Finite Future Time Research Articles

A Mass-Conservation Model for Stability Analysis and Finite-Time Estimation of Spread of COVID-19.

The COVID-19 global pandemic has significantly impacted people throughout the United States and the World. While it was initially believed the virus was transmitted from animal to human, person-to-person transmission is now recognized as the main source of community spread. This article integrates data into physics-based models to analyze stability of the rapid COVID-19 growth and to obtain a data-driven model for spread dynamics among the human population. The proposed mass-conservation model is used to learn the parameters of pandemic growth and to predict the growth of total cases, deaths, and recoveries over a finite future time horizon. The proposed finite-time prediction model is validated by finite-time estimation of the total numbers of infected cases, deaths, and recoveries in the United States from March 12, 2020 to December 9, 2020.

A Stereo Vision-Aided Receding Horizon Vehicle Dynamic Control System for Independent Drive Vehicles Steered by Wire

This paper proposes a stereo vision-aided receding horizon vehicle dynamic control system for independent drive vehicles steered by wire. First, we propose the receding horizon vehicle dynamic control (RHVDC) to track the desired slip angle and yaw rate of a dynamic vehicle. The RHVDC computes and updates control inputs at each sampling time to minimize a quadratic cost function over the finite future time horizon, allowing it to address the time-varying property of dynamic vehicles. Its stability is shown to be guaranteed with appropriate parameters. Second, unlike the conventional steering systems fixed with the driver’s steering wheels, the SBW system improves the controllability of vehicle dynamics and enables better tracking performance. Third, combining a stereo vision system with existing sensors allows state estimation of dynamic vehicles to be more accurate in noisy environments. The three strategies mentioned above ultimately maximize the tracking performance of dynamic vehicles through improvement in terms of theory, facilities, and recognition. Through the software-in-the-loop simulation (SILS) with CarSim, the proposed RHVDC system has the better tracking performance for controlling both the slip angle and the yaw rate compared with the existing ones. It is also observed that the performance enhancement of the proposed RHVDC system is more outstanding on slippery or more severe roads.

Future evolution in a backreaction model and the analogous scalar field cosmology

We investigate the future evolution of the universe using the Buchert framework for averaged backreaction in the context of a two-domain partition of the universe. We show that this approach allows for the possibility of the global acceleration vanishing at a finite future time, provided that none of the subdomains accelerate individually. The model at large scales is analogously described in terms of a homogeneous scalar field emerging with a potential that is fixed and free from phenomenological parametrization. The dynamics of this scalar field is explored in the analogous FLRW cosmology. We use observational data from Type Ia Supernovae, Baryon Acoustic Oscillations, and Cosmic Microwave Background to constrain the parameters of the model for a viable cosmology, providing the corresponding likelihood contours.

Cosmic anisotropic doomsday in Bianchi type I universes

In this paper we study finite time future singularities in anisotropic Bianchi type I models. It is shown that there exist future singularities similar to Big Rip ones (which appear in the framework of phantom Friedmann-Robertson-Walker cosmologies). Specifically, in an ellipsoidal anisotropic scenario or in a fully anisotropic scenario, the three directional and average scale factors may diverge at a finite future time, together with energy densities and anisotropic pressures. We call these singularities “Anisotropic Big Rip Singularities.” We show that there also exist Bianchi type I models filled with matter, where one or two directional scale factors may diverge. Another type of future anisotropic singularities is shown to be present in vacuum cosmologies, i.e., Kasner spacetimes. These singularities are induced by the shear scalar, which also blows up at a finite time. We call such a singularity “Vacuum Rip.” In this case one directional scale factor blows up, while the other two and average scale factors tend to zero.

Removing the big rip singularity from anisotropic universe in super string theory

Recently, various observational data predict the possibility that dark energy could be in the form of phantom field. The positive phantom-energy density grows without limit with the expansion of the Universe and leads to a big-rip singularity at a finite future time. The main question arises: what is the origin of the big rip singularity in a four-dimensional Universe? To answer this question, in this paper, we propose a new model in super string theory that allows taking into account the Dirac and vector string tachyon in addition to the scalar one, which stretches between branes and antibranes. In this model, scalar and Dirac string tachyons cancel each other’s effects and the only effect induced by the vector tachyon can be observed in density and pressures of the universe. We observe that different scale factors, pressures, and dark energy equation of state parameters are produced in different directions because of inhomogeneous tachyon dynamics and consequently one anisotropic universe is formed. Also, these observations are given in terms of effective tachyon potential and the separation between branes and antibranes. Thus, we have shown that the expansion of the anisotropic Universe is controlled by the vector string tachyon and evolves from the non-phantom phase to the phantom one and consequently, the phantom-dominated era of the universe accelerates and ends up in a big-rip singularity.

