Strategic Behavior and Collusion: An Application to the Spanish Electricity Market

The paper has two major contributions to the theory of repeated games. First, we build a supergame oligopoly model where firms compete in supply functions, we show how collusion sustainability is affected by the presence of a convex cost function, the magnitude of both the slope of demand market, and the number of rivals. Then, we compare the results with those of the traditional Cournot reversion under the same structural characteristics. We find how depending on the number of firms and the slope of the linear demand, collusion sustainability is easier under supply function than under Cournot competition. The conclusions of the models are simulated with data from the Spanish wholesale electricity market to predict lower bounds of the discount factors.

A reliable phase unwrapping algorithm based on the local fitting plane and quality map

A fast and reliable phase unwrapping (PhU) algorithm, based on the local quality-guided fitting plane, is presented. Its framework depends on the basic plane-approximated assumption for phase values of local pixels and on the phase derivative variance (PDV) quality map. Compared with other existing popular unwrapping algorithms, the proposed algorithm demonstrated improved robustness and immunity to strong noise and high phase variations, given that the plane assumption for local phase is reasonably satisfied. Its effectiveness is demonstrated by computer-simulated and experimental results.

Análise de Economias de Escala na Produção de Leite

Este trabalho procurou analisar o sistema produtivo da atividade leiteira em Minas Gerais, identificando a capacidade dos produtores em permanecer no negócio, a longo prazo, através da estimação da função custo translogarítmica. O estudo demonstrou que os produtores analisados ainda praticam altos custos por unidade produzida, sugerindo baixa eficiência dos estabelecimentos e falhas na administração do empreendimento. Os resultados econométricos revelam a possibilidade de ganhos de escala, no que se refere à alocação e melhor aproveitamento dos recursos, ou seja, as propriedades apresentam economias de escala. No entanto, retornos crescentes de escala não são compatíveis com a existência de mercados competitivos, sinalizando que os produtores enfrentam restrições geradas pelas imperfeições de mercado. O conhecimento dessas imperfeições é essencial à formulação de políticas econômicas e de organizações privadas que visem ao desenvolvimento econômico deste mercado, que atualmente é o sexto maior do mundo. Além disso, os resultados das elasticidades mostram que o produtor é mais sensível às variações de preços na mão-de-obra do que às variações nos demais fatores, reduzindo em maior proporção o uso do trabalho na produção, à medida que seu preço aumenta. Isto evidencia a principal característica regional da produção leiteira no país, que é o uso intensivo do fator trabalho. Também foi identificado que o os medicamentos, alimentos e energia, denominados no estudo de fator dispêndio, são os mais difíceis é o mais difícil de serem substituídos na produção, devido às particularidades no uso dos componentes deste insumo. Por fim, os valores positivos encontrados para as elasticidades parciais de substituição de Allen confirmam a substitutibilidade entre os fatores.

Mapeamento de difusão no reconhecimento e reconstrução de sinais

Em muitas representações de objetos ou sistemas físicos se faz necessário a utilização de técnicas de redução de dimensionalidade que possibilitam a análise dos dados em baixas dimensões, capturando os parâmetros essenciais associados ao problema. No contexto de aprendizagem de máquina esta redução se destina primordialmente à clusterização, reconhecimento e reconstrução de sinais. Esta tese faz uma análise meticulosa destes tópicos e suas conexões que se encontram em verdadeira ebulição na literatura, sendo o mapeamento de difusão o foco principal deste trabalho. Tal método é construído a partir de um grafo onde os vértices são os sinais (dados do problema) e o peso das arestas é estabelecido a partir do núcleo gaussiano da equação do calor. Além disso, um processo de Markov é estabelecido o que permite a visualização do problema em diferentes escalas conforme variação de um determinado parâmetro t: Um outro parâmetro de escala, Є, para o núcleo gaussiano é avaliado com cuidado relacionando-o com a dinâmica de Markov de forma a poder aprender a variedade que eventualmente seja o suporte do dados. Nesta tese é proposto o reconhecimento de imagens digitais envolvendo transformações de rotação e variação de iluminação. Também o problema da reconstrução de sinais é atacado com a proposta de pré-imagem utilizando-se da otimização de uma função custo com um parâmetro regularizador, γ, que leva em conta também o conjunto de dados iniciais.

