On optimal predefined-time stabilization

This paper addresses the problem of optimal predefined-time stability. Predefined-time stable systems are a class of fixed-time stable dynamical systems for which the minimum bound of the settling-time function can be defined a priori as an explicit parameter of the system. Sufficient conditions for a controller to solve the optimal predefined-time stabilization problem for a given nonlinear system are provided. These conditions involve a Lyapunov function that satisfies a certain differential inequality for guaranteeing predefined-time stability. It also satisfies the steady-state Hamilton–Jacobi–Bellman equation for ensuring optimality. Furthermore, for nonlinear affine systems and a certain class of performance index, a family of optimal predefined-time stabilizing controllers is derived. This class of controllers is applied to optimize the sliding manifold reaching phase in predefined time, considering both the unperturbed and perturbed cases. For the perturbed case, the idea of integral sliding mode control is jointly used to ensure robustness. Finally, as a study case, the predefined-time optimization of the sliding manifold reaching phase in a pendulum system is performed using the developed methods, and numerical simulations are carried out to show their behavior

Predefined-Time Backstepping Control for Tracking a Class of Mechanical Systems

The predefined-time exact tracking of unperturbed fully actuated mechanical systems is considered in this paper. A continuous second-order predefined-time stabilizing backstepping controller, designed using first-order predefined-time stabilizing functions, is developed to solve this problem. As an example, the proposed solution is applied over a two-link planar manipulator and numerical simulations are conducted to show performance of the proposed control scheme.Consejo Nacional de Ciencia y Tecnologí

A Second Order Predefined-Time Control Algorithm

The predefined-time stabilization of second-order systems, i.e. the fixed-time stabilization with settling time as a function of the controller parameters, is revisited in this paper. The proposed controller is a time-based switched controller which first drive the system trajectories to a linear manifold in predefined time and then uses a nested second order controller. The application of the results is demonstrated for the trajectory tracking control in fully actuated mechanical systems. An illustrative example of the control of a two-link planar manipulator with predefined-time convergence shows the effectiveness of the proposed algorithm

Semi-Global Predefined-Time Stable Systems

A Lyapunov-based construction of a predefined-time stabilizing function (a function that stabilizes a system in fixed-time with settling time as function of the controller parameters) for scalar systems is considered in this paper. The constructed function involves the inverse incomplete gamma function, causing this function to be semi-global, i.e., the domain of definition of the function can be made as large as wanted with an appropriate parameter selection. Finally, the constructed function is used to design predefined-time stabilizing controllers which are robust against vanishing and non-vanishing perturbations

Semi-Global Predefined-Time Stable Vector Systems

In this paper, we expose a control function which allows the semi-global predefined-time stabilization of first-order vector systems. The predefined-time stability is a stronger class of finite-time stability that has as main advantage the settling time as a tunable parameter of the proposed function. To design that stabilizing function, we use the unit control principle jointly to the inverse incomplete gamma function. For the resulting expression, the domain of definition the inverse incomplete gamma function can be made as large as wanted with an appropriate parameter selection, and, as consequence, the attraction domain of the systems. Therefore, we say that the system exhibits semi-global predefined-time stability. As an essential feature, the parameter which defines the settling time bound and those that tune the attraction domain are independent of each other. Finally, the constructed function is used to design predefined-time stabilizing controllers which are robust against vanishing and non-vanishing perturbations

Backstepping Design for the Predefined-Time Stabilization of Second-Order Systems

The backstepping design of a controller which stabilizes a class of second-order systems in predefined-time is studied in this paper. The origin of a dynamical system is said to be predefined-time stable if it is fixed-time stable and an upper bound of the settling-time function can be arbitrarily chosen a priori through an appropriate selection of the system parameters. The proposed backstepping construction is based on recently proposed Lyapunov-like sufficient conditions for predefined-time stability. Different from other approaches, the proposed backstepping design allows the simultaneous construction of a Lyapunov function which meets the conditions for guaranteeing predefined-time stability. A simulation example is presented to show the behavior of a developed controller, and to show its advantages against similar schemes.ITESO, A.C

Estimação Robusta para um CSTR Usando uma Ordem Elevada Modo Deslizante Observador e um Estimador Baseado em Observador

