 gesehen. Entgegen diesem Trend haben eine Reihe von Arbeiten im Forschungsbereich der vernetzten Regelungssysteme (engl. networked control systems, NCS) gezeigt, dass die hohen Dienstgüten von URLLC nicht notwendigerweise erforderlich sind, um eine hohe Regelgüte zu erzielen. Das Co-Design von Kommunikation und Regelung ermöglicht eine gemeinsame Optimierung von Regelgüte und Netzwerkparametern durch die Aufweichung der Grenze zwischen Netzwerk- und Applikationsschicht. Durch diese Verschränkung wird jedoch eine fundamentale (gemeinsame) Neuentwicklung von Regelungssystemen und Kommunikationsnetzen nötig, was ein Hindernis für die Verbreitung dieses Ansatzes darstellt. Stattdessen bedient sich diese Dissertation einem Co-Design-Ansatz, der beide Domänen weiterhin eindeutig voneinander abgrenzt, aber das Informationsalter (engl. age of information, AoI) als bedeutenden Schnittstellenparameter ausnutzt.
Diese Dissertation trägt dazu bei, die Echtzeitanwendungszuverlässigkeit als Folge der Überschreitung eines vorgegebenen Informationsalterschwellenwerts zu quantifizieren und fokussiert sich dabei auf den Paketverlust als Ursache. Anhand der Beispielanwendung eines fahrerlosen Transportsystems wird gezeigt, dass die zeitlich negative Korrelation von Paketfehlern, die in heutigen Systemen keine Rolle spielt, für Echtzeitanwendungen äußerst vorteilhaft ist. Mit der Annahme von schnellem Schwund als dominanter Fehlerursache auf der Luftschnittstelle werden durch zeitdiskrete Markovmodelle, die für die zwei Netzwerkarchitekturen Single-Hop und Dual-Hop präsentiert werden, Kommunikationsfehlerfolgen auf einen Applikationsfehler abgebildet. Diese Modellierung ermöglicht die analytische Ableitung von anwendungsbezogenen Zuverlässigkeitsmetriken wie die durschnittliche Dauer bis zu einem Fehler (engl. mean time to failure). Für Single-Hop-Netze wird das neuartige Ressourcenallokationsschema State-Aware Resource Allocation (SARA) entwickelt, das auf dem Informationsalter beruht und die Anwendungszuverlässigkeit im Vergleich zu statischer Multi-Konnektivität um Größenordnungen erhöht, während der Ressourcenverbrauch im Bereich von konventioneller Einzelkonnektivität bleibt.
Diese Zuverlässigkeit kann auch innerhalb eines Systems von Regelanwendungen, in welchem mehrere Agenten um eine begrenzte Anzahl Ressourcen konkurrieren, statistisch garantiert werden, wenn die Anzahl der verfügbaren Ressourcen pro Agent um ca. 10 % erhöht werden. Für das Dual-Hop Szenario wird darüberhinaus ein Optimierungsverfahren vorgestellt, das eine benutzerdefinierte Kostenfunktion minimiert, die niedrige Anwendungszuverlässigkeit, hohes Informationsalter und hohen durchschnittlichen Ressourcenverbrauch bestraft und so das benutzerdefinierte optimale SARA-Schema ableitet. Diese Optimierung kann offline durchgeführt und als Look-Up-Table in der unteren Medienzugriffsschicht zukünftiger industrieller Drahtlosnetze implementiert werden.:1. Introduction 1
1.1. The Need for an Industrial Solution . . . . . . . . . . . . . . . . . . . 3
1.2. Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2. Related Work 7
2.1. Communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2. Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3. Codesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3.1. The Need for Abstraction – Age of Information . . . . . . . . 11
2.4. Dependability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3. Deriving Proper Communications Requirements 17
3.1. Fundamentals of Control Theory . . . . . . . . . . . . . . . . . . . . 18
3.1.1. Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1.2. Performance Requirements . . . . . . . . . . . . . . . . . . . 21
3.1.3. Packet Losses and Delay . . . . . . . . . . . . . . . . . . . . . 22
3.2. Joint Design of Control Loop with Packet Losses . . . . . . . . . . . . 23
3.2.1. Method 1: Reduced Sampling . . . . . . . . . . . . . . . . . . 23
3.2.2. Method 2: Markov Jump Linear System . . . . . . . . . . . . . 25
3.2.3. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3. Focus Application: The AGV Use Case . . . . . . . . . . . . . . . . . . 31
3.3.1. Control Loop Model . . . . . . . . . . . . . . . . . . . . . . . 31
3.3.2. Control Performance Requirements . . . . . . . . . . . . . . . 33
3.3.3. Joint Modeling: Applying Reduced Sampling . . . . . . . . . . 34
3.3.4. Joint Modeling: Applying MJLS . . . . . . . . . . . . . . . . . 34
3.4. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4. Modeling Control-Communication Failures 43
