Lyapunov

This paper presents the model of a fuel cell and the design and simulation of a cascade of two DC-DC converters. First, a detailed mathematical model of fuel cell is presented and simulated. Then, a nonlinear model of the whole controlled system is developed and a robust nonlinear controller of currents is synthesized using a passivity-based control. A formal analysis based on Lyapunov stability and average theory is developed to describe the control currents loops performances. A classical PI controller is used for the voltages loops. The simulation models have been developed and tested in the MATLAB/SIMULINK. Simulated results are displayed to validate the feasibility and the effectiveness of the proposed strategy. Keyword: Cascaded boost Euler lagrange Fuel cell Lyapunov Passivity-based control

The traditional quadcopter control systems should deal with two common problems. Namely, the singularities related to the inverse kinematics and the ambiguity linked to the quaternion representation of the dynamic model. Moreover, the stability problem due to the system nonlinearity and high degree of coupling. This paper provides a solution to the two issues by employing a geometrical integral-backstepping control system. The integral terms were added to improve system ability to track desired trajectories. The high-level control laws are considered as a virtual control and transmitted to the low-level to track the high-level commands. The proposed control system along with the quadcopter dynamic model were expressed in the special Euclidean group SE(3). Finally, the control system robustness against mismatching parameters was studied while tracking various paths.

Resumen-En este trabajo se analiza la estabilidad utilizando métodos de energía en forma general y como aplicación se analiza la estabilidad de una barra delgada finita sujeta en los extremos. Se obtendrán las condiciones de estabilidad para una barra finita sujeta en los extremos.

We consider the motion of a point particle (billiard) in a uniform gravitational field constrained to move in a symmetric wedge-shaped region. The billiard is reflected at the wedge boundary. The phase space of the system naturally divides itself into two regions in which the tangent maps are respectively parabolic and hyperbolic. It is known that the system is integrable for two values of the wedge half-angle 01 and 02 and chaotic for 01 < 0 < 02. We study the system at three levels of approximation: first, where the deterministic dynamics is replaced by a random evolution; second, where, in addition, the tangent map in each region is. replaced by its average; and third, where the tangent map is replaced by a single global average. We show that at all three levels the Lyapunov exponent exhibits power law behavior near 01 and 02 with exponents 1/2 and 1, respectively. We indicate the origin of the exponent 1, which has not been observed in unaccelerated billiards.

Resumen-En este trabajo se analiza la estabilidad utilizando métodos de energía en forma general y como aplicación se analiza la estabilidad de una barra delgada finita sujeta en los extremos. Se obtendrán las condiciones de estabilidad para una barra finita sujeta en los extremos.

The Inverted Pendulum is one of the most important classical problems of Control Engineering. Broom Balancing (Inverted Pendulum, pole on a cart) is a well known example of nonlinear, unstable control problem. The basic control objective of the inverted pendulum problem is to maintain the unstable equilibrium position, by controlling the force applied to the mobile cart in the horizontal direction. In this paper we provide a comparative analysis of two model reference adaptive control (MRAC) methods, the first one based on the stability theory of Lyapunov and the other one based on fuzzy logic (FMRLC - Fuzzy Model Reference Learning Control). The performances of the proposed control algorithms are evaluated and shown by means of digital simulation.

In this paper discusses the different methods to analyze the stability in general and as an application we analyze the stability using energy methods in finite thin rod fixed at the ends.The stability conditions for a finite fixed rod Are obtained.

Bu çalışmada titreşim sönümleme sistemleri için yeni bir “Model Erişimli Gürbüz Kontrol” kuralı tanımlanmış ve bir raylı taşıta uygulanmıştır. Raylı taşıt süspansiyon sistemine sırasıyla PID Kontrol, ‘Model Erişimli Uyarlamalı Kontrol’ ve ‘Model Erişimli Gürbüz Kontrol’ kanunları uygulanmış ve sonuçlar kontrolcüsüz durumla karşılaştırılarak seyir konforunun iyileştirilmesi amaçlanmıştır. “Model Erişimli Gürbüz Kontrol” kanununun kararlılığı, Lyapunov Teoremi ile kanıtlanmıştır. Çeyrek raylı taşıt modeli kullanılmış ve kontrolcülerin belirlenen bir ideal skyhook hareketini yakalaması hedeflenmiştir. Modele önce sinüzoidal sonra sınırlı rampa girişi olmak üzere iki farklı yol girişi uygulanmış, vagon gövdesi, boji gövdesi ve aks-tekerlek takımının bu yol girişleri karşısındaki zaman ve frekans cevapları bilgisayar benzetimlerinde incelenmiştir. Elde edilen sonuçlar, önerilen kontrolcü ile seyir konforunun iyileştiği ve süspansiyon daralması problemine neden olmadığı gözlemlenmiştir.

