Distributed Control and Optimization for Communication and Power Systems

We are at the cusp of a historic transformation of both communication system and electricity system. This creates challenges as well as opportunities for the study of networked systems. Problems of these systems typically involve a huge number of end points that require intelligent coordination in a distributed manner. In this thesis, we develop models, theories, and scalable distributed optimization and control algorithms to overcome these challenges.

This thesis focuses on two specific areas: multi-path TCP (Transmission Control Protocol) and electricity distribution system operation and control. Multi-path TCP (MP-TCP) is a TCP extension that allows a single data stream to be split across multiple paths. MP-TCP has the potential to greatly improve reliability as well as efficiency of communication devices. We propose a fluid model for a large class of MP-TCP algorithms and identify design criteria that guarantee the existence, uniqueness, and stability of system equilibrium. We clarify how algorithm parameters impact TCP-friendliness, responsiveness, and window oscillation and demonstrate an inevitable tradeoff among these properties. We discuss the implications of these properties on the behavior of existing algorithms and motivate a new algorithm Balia (balanced linked adaptation) which generalizes existing algorithms and strikes a good balance among TCP-friendliness, responsiveness, and window oscillation. We have implemented Balia in the Linux kernel. We use our prototype to compare the new proposed algorithm Balia with existing MP-TCP algorithms.

Our second focus is on designing computationally efficient algorithms for electricity distribution system operation and control. First, we develop efficient algorithms for feeder reconfiguration in distribution networks. The feeder reconfiguration problem chooses the on/off status of the switches in a distribution network in order to minimize a certain cost such as power loss. It is a mixed integer nonlinear program and hence hard to solve. We propose a heuristic algorithm that is based on the recently developed convex relaxation of the optimal power flow problem. The algorithm is efficient and can successfully computes an optimal configuration on all networks that we have tested. Moreover we prove that the algorithm solves the feeder reconfiguration problem optimally under certain conditions. We also propose a more efficient algorithm and it incurs a loss in optimality of less than 3% on the test networks.

Second, we develop efficient distributed algorithms that solve the optimal power flow (OPF) problem on distribution networks. The OPF problem determines a network operating point that minimizes a certain objective such as generation cost or power loss. Traditionally OPF is solved in a centralized manner. With increasing penetration of volatile renewable energy resources in distribution systems, we need faster and distributed solutions for real-time feedback control. This is difficult because power flow equations are nonlinear and kirchhoff's law is global. We propose solutions for both balanced and unbalanced radial distribution networks. They exploit recent results that suggest solving for a globally optimal solution of OPF over a radial network through a second-order cone program (SOCP) or semi-definite program (SDP) relaxation. Our distributed algorithms are based on the alternating direction method of multiplier (ADMM), but unlike standard ADMM-based distributed OPF algorithms that require solving optimization subproblems using iterative methods, the proposed solutions exploit the problem structure that greatly reduce the computation time. Specifically, for balanced networks, our decomposition allows us to derive closed form solutions for these subproblems and it speeds up the convergence by 1000x times in simulations. For unbalanced networks, the subproblems reduce to either closed form solutions or eigenvalue problems whose size remains constant as the network scales up and computation time is reduced by 100x compared with iterative methods.

Control mechanisms in the human binocular oculomotor system

A study of human eye movements was made in order to elucidate the nature of the control mechanism in the binocular oculomotor system.

We first examined spontaneous eye movements during monocular and binocular fixation in order to determine the corrective roles of flicks and drifts. It was found that both types of motion correct fixational errors, although flicks are somewhat more active in this respect. Vergence error is a stimulus for correction by drifts but not by flicks, while binocular vertical discrepancy of the visual axes does not trigger corrective movements.