Optimal control predicts human performance on objects with internal degrees of freedom.

On a daily basis, humans interact with a vast range of objects and tools. A class of tasks, which can pose a serious challenge to our motor skills, are those that involve manipulating objects with internal degrees of freedom, such as when folding laundry or using a lasso. Here, we use the framework of optimal feedback control to make predictions of how humans should interact with such objects. We confirm the predictions experimentally in a two-dimensional object manipulation task, in which subjects learned to control six different objects with complex dynamics. We show that the non-intuitive behavior observed when controlling objects with internal degrees of freedom can be accounted for by a simple cost function representing a trade-off between effort and accuracy. In addition to using a simple linear, point-mass optimal control model, we also used an optimal control model, which considers the non-linear dynamics of the human arm. We find that the more realistic optimal control model captures aspects of the data that cannot be accounted for by the linear model or other previous theories of motor control. The results suggest that our everyday interactions with objects can be understood by optimality principles and advocate the use of more realistic optimal control models for the study of human motor neuroscience.

Designing MPC controllers by reverse-engineering existing LTI controllers

This technical report presents a method for designing a constrained output-feedback model predictive controller (MPC) that behaves in the same way as an existing baseline stabilising linear time invariant output-feedback controller when constraints are inactive. The baseline controller is cast into an observer-compensator form and an inverse-optimal cost function is used as the basis of the MPC controller. The available degrees of design freedom are explored, and some guidelines provided for the selection of an appropriate observer-compensator realisation that will best allow exploitation of the constraint-handling and redundancy management capabilities of MPC. Consideration is given to output setpoint tracking, and the method is demonstrated with three different multivariable plants of varying complexity.

Fault-tolerant aspects of MPC

The architecture of model predictive control (MPC), with its explicit internal model and constrained optimization is presented. Since MPC relies on an explicit internal model, one can imagine dealing with failures by updating the internal model, and letting the on-line optimizer work out how to control the system in its new condition. This aspects rely on assumptions such that the nature of the fault can be located, and the model can be updated automatically. A standard form of MPC, with linear inequality constraints on inputs and outputs, linear internal model, and quadriatic cost function.

An experimental model of relay deployment planning tool for a wireless sensor network system to monitor civil engineering structures

It is essential to monitor deteriorated civil engineering structures cautiously to detect symptoms of their serious disruptions. A wireless sensor network can be an effective system for monitoring civil engineering structures. It is fast to deploy sensors especially in difficult-to-access areas, and it is extendable without any cable extensions. Since our target is to monitor deteriorations of civil engineering structures such as cracks at tunnel linings, most of the locations of sensors are known, and sensors are not required to move dynamically. Therefore, we focus on developing a deployment plan of a static network in order to reduce the value of a cost function such as initial installation cost and summation of communication distances of the network. The key issue of the deployment is the location of relays that forward sensing data from sensors to a data collection device called a gateway. In this paper, we propose a relay deployment-planning tool that can be used to design a wireless sensor network for monitoring civil engineering structures. For the planning tool, we formalize the model and implement a local search based algorithm to find a quasi-optimal solution. Our solution guarantees two routings from a sensor to a gateway, which can provide higher reliability of the network. We also show the application of our experimental tool to the actual environment in the London Underground.

Surface excavation with model predictive control

This paper describes the application of variable-horizon model predictive control to trajectory generation in surface excavation. A nonlinear dynamic model of a surface mining machine digging in oil sand is developed as a test platform. This model is then stabilised with an inner-loop controller before being linearised to generate a prediction model. The linear model is used to design a predictive controller for trajectory generation. A variable horizon formulation is augmented with extra terms in the cost function to allow more control over digging, whilst still preserving the guarantee of finite-time completion. Simulations show the generation of realistic trajectories, motivating new applications of variable horizon MPC for autonomy that go beyond the realm of vehicle path planning. ©2010 IEEE.

