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

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

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

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

Estimate of the theoretical uncertainty of the cross sections for nucleon knockout in neutral-current neutrino-oxygen interactions

Free nucleons propagating in water are known to produce gamma rays, which form a background to the searches for diffuse supernova neutrinos and sterile neutrinos carried out with Cherenkov detectors. As a consequence, the process of nucleon knockout induced by neutral-current quasielastic interactions of atmospheric (anti)neutrinos with oxygen needs to be under control at the quantitative level in the background simulations of the ongoing and future experiments. In this paper, we provide a quantitative assessment of the uncertainty associated with the theoretical description of the nuclear cross sections, estimating it from the discrepancies between the predictions of different models.Comment: 7 pages, 2 figure

Island operation capability in the Colombian electrical market: a promising ancillary service of distributed energy resources

Hoy en día, la mayoría de los generadores distribuidos no están diseñados para operar bajo condiciones de isla. El servicio complementario de capacidad de operación por islas se presenta como un servicio de soporte técnico con la capacidad de aumentar la resiliencia, confiabilidad, seguridad y flexibilidad de un sistema eléctrico de distribución. Sin embargo, la operación por islas presenta unos desafíos técnicos, económicos y sociales que deben discutirse y analizarse durante la etapa de planificación.En este artículo, se presenta una comparación entre una operación intencional por islas y una isla planificada previamente, así como una descripción de los principales desafíos y beneficios de la operación por islas. Además, se realiza una evaluación económica de la confiabilidad del servicio de energía eléctrica al implementar la capacidad de operación por islas como un servicio complementario. Dicha evaluación muestra que la operación por islas tiene el potencial de minimizar la energía no suministrada hasta en un 50%. Además, se muestra un análisis técnico para la implementación del servicio complementario de capacidad de operación por islas. Luego, se estudia un sistema eléctrico de distribución existente con pequeñas centrales hidroeléctricas como un estudio de caso, con el fin de identificar los requisitos técnicos establecidos tanto para el sistema de distribución como para la fuente de generación. Finalmente, y teniendo en cuenta las normativas y regulaciones vigentes, se esboza una propuesta para la implementación del servicio complementario de capacidad de operación por islas en el sistema eléctrico colombiano.Nowadays most distributed generators are not designed to operate under islanded conditions. The ancillary service of islanded operation capability is proposed as a technical support service with the ability to increase the reliability, security and flexibility of an electrical distribution system. Nevertheless, island operation entails technical, economic and social issues that must be discussed and analyzed during the planning stage.This article compares an intentional island project to a preplanned island and describes the main issues and benefits of islanded operation. Additionally, the reliability of the service to implement the islanded operation capability as an ancillary service is economically assessed, which shows that island-based operation has the potential to minimize non-supplied energy up to 50%. Also, a technical analysis of implementing island operation capability ancillary service is presented. Subsequently, an existing electrical distribution system with small hydropower plants is considered as a study case in order to identify the technical requirements set out for both, the distribution system and the generation source. Finally, taking into account the current Law and regulations, a proposal is outlined for the implementation of the island operation capability ancillary service in the Colombian electrical system

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

Predefined-time stabilization of high order systems

The aim of this paper is to introduce a controller that stabilizes a class of arbitrary order systems in predefined-time. The proposed controller is designed with basis on the block-control principle yielding in a nested structure similar to high order sliding mode algorithms and terminal sliding mode algorithms. For this case, it is assumed the availability of the state and the absence of perturbations. Numerical simulations expose the desired performance of this controller