Second, we investigated the non-linearities of the oculomotor system by examining the eye movement responses to point targets moving in two dimensions in a subjectively unpredictable manner. Such motions consisted of hand-limited Gaussian random motion and also of the sum of several non-integrally related sinusoids. We found that there is no direct relationship between the phase and the gain of the oculomotor system. Delay of eye movements relative to target motion is determined by the necessity of generating a minimum afferent (input) signal at the retina in order to trigger corrective eye movements. The amplitude of the response is a function of the biological constraints of the efferent (output) portion of the system: for target motions of narrow bandwidth, the system responds preferentially to the highest frequency; for large bandwidth motions, the system distributes the available energy equally over all frequencies. Third, the power spectra of spontaneous eye movements were compared with the spectra of tracking eye movements for Gaussian random target motions of varying bandwidths. It was found that there is essentially no difference among the various curves. The oculomotor system tracks a target, not by increasing the mean rate of impulses along the motoneurons of the extra-ocular muscles, but rather by coordinating those spontaneous impulses which propagate along the motoneurons during stationary fixation. Thus, the system operates at full output at all times.

Fourth, we examined the relative magnitude and phase of motions of the left and the right visual axes during monocular and binocular viewing. We found that the two visual axes move vertically in perfect synchronization at all frequencies for any viewing condition. This is not true for horizontal motions: the amount of vergence noise is highest for stationary fixation and diminishes for tracking tasks as the bandwidth of the target motion increases. Furthermore, movements of the occluded eye are larger than those of the seeing eye in monocular viewing. This effect is more pronounced for horizontal motions, for stationary fixation, and for lower frequencies.

Finally, we have related our findings to previously known facts about the pertinent nerve pathways in order to postulate a model for the neurological binocular control of the visual axes.

Distributed Optimal Control of Cyber-Physical Systems: Controller Synthesis, Architecture Design and System Identification

The centralized paradigm of a single controller and a single plant upon which modern control theory is built is no longer applicable to modern cyber-physical systems of interest, such as the power-grid, software defined networks or automated highways systems, as these are all large-scale and spatially distributed. Both the scale and the distributed nature of these systems has motivated the decentralization of control schemes into local sub-controllers that measure, exchange and act on locally available subsets of the globally available system information. This decentralization of control logic leads to different decision makers acting on asymmetric information sets, introduces the need for coordination between them, and perhaps not surprisingly makes the resulting optimal control problem much harder to solve. In fact, shortly after such questions were posed, it was realized that seemingly simple decentralized optimal control problems are computationally intractable to solve, with the Wistenhausen counterexample being a famous instance of this phenomenon. Spurred on by this perhaps discouraging result, a concerted 40 year effort to identify tractable classes of distributed optimal control problems culminated in the notion of quadratic invariance, which loosely states that if sub-controllers can exchange information with each other at least as quickly as the effect of their control actions propagates through the plant, then the resulting distributed optimal control problem admits a convex formulation.

The identification of quadratic invariance as an appropriate means of "convexifying" distributed optimal control problems led to a renewed enthusiasm in the controller synthesis community, resulting in a rich set of results over the past decade. The contributions of this thesis can be seen as being a part of this broader family of results, with a particular focus on closing the gap between theory and practice by relaxing or removing assumptions made in the traditional distributed optimal control framework. Our contributions are to the foundational theory of distributed optimal control, and fall under three broad categories, namely controller synthesis, architecture design and system identification.

We begin by providing two novel controller synthesis algorithms. The first is a solution to the distributed H-infinity optimal control problem subject to delay constraints, and provides the only known exact characterization of delay-constrained distributed controllers satisfying an H-infinity norm bound. The second is an explicit dynamic programming solution to a two player LQR state-feedback problem with varying delays. Accommodating varying delays represents an important first step in combining distributed optimal control theory with the area of Networked Control Systems that considers lossy channels in the feedback loop. Our next set of results are concerned with controller architecture design. When designing controllers for large-scale systems, the architectural aspects of the controller such as the placement of actuators, sensors, and the communication links between them can no longer be taken as given -- indeed the task of designing this architecture is now as important as the design of the control laws themselves. To address this task, we formulate the Regularization for Design (RFD) framework, which is a unifying computationally tractable approach, based on the model matching framework and atomic norm regularization, for the simultaneous co-design of a structured optimal controller and the architecture needed to implement it. Our final result is a contribution to distributed system identification. Traditional system identification techniques such as subspace identification are not computationally scalable, and destroy rather than leverage any a priori information about the system's interconnection structure. We argue that in the context of system identification, an essential building block of any scalable algorithm is the ability to estimate local dynamics within a large interconnected system. To that end we propose a promising heuristic for identifying the dynamics of a subsystem that is still connected to a large system. We exploit the fact that the transfer function of the local dynamics is low-order, but full-rank, while the transfer function of the global dynamics is high-order, but low-rank, to formulate this separation task as a nuclear norm minimization problem. Finally, we conclude with a brief discussion of future research directions, with a particular emphasis on how to incorporate the results of this thesis, and those of optimal control theory in general, into a broader theory of dynamics, control and optimization in layered architectures.