This paper presents an estimation structure for a continuous stirred-tank reactor, which is comprised of a sliding mode observer-based estimator coupled with a high-order sliding-mode observer. The whole scheme allows the robust estimation of the state and some parameters, specifically the concentration of the reactive mass, the heat of reaction and the global coefficient of heat transfer, by measuring the temperature inside the reactor and the temperature inside the jacket. In order to verify the results, the convergence proof of the proposed structure is done, and numerical simulations are presented with noiseless and noisy measurements, suggesting the applicability of the posed approach.Este trabajo presenta una estructura de estimación para un reactor de tanque agitado en continuo, la cual se compone de un estimador basado en observador por modos deslizantes acoplado con un observador por modos deslizantes de alto orden. Todo el esquema permite la estimación robusta del estado y algunos parámetros, concretamente la concentración de la masa reactiva, el calor de reacción y el coeficiente global de transferencia de calor, a partir de la medición de las temperaturas al interior del reactor y de la chaqueta. Para verificar los resultados, se realizan pruebas de convergencia de la estructura propuesta, y se presentan simulaciones numéricas con mediciones ruidosas y sin ruido, lo que sugiere la aplicabilidad del enfoque planteado.Este trabalho apresenta uma estrutura de estimativa para um reator de tanque agitado continuamente, que é composta por um estimador baseado em observador deslizante de modo acoplado com um alto ordem modo deslizante observador. Todo o esquema permite a estimativa robusta do estado e alguns parâmetros, a saber, a concentração da massa de reação, o calor da reação e o coeficiente de transferência total de calor, a partir da medição da temperatura no interior do reator e da jaqueta. Para verificar os resultados, as evidências de convergência da estrutura proposta são feitas, e simulações numéricas são apresentadas com medidas ruidosas e sem ruído, o que sugere a aplicação da abordagem proposta

"Observatorio Social Elena Coda": la guía de recursos sociales como respuesta a las nuevas necesidades.

La iniciativa que se presenta en este artículo se constituye como un instrumento que contribuya a facilitar a la población el acceso a información sobre recursos, servicios y prestaciones sociales y con ello, permita alcanzar unas mayores cotas de bienestar en el marco de la sociedad actual. Supone la puesta a disposición de la ciudadania leonesa de una Guía de Recursos Sociales de León y su Alfo

On twin peak quasi-periodic oscillations resulting from the interaction between discoseismic modes and turbulence in accretion discs around black holes

Versión preprintGiven the peculiar and (in spite of many efforts) unexplained quasi-periodic oscillation (QPO) twin peak phenomena in accretion disc psd observations, the present exploratory analytical article tries to inquire deeper into the relationship between discoseismic modes and the underlying driving turbulence in order to assess its importance. We employ a toy model in the form of a Gaussian white noise driven damped harmonic oscillator with stochastic frequency. This oscillator represents the discoseismic mode. (Stochastic damping was also considered, but interestingly found to be less relevant for the case at hand.) In the context of this model, we find that turbulence interacts with disc oscillations in interesting ways. In particular, the stochastic part in the oscillator frequency behaves as a separate driving agent. This gives rise to 3:2 twin peaks for some values of the physical parameters, which we find. We conclude with the suggestion that the study of turbulence be brought to the forefront of disc oscillation dynamics, as opposed to being a mere background feature. This change of perspective carries immediate observable consequences, such as considerably shifting the values of the (discoseismic) oscillator frequencies.Universidad de Costa Rica/[805-B6-148]/UCR/Costa RicaUCR::Vicerrectoría de Investigación::Unidades de Investigación::Ciencias Básicas::Centro de Investigaciones Geofísicas (CIGEFI)UCR::Vicerrectoría de Docencia::Ciencias Básicas::Facultad de Ciencias::Escuela de Físic

Non-Singular Predefined-Time Stable Manifolds

In this paper it is introduced a class of non-singular manifolds with predefinedtime stability. That is, for a given dynamical system with its trajectories constrained to this manifold it can be shown predefined-time stability to the origin. In addition, the function that defines the manifold and its derivative along the system trajectories are continuous, therefore no singularities are presented for the system evolution once the constrained motion starts. The problem of reaching the proposed manifold is solved by means of a continuous predefined-time stable controller. The proposal is applied to the predefined-time exact tracking of fully actuated and unperturbed mechanical systems. It is assumed the availability of the state and the desired trajectory as well as its two first derivatives. As an example, the proposed solution is applied over a two-link planar manipulator and numerical simulations are conducted to show its performance.ITESO, A.C.CINVESTAV-IP