Ingeniería Eléctrica y Electrónica

The notation normally associated with the projection-slice theorem often presents difficulties for students of Fourier optics and digital image processing. Simple single-line forms of the theorem that are relatively easily interpreted can be obtained for n-dimensional functions by exploiting the convolution theorem and the rotation theorem of Fourier transform theory. The projection-slice theorem is presented in this form for two-and three-dimensional functions; generalization to higher dimensionality is briefly discussed.

Bioinspired design approaches seek to exploit nature in order to construct robust and optimal solutions. One useful concept from behavioral ecology is the ideal free distribution (IFD). Here, we relax the IFD main assumptions using the standing crop idea to introduce dynamics to the resources. Using the IFD, the standing crop, and the replicator dynamics concepts, we make some analogies with a temperature control in order to get a maximum uniform temperature. We analytically show that the equilibrium point of the system (i.e., the IFD) is a locally asymptotically stable point, and it is a globally asymptotically stable point for one special case.

The sum of squares (SOS) decomposition technique allows numerical methods such as semidefinite programming to be used for proving the positivity of multivariable polynomial functions. It is well known that it is not an easy task to find Lyapunov functions for stability analysis of nonlinear systems. An algorithmic tool is used in this work for solving this problem. This approach is presented as SOS programming and solutions were obtained with a Matlab toolbox. Simple examples of SOS concepts, stability analysis for nonlinear polynomial and rational systems with uncertainties in parameters are presented to show the use of this tool. Besides these approaches, an alternative stability analysis for switched systems using a polynomial approach is also presented.

Recently, there has been an increasing interest in studying large-scale distributed systems in the control community. Efforts have been invested in developing several techniques wishing to address the main challenges found in this kind of problems, for instance, the amount of information to guarantee the proper operation of the system and the economic costs associated to the required communication structure. Moreover, another issue appears when there is a large amount of required data to control the system. The measuring and transmission processes, and the computation of the control inputs make closed-loop systems suffer from high computational burden. One way to overcome such problems is to consider the use of multi-agent systems framework, which may be cast in game-theoretical terms. Game theory studies interactions between self-interested agents. Particularly, this theory tackles with the problem of interaction between agents using different strategies that wish to maximize their welfares. For instance in [1], the authors provide connections between games, optimization, and learning for signal processing in networks. Other approaches in terms of learning and games can be found in [2]. In [3], distributed computation algorithms are developed based on generalized convex games that do not require full information, and where there is a dynamic change in terms of network topologies. Applications of game theory in control of optical networks and game-theoretic methods for smart grids are described in [4], [5], [6]. Another approach in game theoretical methods is to design protocols or mechanisms that possess some desirable properties [7]. This approach leads to a broad analysis of multi-agent interactions, particularly those involving negotiation and coordination problems [8]. Other game-theoretical applications to engineering are reported in [9]. From a game-theoretical perspective, it can be distinguished among three types of games: matrix games, continuous games, and differential/dynamic games (see "The relationship among matricial games, full-potential population games, and resource allocation problems"). In matrix games (that generally use the normal form), individuals play simultaneously and only once, and the decision is mainly based on a static terms. In this case, players or agents are individually treated. Differently, in continuous games, players have infinitely many pure strategies [10], [11]. On the other hand, in dynamic games it is assumed that players can use some type of learning mechanism that allows them to adjust the actions taken based on their past decisions. Basically, it can be said that dynamic games are characterized by three main problems: i) how to model the environment where players interact; ii) how to model the objectives of players; and iii) how to specify the order in which the actions are taken and how much information each player possesses. In this case, it is assumed that there are interactions between large number of agents (which are usually unknown) [12]. Among these dynamic games, there exist the evolutionary game dynamics, which are

Temperature control in buildings is a dynamic resource allocation problem, which can be approached using nonlinear methods based on population dynamics (i.e., replicator dynamics). A mathematical model of the proposed control technique is shown, including a stability analysis using passivity concepts for an interconnection of a linear multivariable plant driven by a nonlinear control system. In order to illustrate our control strategy, some simulations are performed, and we compare our proposed technique with another control strategy (conventional PI) in a model with a fixed structure.

The sum of squares (SOS) decomposition technique allows numerical methods such as semidefinite programming to be used for proving the positivity of multivariable polynomial functions. It is well known that it is not an easy task to find Lyapunov functions for stability analysis of nonlinear systems. An algorithmic tool is used in this work for solving this problem. This approach is presented as SOS programming and solutions were obtained with a Matlab toolbox. Simple examples of SOS concepts, stability analysis for nonlinear polynomial and rational systems with uncertainties in parameters are presented to show the use of this tool. Besides these approaches, an alternative stability analysis for switched systems using a polynomial approach is also presented.

Temperature control in buildings is a dynamic resource allocation problem, which can be approached using nonlinear methods based on population dynamics (i.e., replicator dynamics). A mathematical model of the proposed control technique is shown, including a stability analysis using passivity concepts for an interconnection of a linear multivariable plant driven by a nonlinear control system. In order to illustrate our control strategy, some simulations are performed, and we compare our proposed technique with another control strategy in a model with a fixed structure.

