Multiplex PI-Control for Consensus in Networks of Heterogeneous Linear Agents

In this paper, we propose a multiplex proportional-integral approach, for solving consensus problems in networks of heterogeneous nodes dynamics affected by constant disturbances. The proportional and integral actions are deployed on two different layers across the network, each with its own topology. Sufficient conditions for convergence are derived that depend upon the structure of the network, the parameters characterizing the control layers and the node dynamics. The effectiveness of the theoretical results is illustrated using a power network model as a representative example.Comment: 13 pages, 6 Figures, Preprint submitted to Automatic

Analysis of quantization errors in a buck power converter controlled by ZAD strategy

En los últimos años, el control del convertidor buck con estrategia ZAD ha sido objeto de estudio, debido principalmente a que esta técnica ofrece frecuencia fija de conmutación, con una bajo error de estado estacionario. Sin embargo, la forma de calcular el ciclo de trabajo ha incluido la medida de la derivada de la superficie S(x) y el conocimiento a priori de todos los parámetros del sistema, incluyendo el valor de la carga R. Esto, desde un punto de vista práctico, es difícil de lograr; por otro lado, los resultados numéricos y experimentales no han tenido una alta concordancia. Así pues, en el presente trabajo de investigación se busca una forma diferente de generar la acción de control basada en ZAD, pero haciendo uso de las redes neuronales articules, con lo cual se evita medir la derivada de la superficie y no se requiere el conocimiento de la carga; además se propone hacer un ajuste del modelo matemático teniendo en cuenta algunos aspectos del experimento tales como la digitalización de las variables de estado y de la señal de control. El trabajo se divide en 4 etapas: la primera, generación de la regla de control mediante una red neuronal artificial entrenada bajo estrategia ZAD. Con la red se logra reproducir satisfactoriamente el controlador ZAD para cierta región de parámetros y tiene la ventaja adicional que requiere menos información para generar la regla de control; no se requiere el conocimiento de la carga, ni medir la derivada de la superficie. La segunda etapa, consiste en el estudio del efecto de la cuantización en la dinámica periódica y caótica del sistema controlado por ZAD. Con esto se demuestra que a mayor error de cuantización el sistema pierde completamente la transición al caos cambiando a cascadas de órbitas periódicas y a su vez aumenta la sensibilidad a las condiciones iniciales. La tercera etapa trata sobre técnicas para la reducción de los efectos de cuantización en el ZAD. Con estas técnicas se logran disminuir las oscilaciones presentes en la salida del sistema, causadas por la digitalización de las variables de estado, en aproximadamente 60% con la técnica GZAD y 90% con la media del ciclo de trabajo y FPIC. Finalmente, la cuarta parte es una implementación física a pequeña escala que permite comprobar los efectos del error de cuantización y las técnicas para reducirlo / Abstract: In recent years, the DC-DC buck power converter controlled by ZAD strategy has been widely studied. The ZAD- controlled buck has shown the main following features: xed switching frequency with low steady state error. However the computation of the duty cycle has included the value of the load and the measure of the derivative of S(x) function; besides, experimental and numerical result did not agree. In this research, we compute the duty cycle using neural networks, and we propose an improved mathematical model with the aim to obtain agreement between experimental and analytical results. This model includes state variables and signal control digitalization. In general, the work has four stages: the rst one is devoted to compute the control law with an arti_cial neural network trained by ZAD strategy. We obtain similar results to already reported. In this case, the load value and the derivative of the function are not required to be known. The second stage is a study of quantization effects in the periodic and chaotic behavior. Global phenomena such as the coexistence of periodic and non-periodic attractors, fractal basin boundaries or transient chaos are exclusively caused by state variables digitalization. Third stage is about techniques to decrease quantization errors. GZAD technique achieves to reduce the oscillations by 60%. We propose a new alternative focused on duty cycle mean and obtained reductions of up to 90% using FPIC control. Finally, the fourth step is a normalized buck converter implementation, with the aim to prove the quantization effects in the system dynamic behavior and the techniques to reduce it.Maestrí