A Data Dropout Compensation Algorithm Based on the Iterative Learning Control Methodology for Discrete-Time Systems

This paper deals with the convergence of a remote iterative learning control system subject to data dropouts. The system is composed by a set of discrete-time multiple input-multiple output linear models, each one with its corresponding actuator device and its sensor. Each actuator applies the input signals vector to its corresponding model at the sampling instants and the sensor measures the output signals vector. The iterative learning law is processed in a controller located far away of the models so the control signals vector has to be transmitted from the controller to the actuators through transmission channels. Such a law uses the measurements of each model to generate the input vector to be applied to its subsequent model so the measurements of the models have to be transmitted from the sensors to the controller. All transmissions are subject to failures which are described as a binary sequence taking value 1 or 0. A compensation dropout technique is used to replace the lost data in the transmission processes. The convergence to zero of the errors between the output signals vector and a reference one is achieved as the number of models tends to infinity.

Alveolar nitric oxide and its role in pediatric asthma control assessment

Resumen Background: Nitric oxide can be measured at multiple flow rates to determine proximal (maximum airway nitric oxide flux; Jaw(NO)) and distal inflammation (alveolar nitric oxide concentration; CA(NO)). The main aim was to study the association among symptoms, lung function, proximal (maximum airway nitric oxide flux) and distal (alveolar nitric oxide concentration) airway inflammation in asthmatic children treated and not treated with inhaled glucocorticoids. Methods: A cross-sectional study with prospective data collection was carried out in a consecutive sample of girls and boys aged between 6 and 16 years with a medical diagnosis of asthma. Maximum airway nitric oxide flux and alveolar nitric oxide concentration were calculated according to the two-compartment model. In asthmatic patients, the asthma control questionnaire (CAN) was completed and forced spirometry was performed. In controls, differences between the sexes in alveolar nitric oxide concentration and maximum airway nitric oxide flux and their correlation with height were studied. The correlation among the fraction of exhaled NO at 50 ml/s (FENO50), CA(NO), Jaw(NO), forced expiratory volume in 1 second (FEV1) and the CAN questionnaire was measured and the degree of agreement regarding asthma control assessment was studied using Cohen's kappa. Results: We studied 162 children; 49 healthy (group 1), 23 asthmatic participants without treatment (group 2) and 80 asthmatic patients treated with inhaled corticosteroids (group 3). CA(NO) (ppb) was 2.2 (0.1-4.5), 3 (0.2-9.2) and 2.45 (0.1-24), respectively. Jaw(NO) (pl/s) was 516 (98.3-1470), 2356.67 (120-6110) and 1426 (156-11805), respectively. There was a strong association (r = 0.97) between FENO50 and Jaw(NO) and the degree of agreement was very good in group 2 and was good in group 3. There was no agreement or only slight agreement between the measures used to monitor asthma control (FEV1, CAN questionnaire, CA(NO) and Jaw(NO)). Conclusions: The results for CA(NO) and Jaw(NO) in controls were similar to those found in other reports. There was no agreement or only slight agreement among the three measure instruments analyzed to assess asthma control. In our sample, no additional information was provided by CA(NO) and Jaw(NO).

Control de vuelo de un cuadricóptero AR-Drone

[ES]En este TFG se obtendrá un algoritmo de generación de trayectorias para el cuadricóptero AR-Drone capaz de conseguir trazados lo más rápidos posibles teniendo en cuenta la dinámica del modelo y las limitaciones del entorno. Así mismo se propondrá un control primitivo para la detección de obstáculos. Mediante las comunicaciones con el cuadricóptero y el control de los parámetros característicos del medio, se establecerá usando el lenguaje C# los bucles de programación necesarios para discriminar todas las trayectorias desfavorables y obtener una que se adecue a nuestros criterios.