4.1. Communication Assumptions . . . . . . . . . . . . . . . . . . . . . . 43
4.1.1. Small-Scale Fading as a Cause of Failure . . . . . . . . . . . . 44
4.1.2. Connectivity Models . . . . . . . . . . . . . . . . . . . . . . . 46
4.2. Failure Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2.1. Single-hop network . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2.2. Dual-hop network . . . . . . . . . . . . . . . . . . . . . . . . 51
4.3. Performance Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.3.1. Mean Time to Failure . . . . . . . . . . . . . . . . . . . . . . . 54
4.3.2. Packet Loss Ratio . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.3.3. Average Number of Assigned Channels . . . . . . . . . . . . . 57
4.3.4. Age of Information . . . . . . . . . . . . . . . . . . . . . . . . 57
4.4. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5. Single Hop – Single Agent 61
5.1. State-Aware Resource Allocation . . . . . . . . . . . . . . . . . . . . 61
5.2. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.3. Erroneous Acknowledgments . . . . . . . . . . . . . . . . . . . . . . 67
5.4. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6. Single Hop – Multiple Agents 71
6.1. Failure Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6.1.1. Admission Control . . . . . . . . . . . . . . . . . . . . . . . . 72
6.1.2. Transition Probabilities . . . . . . . . . . . . . . . . . . . . . . 73
6.1.3. Computational Complexity . . . . . . . . . . . . . . . . . . . 74
6.1.4. Performance Metrics . . . . . . . . . . . . . . . . . . . . . . . 75
6.2. Illustration Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
6.3. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
6.3.1. Verification through System-Level Simulation . . . . . . . . . 78
6.3.2. Applicability on the System Level . . . . . . . . . . . . . . . . 79
6.3.3. Comparison of Admission Control Schemes . . . . . . . . . . 80
6.3.4. Impact of the Packet Loss Tolerance . . . . . . . . . . . . . . . 82
6.3.5. Impact of the Number of Agents . . . . . . . . . . . . . . . . . 84
6.3.6. Age of Information . . . . . . . . . . . . . . . . . . . . . . . . 84
6.3.7. Channel Saturation Ratio . . . . . . . . . . . . . . . . . . . . 86
6.3.8. Enforcing Full Channel Saturation . . . . . . . . . . . . . . . 86
6.4. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
7. Dual Hop – Single Agent 91
7.1. State-Aware Resource Allocation . . . . . . . . . . . . . . . . . . . . 91
7.2. Optimization Targets . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.3. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7.3.1. Extensive Simulation . . . . . . . . . . . . . . . . . . . . . . . 96
7.3.2. Non-Integer-Constrained Optimization . . . . . . . . . . . . . 98
7.4. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
8. Conclusions and Outlook 105
8.1. Key Results and Conclusions . . . . . . . . . . . . . . . . . . . . . . . 105
8.2. Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
A. DC Motor Model 111
Bibliography 113
Publications of the Author 127
List of Figures 129
List of Tables 131
List of Operators and Constants 133
List of Symbols 135
List of Acronyms 137
Curriculum Vitae 139In industrial manufacturing, Industry 4.0 refers to the ongoing convergence of the real and virtual worlds, enabled through intelligently interconnecting industrial machines and processes through information and communications technology. Ultrareliable low-latency communication (URLLC) is widely regarded as the enabling technology for Industry 4.0 due to its ability to fulfill highest quality-of-service (QoS) comparable to those of industrial wireline connections. In contrast to this trend, a range of works in the research domain of networked control systems have shown that URLLC’s supreme QoS is not necessarily required to achieve high quality-ofcontrol; the co-design of control and communication enables to jointly optimize and balance both quality-of-control parameters and network parameters through blurring the boundary between application and network layer. However, through the tight interlacing, this approach requires a fundamental (joint) redesign of both control systems and communication networks and may therefore not lead to short-term widespread adoption. Therefore, this thesis instead embraces a novel co-design approach which keeps both domains distinct but leverages the combination of control and communications by yet exploiting the age of information (AoI) as a valuable interface metric.