Activity‑driven network modeling and control of the spread of two concurrent epidemic strains

The emergency generated by the current COVID-19 pandemic has claimed millions of lives worldwide. There have been multiple waves across the globe that emerged as a result of new variants, due to arising from unavoidable mutations. The existing network toolbox to study epidemic spreading cannot be readily adapted to the study of multiple, coexisting strains. In this context, particularly lacking are models that could elucidate re-infection with the same strain or a different strain—phenomena that we are seeing experiencing more and more with COVID-19. Here, we establish a novel mathematical model to study the simultaneous spreading of two strains over a class of temporal networks. We build on the classical susceptible–exposed–infectious–removed model, by incorporating additional states that account for infections and re-infections with multiple strains. The temporal network is based on the activity-driven network paradigm, which has emerged as a model of choice to study dynamic processes that unfold at a time scale comparable to the network evolution. We draw analytical insight from the dynamics of the stochastic network systems through a mean-field approach, which allows for characterizing the onset of different behavioral phenotypes (non-epidemic, epidemic, and endemic). To demonstrate the practical use of the model, we examine an intermittent stay-at-home containment strategy, in which a fraction of the population is randomly required to isolate for a fixed period of time

Distributed PID Control for Consensus and Synchronization of Multi-agent Networks

We investigate the use of distributed PID actions to achieve consensus and synchronization in networks of homogeneous and heterogeneous agents. We first analyze the case of distributed PID control on networks with heterogeneous nodes described by first-order linear systems. Convergence of the strategy is proved using appropriate state transformations and Lyapunov functions. Then, we propose a multiplex proportional-integral approach, for solving consensus problems in networks of heterogeneous n-dimensional node dynamics affected by constant disturbances. The proportional and integral actions are deployed on two different layers across the network, each with its own topology. Furthermore, the contribution of the network topology and node dynamics have been systematically separated giving some sufficient conditions guaranteeing convergence. Finally, an extension to networks of identical nonlinear node dynamics is presented. We provide local and global stability analysis together with a detailed performance assessment where heterogeneity among nodes and disturbances are considered. The effectiveness of the theoretical results is illustrated via its application to a representative power grid model recently presented in the literature and also for synchronization in networks of chaotic circuits

Consensus and synchronization of complex networks via proportional-integral coupling

In this paper we investigate the use of distributed PI actions to achieve consensus and synchronization in complex networks. We show that by extending the classical linear diffusive coupling with an integral action it is possible to achieve better performance and steady-state behavior than with more traditional strategies. After briefly summarizing the theoretical results, we investigate the viability of the proposed strategy via numerical simulations including a representative example inspired from power system models recently presented in the literature

Activity-driven network modeling and control of the spread of two concurrent epidemic strains

The emergency generated by the current COVID-19 pandemic has claimed millions of lives worldwide. There have been multiple waves across the globe that emerged as a result of new variants, due to arising from unavoidable mutations. The existing network toolbox to study epidemic spreading cannot be readily adapted to the study of multiple, coexisting strains. In this context, particularly lacking are models that could elucidate re-infection with the same strain or a different strain—phenomena that we are seeing experiencing more and more with COVID-19. Here, we establish a novel mathematical model to study the simultaneous spreading of two strains over a class of temporal networks. We build on the classical susceptible–exposed–infectious–removed model, by incorporating additional states that account for infections and re-infections with multiple strains. The temporal network is based on the activity-driven network paradigm, which has emerged as a model of choice to study dynamic processes that unfold at a time scale comparable to the network evolution. We draw analytical insight from the dynamics of the stochastic network systems through a mean-field approach, which allows for characterizing the onset of different behavioral phenotypes (non-epidemic, epidemic, and endemic). To demonstrate the practical use of the model, we examine an intermittent stay-at-home containment strategy, in which a fraction of the population is randomly required to isolate for a fixed period of time