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The centralized paradigm of a single controller and a single plant upon which modern control theory is built is no longer applicable to modern cyber-physical systems of interest, such as the power-grid, software defined networks or automated highways systems, as these are all large-scale and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.

The oculomotor system: (1) Vertical-horizontal interaction and signal recognition, (2) Time delays and power spectra

In the first section of this thesis, two-dimensional properties of the human eye movement control system were studied. The vertical - horizontal interaction was investigated by using a two-dimensional target motion consisting of a sinusoid in one of the directions vertical or horizontal, and low-pass filtered Gaussian random motion of variable bandwidth (and hence information content) in the orthogonal direction. It was found that the random motion reduced the efficiency of the sinusoidal tracking. However, the sinusoidal tracking was only slightly dependent on the bandwidth of the random motion. Thus the system should be thought of as consisting of two independent channels with a small amount of mutual cross-talk.

These target motions were then rotated to discover whether or not the system is capable of recognizing the two-component nature of the target motion. That is, the sinusoid was presented along an oblique line (neither vertical nor horizontal) with the random motion orthogonal to it. The system did not simply track the vertical and horizontal components of motion, but rotated its frame of reference so that its two tracking channels coincided with the directions of the two target motion components. This recognition occurred even when the two orthogonal motions were both random, but with different bandwidths.

In the second section, time delays, prediction and power spectra were examined. Time delays were calculated in response to various periodic signals, various bandwidths of narrow-band Gaussian random motions and sinusoids. It was demonstrated that prediction occurred only when the target motion was periodic, and only if the harmonic content was such that the signal was sufficiently narrow-band. It appears as if general periodic motions are split into predictive and non-predictive components.

For unpredictable motions, the relationship between the time delay and the average speed of the retinal image was linear. Based on this I proposed a model explaining the time delays for both random and periodic motions. My experiments did not prove that the system is sampled data, or that it is continuous. However, the model can be interpreted as representative of a sample data system whose sample interval is a function of the target motion.

It was shown that increasing the bandwidth of the low-pass filtered Gaussian random motion resulted in an increase of the eye movement bandwidth. Some properties of the eyeball-muscle dynamics and the extraocular muscle "active state tension" were derived.

NEW METHODOLOGY FOR FEEDER RECONFIGURATION IN DISTRIBUTION NETWORKS WITH DISTRIBUTED ENERGY RESOURCES

This doctoral Thesis defines and develops a new methodology for feeder reconfiguration in distribution networks with Distributed Energy Resources (DER). The proposed methodology is based on metaheuristic Ant Colony Optimization (ACO) algorithms. The methodology is called Item Oriented Ant System (IOAS) and the doctoral Thesis also defines three variations of the original methodology, Item Oriented Ant Colony System (IOACS), Item Oriented Max-min Ant System (IOMMAS) y Item Oriented Max-min Ant Colony System (IOACS). All methodologies pursue a twofold objective, to minimize the power losses and maximize DER penetration in distribution networks. The aim of the variations is to find the algorithm that adapts better to the present optimization problem, solving it most efficiently. The main feature of the methodology lies in the fact that the heuristic information and the exploitation information (pheromone) are attached to the item not to the path. Besides, the doctoral Thesis proposes to use feeder reconfiguration in order to increase the distribution network capacity of accepting a major degree of DER. The proposed methodology and its three variations have been tested and verified in two distribution networks well documented in the existing bibliography. These networks have been modeled and used to test all proposed methodologies for different scenarios with various DER penetration degrees.

Single mode Er-doped pi-phase-shifted distributed feedback fibre grating laser

A novel method incorporating the shielded method and the post-processing method has been proposed to fabricate the pi-phase-shilted fibre grating. Then an Er-doped pi-phase-shifted distributed feedback fibre grating laser has been fabricated using the grating. The laser threshold is 20 mW. When pumped with 90 mW light at 980 nm, the laser gives an output of 1.1 mW. Its signal-to-noise ratio is better than 60 dB. It is demonstrated that the laser is single mode operation by means of a Fabry-Perot scanning interferometer.