This thesis contributes to quantifying application dependability as a consequence of exceeding a given peak AoI with the particular focus on packet losses. The beneficial influence of negative temporal packet loss correlation on control performance is demonstrated by means of the automated guided vehicle use case. Assuming small-scale fading as the dominant cause of communication failure, a series of communication failures are mapped to an application failure through discrete-time Markov models for single-hop (e.g, only uplink or downlink) and dual-hop (e.g., subsequent uplink and downlink) architectures. This enables the derivation of application-related dependability metrics such as the mean time to failure in closed form. For single-hop networks, an AoI-aware resource allocation strategy termed state-aware resource allocation (SARA) is proposed that increases the application reliability by orders of magnitude compared to static multi-connectivity while keeping the resource consumption in the range of best-effort single-connectivity. This dependability can also be statistically guaranteed on a system level – where multiple agents compete for a limited number of resources – if the provided amount of resources per agent is increased by approximately 10 %. For the dual-hop scenario, an AoI-aware resource allocation optimization is developed that minimizes a user-defined penalty function that punishes low application reliability, high AoI, and high average resource consumption. This optimization may be carried out offline and each resulting optimal SARA scheme may be implemented as a look-up table in the lower medium access control layer of future wireless industrial networks.:1. Introduction 1
1.1. The Need for an Industrial Solution . . . . . . . . . . . . . . . . . . . 3
1.2. Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2. Related Work 7
2.1. Communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2. Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3. Codesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3.1. The Need for Abstraction – Age of Information . . . . . . . . 11
2.4. Dependability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3. Deriving Proper Communications Requirements 17
3.1. Fundamentals of Control Theory . . . . . . . . . . . . . . . . . . . . 18
3.1.1. Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1.2. Performance Requirements . . . . . . . . . . . . . . . . . . . 21
3.1.3. Packet Losses and Delay . . . . . . . . . . . . . . . . . . . . . 22
3.2. Joint Design of Control Loop with Packet Losses . . . . . . . . . . . . 23
3.2.1. Method 1: Reduced Sampling . . . . . . . . . . . . . . . . . . 23
3.2.2. Method 2: Markov Jump Linear System . . . . . . . . . . . . . 25
3.2.3. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3. Focus Application: The AGV Use Case . . . . . . . . . . . . . . . . . . 31
3.3.1. Control Loop Model . . . . . . . . . . . . . . . . . . . . . . . 31
3.3.2. Control Performance Requirements . . . . . . . . . . . . . . . 33
3.3.3. Joint Modeling: Applying Reduced Sampling . . . . . . . . . . 34
3.3.4. Joint Modeling: Applying MJLS . . . . . . . . . . . . . . . . . 34
3.4. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4. Modeling Control-Communication Failures 43
4.1. Communication Assumptions . . . . . . . . . . . . . . . . . . . . . . 43
4.1.1. Small-Scale Fading as a Cause of Failure . . . . . . . . . . . . 44
4.1.2. Connectivity Models . . . . . . . . . . . . . . . . . . . . . . . 46
4.2. Failure Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2.1. Single-hop network . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2.2. Dual-hop network . . . . . . . . . . . . . . . . . . . . . . . . 51
4.3. Performance Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.3.1. Mean Time to Failure . . . . . . . . . . . . . . . . . . . . . . . 54
4.3.2. Packet Loss Ratio . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.3.3. Average Number of Assigned Channels . . . . . . . . . . . . . 57
4.3.4. Age of Information . . . . . . . . . . . . . . . . . . . . . . . . 57
4.4. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5. Single Hop – Single Agent 61
5.1. State-Aware Resource Allocation . . . . . . . . . . . . . . . . . . . . 61
5.2. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.3. Erroneous Acknowledgments . . . . . . . . . . . . . . . . . . . . . . 67
5.4. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6. Single Hop – Multiple Agents 71
6.1. Failure Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6.1.1. Admission Control . . . . . . . . . . . . . . . . . . . . . . . . 72
6.1.2. Transition Probabilities . . . . . . . . . . . . . . . . . . . . . . 73
6.1.3. Computational Complexity . . . . . . . . . . . . . . . . . . . 74
6.1.4. Performance Metrics . . . . . . . . . . . . . . . . . . . . . . . 75
6.2. Illustration Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
6.3. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
6.3.1. Verification through System-Level Simulation . . . . . . . . . 78
6.3.2. Applicability on the System Level . . . . . . . . . . . . . . . . 79
6.3.3. Comparison of Admission Control Schemes . . . . . . . . . . 80
6.3.4. Impact of the Packet Loss Tolerance . . . . . . . . . . . . . . . 82
6.3.5. Impact of the Number of Agents . . . . . . . . . . . . . . . . . 84
6.3.6. Age of Information . . . . . . . . . . . . . . . . . . . . . . . . 84
6.3.7. Channel Saturation Ratio . . . . . . . . . . . . . . . . . . . . 86
6.3.8. Enforcing Full Channel Saturation . . . . . . . . . . . . . . . 86
6.4. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
7. Dual Hop – Single Agent 91
7.1. State-Aware Resource Allocation . . . . . . . . . . . . . . . . . . . . 91
7.2. Optimization Targets . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.3. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7.3.1. Extensive Simulation . . . . . . . . . . . . . . . . . . . . . . . 96
7.3.2. Non-Integer-Constrained Optimization . . . . . . . . . . . . . 98
7.4. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
8. Conclusions and Outlook 105
8.1. Key Results and Conclusions . . . . . . . . . . . . . . . . . . . . . . . 105
8.2. Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
A. DC Motor Model 111
Bibliography 113
Publications of the Author 127
List of Figures 129
List of Tables 131
List of Operators and Constants 133
List of Symbols 135
List of Acronyms 137
Curriculum Vitae 13
El Tlacuache Núm. 482 (2011). 482 Año 11 (2011) agosto. El Tlacuache
No full textUn cabildo a modo por Paul Hersch Martínez. -Recuperar las soluciones ignoradas. La conservación en el antiguo convento de Tepoztlán por Beatriz Sandoval Zarauz
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