Altered expression of Alzheimer's disease-related genes in the cerebellum of autistic patients: a model for disrupted brain connectome and therapy

Autism and Alzheimer's disease (AD) are, respectively, neurodevelopmental and degenerative diseases with an increasing epidemiological burden. The AD-associated amyloid-beta precursor protein-alpha has been shown to be elevated in severe autism, leading to the 'anabolic hypothesis' of its etiology. Here we performed a focused microarray analysis of genes belonging to NOTCH and WNT signaling cascades, as well as genes related to AD and apoptosis pathways in cerebellar samples from autistic individuals, to provide further evidence for pathological relevance of these cascades for autism. By using the limma package from R and false discovery rate, we demonstrated that 31% (116 out of 374) of the genes belonging to these pathways displayed significant changes in expression (corrected P-values <0.05), with mitochondria- related genes being the most downregulated. We also found upregulation of GRIN1, the channel-forming subunit of NMDA glutamate receptors, and MAP3K1, known activator of the JNK and ERK pathways with anti-apoptotic effect. Expression of PSEN2 (presinilin 2) and APBB1 (or F65) were significantly lower when compared with control samples. Based on these results, we propose a model of NMDA glutamate receptor-mediated ERK activation of alpha-secretase activity and mitochondrial adaptation to apoptosis that may explain the early brain overgrowth and disruption of synaptic plasticity and connectome in autism. Finally, systems pharmacology analyses of the model that integrates all these genes together (NOWADA) highlighted magnesium (Mg2+) and rapamycin as most efficient drugs to target this network model in silico. Their potential therapeutic application, in the context of autism, is therefore discussed.

Robust Sliding Control of SEIR Epidemic Models

This paper is aimed at designing a robust vaccination strategy capable of eradicating an infectious disease from a population regardless of the potential uncertainty in the parameters defining the disease. For this purpose, a control theoretic approach based on a sliding-mode control law is used. Initially, the controller is designed assuming certain knowledge of an upper-bound of the uncertainty signal. Afterwards, this condition is removed while an adaptive sliding control system is designed. The closed-loop properties are proved mathematically in the nonadaptive and adaptive cases. Furthermore, the usual sign function appearing in the sliding-mode control is substituted by the saturation function in order to prevent chattering. In addition, the properties achieved by the closed-loop system under this variation are also stated and proved analytically. The closed-loop system is able to attain the control objective regardless of the parametric uncertainties of the model and the lack of a priori knowledge on the system.

Effect of Neonatal Asphyxia on the Impairment of the Auditory Pathway by Recording Auditory Brainstem Responses in Newborn Piglets: A New Experimentation Model to Study the Perinatal Hypoxic-Ischemic Damage on the Auditory Syste

Introduction Hypoxia-ischemia (HI) is a major perinatal problem that results in severe damage to the brain impairing the normal development of the auditory system. The purpose of the present study is to study the effect of perinatal asphyxia on the auditory pathway by recording auditory brain responses in a novel animal experimentation model in newborn piglets. Method Hypoxia-ischemia was induced to 1.3 day-old piglets by clamping 30 minutes both carotid arteries by vascular occluders and lowering the fraction of inspired oxygen. We compared the Auditory Brain Responses (ABRs) of newborn piglets exposed to acute hypoxia/ischemia (n = 6) and a control group with no such exposure (n = 10). ABRs were recorded for both ears before the start of the experiment (baseline), after 30 minutes of HI injury, and every 30 minutes during 6 h after the HI injury. Results Auditory brain responses were altered during the hypoxic-ischemic insult but recovered 30-60 minutes later. Hypoxia/ischemia seemed to induce auditory functional damage by increasing I-V latencies and decreasing wave I, III and V amplitudes, although differences were not significant. Conclusion The described experimental model of hypoxia-ischemia in newborn piglets may be useful for studying the effect of perinatal asphyxia on the impairment of the auditory pathway.