Theoretical modelling of the effect of photon lifetime on the output dynamics of Er-doped distributed feedback fibre lasers

By employing a simple model of describing three-level lasers, we have theoretically investigated the effect of photon lifetime on the output dynamics of Er-doped distributed feedback fibre lasers. And based on the theoretical analysis we have proposed a promising method to suppress self-pulsing behaviour in the fibre lasers.

"Quando eu descobri tive um baque: os desafios da prevenção da transmissão vertical do HIV

A eficácia da quimioprofilaxia da transmissão vertical do HIV tem contribuído para minimizar o numero de crianças infectadas pelo vírus. No entanto é essencial para essa finalidade o uso correto do protocolo pela mãe. Mas onde estão as falhas desse processo? Porque ainda há crianças sendo desnecessariamente expostas ao vírus HIV? Foi objetivo desse estudo conhecer as concepções sobre gravidez, HIV/AIDS e transmissão vertical de gestantes e mães soropositivas. A partir disso, fornecer subsídios para o aperfeiçoamento da prevenção da transmissão vertical. Partiu-se da hipótese de que aspectos sociais, culturais e econômicos das mulheres podem estar envolvidos na adesão ou não da prevenção da transmissão vertical da AIDS. Quatorze mulheres soropositivas, sendo onze com filhos já nascidos e três gestantes, deram seus depoimentos através de entrevistas semi-estruturadas orientadas por roteiro. Os Fatores sócio culturais das mulheres não foram investigados de forma direta, mas foi possível registrar através das falas uma possível associação destes com a quimioprofilaxia da transmissão vertical do HIV. Ainda que de forma incompleta todas realizaram a quimioprofilaxia, com exceção de uma mulher que teve o diagnostico somente após o parto. Através da análise dos depoimentos foi possível identificar que as mulheres que possuíam nível sócio cultural mais elevado demonstraram maior domínio quanto à importância do tratamento, embora a principal motivação para a realização do tratamento tenha sido a não contaminação de seus filhos. Foram descritos alguns determinantes envolvidos na adesão das mulheres ao tratamento, dentre eles; o conhecimento acerca do tratamento e aspectos ligados aos serviços de saúde. Algumas falhas no pré-natal foram apontadas como ponto negativo neste processo. Dentre os resultados encontrados ocasionalmente foi ressaltado a forma que os companheiros reagiram à doença. E a constatação de que a grande maioria das mulheres ao não reconhecerem sua posição de risco para a infecção pelo HIV, descobrem-se soropositivas somente no pré-natal.

Unveiling the factors shaping the distribution of widely distributed alpine vertebrates, using multi-scale ecological niche modelling of the bat Plecotus macrobullaris

Several alpine vertebrates share a distribution pattern that extends across the South-western Palearctic but is limited to the main mountain massifs. Although they are usually regarded as cold-adapted species, the range of many alpine vertebrates also includes relatively warm areas, suggesting that factors beyond climatic conditions may be driving their distribution. In this work we first recognize the species belonging to the mentioned biogeographic group and, based on the environmental niche analysis of Plecotus macrobullaris, we identify and characterize the environmental factors constraining their ranges. Distribution overlap analysis of 504 European vertebrates was done using the Sorensen Similarity Index, and we identified four birds and one mammal that share the distribution with P. macrobullaris. We generated 135 environmental niche models including different variable combinations and regularization values for P. macrobullaris at two different scales and resolutions. After selecting the best models, we observed that topographic variables outperformed climatic predictors, and the abruptness of the landscape showed better predictive ability than elevation. The best explanatory climatic variable was mean summer temperature, which showed that P. macrobullaris is able to cope with mean temperature ranges spanning up to 16 degrees C. The models showed that the distribution of P. macrobullaris is mainly shaped by topographic factors that provide rock-abundant and open-space habitats rather than climatic determinants, and that the species is not a cold-adapted, but rather a cold-tolerant eurithermic organism. P. macrobullaris shares its distribution pattern as well as several ecological features with five other alpine vertebrates, suggesting that the conclusions obtained from this study might be extensible to them. We concluded that rock-dwelling and open-space foraging vertebrates with broad temperature tolerance are the best candidates to show wide alpine distribution in the Western Palearctic.