Verifying stability of approximate explicit MPC

Several authors have proposed algorithms for approximate explicit MPC [1],[2],[3]. These algorithms have in common that they develop a stability criterion for approximate explicit MPC that require the approximate cost function to be within a certain distance from the optimal cost function. In this paper, stability is instead ascertained by considering only the cost function of the approximate MPC. If a region of the state space is found where the cost function is not decreasing, this indicates that an improved approximation (to the optimal control) is required in that region. If the approximate cost function is decreasing everywhere, no further refinement of the approximate MPC is necessary, since stability is guaranteed. ©2009 IEEE.

Automatic object segmentation from calibrated images

This paper addresses the problem of automatically obtaining the object/background segmentation of a rigid 3D object observed in a set of images that have been calibrated for camera pose and intrinsics. Such segmentations can be used to obtain a shape representation of a potentially texture-less object by computing a visual hull. We propose an automatic approach where the object to be segmented is identified by the pose of the cameras instead of user input such as 2D bounding rectangles or brush-strokes. The key behind our method is a pairwise MRF framework that combines (a) foreground/background appearance models, (b) epipolar constraints and (c) weak stereo correspondence into a single segmentation cost function that can be efficiently solved by Graph-cuts. The segmentation thus obtained is further improved using silhouette coherency and then used to update the foreground/background appearance models which are fed into the next Graph-cut computation. These two steps are iterated until segmentation convergences. Our method can automatically provide a 3D surface representation even in texture-less scenes where MVS methods might fail. Furthermore, it confers improved performance in images where the object is not readily separable from the background in colour space, an area that previous segmentation approaches have found challenging. © 2011 IEEE.

Performance evaluation of multiplexed model predictive control for a large airliner in nominal and contingency scenarios

Model predictive control allows systematic handling of physical and operational constraints through the use of constrained optimisation. It has also been shown to successfully exploit plant redundancy to maintain a level of control in scenarios when faults are present. Unfortunately, the computational complexity of each individual iteration of the algorithm to solve the optimisation problem scales cubically with the number of plant inputs, so the computational demands are high for large MIMO plants. Multiplexed MPC only calculates changes in a subset of the plant inputs at each sampling instant, thus reducing the complexity of the optimisation. This paper demonstrates the application of multiplexed model predictive control to a large transport airliner in a nominal and a contingency scenario. The performance is compared to that obtained with a conventional synchronous model predictive controller, designed using an equivalent cost function. © 2012 AACC American Automatic Control Council).

Consensus optimization on manifolds

The present paper considers distributed consensus algorithms that involve N agents evolving on a connected compact homogeneous manifold. The agents track no external reference and communicate their relative state according to a communication graph. The consensus problem is formulated in terms of the extrema of a cost function. This leads to efficient gradient algorithms to synchronize (i.e., maximizing the consensus) or balance (i.e., minimizing the consensus) the agents; a convenient adaptation of the gradient algorithms is used when the communication graph is directed and time-varying. The cost function is linked to a specific centroid definition on manifolds, introduced here as the induced arithmetic mean, that is easily computable in closed form and may be of independent interest for a number of manifolds. The special orthogonal group SO (n) and the Grassmann manifold Grass (p, n) are treated as original examples. A link is also drawn with the many existing results on the circle. © 2009 Society for Industrial and Applied Mathematics.

Collective optimization over average quantities

This paper addresses the design of algorithms for the collective optimization of a cost function defined over average quantities in the presence of limited communication. We argue that several meaningful collective optimization problems can be formulated in this way. As an application of the proposed approach, we propose a novel algorithm that achieves synchronization or balancing in phase models of coupled oscillators under mild connectedness assumptions on the (possibly time-varying and unidirectional) communication graphs. © 2006 IEEE.

Continuous dynamical systems that realize discrete optimization on the hypercube

We study the problem of finding a local minimum of a multilinear function E over the discrete set {0,1}n. The search is achieved by a gradient-like system in [0,1]n with cost function E. Under mild restrictions on the metric, the stable attractors of the gradient-like system are shown to produce solutions of the problem, even when they are not in the vicinity of the discrete set {0,1}n. Moreover, the gradient-like system connects with interior point methods for linear programming and with the analog neural network studied by Vidyasagar (IEEE Trans. Automat. Control 40 (8) (1995) 1359), in the same context. © 2004 Elsevier B.V. All rights reserved.