Abstract. In this Letter we have studied the behavior of the Fast-Lyapunov Indicators for various attractors of the Gumowski-Mira map. It was observed that the Fast-Lyapunov indicators show a typical type of behavior for different kinds of attractors, viz. chaotic, periodic, and bounded attractors. We have shown the possibility of a transient chaos in GM-map. The importance of FLI in dynamical system or maps is suggested. 1.

This paper is devoted to studying both the global and local stability of dynamical neural networks. In particular, it has focused on nonlinear neural networks with perturbation. Properties relating to asymptotic and exponential stability and instability have been detailed. This paper also looks at the robustness of neural networks to perturbations and examines if the related properties have been preserved. Circumstances for global and local exponential stability of nonlinear neural network dynamics have been studied. We mentioned that the local exponential stability of any equilibrium point of dynamical neural networks is equivalent to the stability of the linearized system around that equilibrium point. From this, some well-known and new sufficient conditions for local exponential stability of neural networks have been obtained. The Lyapunov’s procedure has been used to analyze the stability property of nonlinear dynamical systems and many outcomes have been combined and generalize...

This paper presents a formal framework for business process modeling and analysis using partially ordered transition Decision Process Petri nets (DPPN). The advantage of this approach is its ability to represent the dynamic behavior of the business process. The business process model is supported by an information technology strategic planning (ITSP) model and methodology. The modeling methodology is based in business strategy transformation. High-level business strategies are re…ned up to the point when they can be described in terms of the activities needed to achieve a certain tactical business strategy given only in terms of goals and strategies. At this point, partially ordered DPPN are used for business process representation and analysis. DPPN extends the place-transitions Petri net theoretic approach including the Markov decision process. In this sense, DPPN corresponds to a series of strategies which guide the selection of actions that lead to a …nal (decision) state. By taking into account di¤erent possible courses of action the overall utility of each strategy is considered. The utility function of each business process is represented by a Lyapunov like function. Conditions of equilibrium and stability for the DPPN are analyzed. For illustration purposes, two examples are presented.

This paper studies an approximate dynamic programming (ADP) strategy of a group of nonlinear switched systems, where the external disturbances are considered. The neural network (NN) technique is regarded to estimate the unknown part of actor as well as critic to deal with the corresponding nominal system. The training technique is simultaneously carried out based on the solution of minimizing the square error Hamilton function. The closed system's tracking error is analyzed to converge to an attraction region of origin point with the uniformly ultimately bounded (UUB) description. The simulation results are implemented to determine the effectiveness of the ADP based controller. This is an open access article under the CC BY-SA license.

Resumen. En este artículo se estudia la dinámica global del modelo de Evasión-Inmune presentado por Arciero, Jackson y Kirschner [1], el cual describe la interacción entre células efectoras, células cancerígenas y las citocinas IL − 2 y T GF − β en el sitio del tumor. El sistema modela distintos comportamientos, como lo son: puntos de equilibrio,órbitas periódicas y ciclos límite estables. Utilizando el método de Localización de Conjuntos Compactos Invariantes se logra definir un dominio en el espacio de estados donde se localizan todas las dinámicas que exhibe el modelo de Evasión-inmune. La localización de dicho dominio es importante debido a que proporciona información sobre la salud del individuo en corto y largo plazo. Los límites de tal dominio representan los valores mínimos y máximos de las variables de estado y se expresan mediante desigualdades algebraicas dadas por una combinación de los parámetros del sistema. Adicionalmente, mediante una función candidata de Lyapunov, se demuestra que la región de localización es un dominio positivamente invariante, lo que permite asegurar que dada cualquier condición inicial, las trayectorias del sistema no divergen. Finalmente, se presentan simulaciones numéricas y se realiza un análisis de las posibles implicaciones biológicas de los resultados obtenidos. Palabras clave. Conjunto compacto invariante, dominio acotado positivamente invariante, Lyapunov, cáncer, sistema biológico.

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En este artículo se presenta el modelado y análisis de un sistema de teloperación bilateral no lineal de n grados de libertad controlado por convergencia de estado. Se considera que el operador humano aplica una fuerza constante sobre el manipulador local mientras realiza la tarea. Además, la interacción entre el manipulador remoto y el entorno se considera pasiva. La comunicación entre el sitio local y remoto se realiza mediante un canal de comunicación con retardo de tiempo. El análisis presentado en este artículo considerada que éste es variable. En este artículo también se demuestra la estabilidad del sistema utilizando la teoría de Lyapunov-Krasovskii demostrándose que el esquema de control por convergencia de estado para el caso con retardo de tiempo variable asegura la estabilidad del sistema de teleoperación no lineal. También se muestra experimentalmente que, para el caso de protocolos de comunicación fiables, el esquema propuesto garantiza que se logra la coordinación posición local-remoto. < Palabras Clave: Teleoperación, estabilidad, Lyapunov-Krasovskii, control no lineal, retardo de tiempo, convergencia de estado.