The replicator dynamics model is an evolutionary game concept that describes the state of a population in a process inspired by natural selection. This model is used to analyze a resource allocation problem in distributed networked systems. The main properties of the replicator equation are analyzed to propose a novel technique based only on the available information of a system modeled as a connected graph. Likewise, we analyze the stability of the equilibrium points as a function of a certain class of fitness. Finally, an economic dispatch in distributed generation systems is presented in order to illustrate the theoretical results.

Dimensionality reduction (DR) methods represent a suitable alternative to visualizing data. Nonetheless, most of them still lack the properties of interactivity and controllability. In this work, we propose a data visualization interface that allows for user interaction within an interactive framework. Specifically, our interface is based on a mathematic geometric model, which combines DR methods through a weighted sum. Interactivity is provided in the sense that weighting factors are given by the user via the selection of points inside a geometric surface. Then, (even non-expert) users can intuitively either select a concrete DR method or carry out a mixture of methods. Experimental results are obtained using artificial and real datasets, demonstrating the usability and applicability of our interface in DR-based data visualization.

In a multi-agent framework, distributed optimization problems are generally described as the minimization of a global objective function, where each agent can get information only from a neighborhood defined by a network topology. To solve the problem, this work presents an information-constrained strategy based on population dynamics, where payoff functions and tasks are assigned to each node in a connected graph. We prove that the so-called distributed replicator equation (DRE) converges to an optimal global outcome by means of the local-information exchange subject to the topological constraints of the graph. To show the application of the proposed strategy, we implement the DRE to solve an economic dispatch problem with distributed generation. We also present some simulation results to illustrate the theoretic optimality and stability of the equilibrium points and the effects of typical network topologies on the convergence rate of the algorithm.

Sweden is a country with abundant hydro power and has expectations to include more renewable energy sources, namely from wind power, into its electrical system. Currently, in order to improve the frequency response requirements of its electrical system, the country is considering upgrading its hydro-governors. This effort is part of maintaining the system frequency and reaction within their limits following any disturbance events. To partially compensate for increased frequency fluctuations due to an increased share of renewables on its system, the frequency response of hydro-governors should be improved. This paper proposes an innovative network control system, through a supplementary control, for the improvement of the hydro-governor's action. This supplementary control allows having more flexibility over the control action and improves the primary frequency control, and thereby the overall system frequency response. The proposed supplementary control, based on an evolutionary game theory strategy, uses remote measurements and a hierarchical dynamic adjustment of the control. Additionally, in order to guarantee an optimal response, a Simulated Annealing algorithm is combined with the supplementary control. This paper illustrates the analysis and design of the proposed methodology, and is tested on two power systems models: (i) an aggregated model that represents the frequency response of Sweden, Norway and Finland, and (ii) The Nordic 32 test system.

We present a novel distributed heterogeneous multi-population evolutionary dynamics approach, which can be used in diverse engineering applications as a distributed optimizationbased algorithm. We also provide stability certificates of Nash equilibria under the proposed approach. Finally, over the end of this paper, an example illustrates the performance of the aforementioned multi-population evolutionary dynamics.

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Context: This work presents different models based on artificial neural networks, among them NNARX, for estimating global solar radiation from UV index measurements. The objective is to determine the efficiency of the models studied to estimate global solar radiation in terms of the coefficient of determination (R2), the root-mean-square error (RMSE), and the mean absolute error (MAE). Methodology: It is divided into four stages: i) conformation of the training dataset (in this case, it uses a training set of 213.019 data collected over five years in the city of Pasto, Colombia, with the Davis Vantage Pro 2.0 station); ii) pre-processing of data to remove erroneous and unusual data; iii) definition of models based on recurrent and conventional artificial neural networks according to an analysis of topologies, e.g. NNFIR and NNARX; iv) training of the models and evaluation of the estimation efficiency through metrics such as R2, RMSE, and MAE. To validate the model, a new dataset col...

In this paper, we present the first study of the long-term climate-change impact on photovoltaic power potential in Nariño, Colombia. In this region, more than half of the territory does not have a constant electricity supply, but it has great potential for solutions with renewable energy sources. Based on the Coordinated Regional Downscaling Experiment (CORDEX), we assess the change in photovoltaic power potential towards the end of this century, considering two climate change scenarios, one optimistic and the other pessimistic. Our results suggest that changes in photovoltaic power potential, by the end of the century, will have a maximum decrease of around 2.49% in the central zone of Nariño, with some non-affected areas, and a maximum increase of 2.52% on the southeastern side with respect to the pessimistic climate change scenario.

The sum of squares (SOS) decomposition technique allows numerical methods such as semidefinite programming to be used for proving the positivity of multivariable polynomial functions. It is well known that it is not an easy task to find Lyapunov functions for stability analysis of nonlinear systems. An algorithmic tool is used in this work for solving this problem. This approach is presented as SOS programming and solutions were obtained with a Matlab toolbox. Simple examples of SOS concepts, stability analysis for nonlinear polynomial and rational systems with uncertainties in parameters are presented to show the use of this tool. Besides these approaches, an alternative stability analysis for switched systems using a polynomial approach is also presented.