Stable Model-Based Predictive Control for Wheeled Mobile Robots using Linear Matrix Inequalities

This paper presents practical results from the application of a new synthesis methodology based on model predictive control (MPC) applied to a three-wheeled omnidirectional mobile robot seeking to follow pre-established trajectories. The approach is based on the definition of an objective function with a finite future time horizon. The resulting optimization problem is declared in the form of linear matrix inequalities (LMIs). The closed loop stability of the system is guaranteed through constraints related to the non-increasing monotonicity of the objective function. Constraints are also implemented in the manipulated variables with the objective of adapting the control system to the physical limitations of the robot. Additionally, methods are described to handle the computational delay in the robot model and to adjust the control law to improve the global performance of the system.

Invariant-driven specifications in Maude

This work presents a general mechanism for executing specifications that comply with given invariants, which may be expressed in different formalisms and logics. We exploit Maude’s reflective capabilities and its properties as a general semantic framework to provide a generic strategy that allows us to execute Maude specifications taking into account user-defined invariants. The strategy is parameterized by the invariants and by the logic in which such invariants are expressed. We experiment with different logics, providing examples for propositional logic, (finite future time) linear temporal logic and metric temporal logic.

Astronomical bounds on a future Big Freeze singularity

It was recently found that dark energy in the form of phantom generalized Chaplygin gas may lead to a new form of a cosmic doomsday, the Big Freeze singularity. Like the Big Rip singularity, the Big Freeze singularity would also take place at finite future cosmic time, but, unlike the Big Rip, it happens for a finite scale factor. Our goal is to test if a universe filled with phantom generalized Chaplygin gas can conform to the data of astronomical observations. We shall see that if the universe is only filled with generalized phantom Chaplygin gas with the equation of state p = −c 2 s 2/ρ α with α < −1, then such a model cannot be matched to the observational data; generally speaking, such a universe has an infinite age. To construct more realistic models, one actually need to add dark matter. This procedure results in cosmological scenarios which do not contradict the values of universe age and expansion rate and allow one to estimate how long we are now from the future Big Freeze doomsday.

Worse than a big rip?

We show that a generalised phantom Chaplygin gas can present a future singularity in a finite future cosmic time. Unlike the big rip singularity, this singularity happens for a finite scale factor, but like the big rip singularity, it would also take place at a finite future cosmic time. In addition, we define a dual of the generalised phantom Chaplygin gas which satisfies the null energy condition. Then, in a Randall–Sundrum 1 brane-world scenario, we show that the same kind of singularity at a finite scale factor arises for a brane filled with a dual of the generalised phantom Chaplygin gas.

The different faces of a phantom

The SNe type Ia data admit that the universe today may be dominated by some exotic matter with negative pressure violating all energy conditions. Such exotic matter is called phantom matter due to the anomalies connected with violation of the energy conditions. If a phantom matter dominates the matter content of the universe, it can develop a singularity in a finite future proper time. Here we show that, under certain conditions, the evolution of perturbations of this matter may lead to avoidance of this future singularity (the big rip). At the same time, we show that local concentrations of a phantom field may form, among other regular configurations, black holes with asymptotically flat static regions, separated by an event horizon from an expanding, singularity-free, asymptotically de Sitter universe.

Quantum driven bounce of the future universe

It is demonstrated that due to back-reaction of quantum effects, expansion of the universe stops at its maximum and takes a turnaround. Later on, it contracts to a very small size in finite future time. This phenomenon is followed by a bounce with re-birth of an exponentially expanding non-singular universe.

Design of a nuclear reactor controller using a model predictive control method

A model predictive controller is designed to control thermal power in a nuclear reactor. The basic concept of the model predictive control is to solve an optimization problem for finite future time steps at current time, to implement only the first optimal control input among the solved control inputs, and to repeat the procedure at each subsequent instant. A controller design model used for designing the model predictive controller is estimated every time step by applying a recursive parameter estimation algorithm. A 3-dimensional nuclear reactor analysis code, MASTER that was developed by Korea Atomic Energy Research Institute (KAERI), was used to verify the proposed controller for a nuclear reactor. It was known that the nuclear power controlled by the proposed controller well tracks the desired power level and the desired axial power distribution.

More general sudden singularities

We present a general form for the solution of an expanding general-relativistic Friedmann universe that encounters a singularity at finite future time. The singularity occurs in the material pressure and acceleration whilst the scale factor, expansion rate and material density remain finite and the strong energy condition holds. We also show that the same phenomenon occurs, but under different conditions, for Friedmann universes in gravity theories arising from the variation of an action that is an arbitrary analytic function of the scalar curvature.

Bigger Rip with no dark energy

By studying a modified Friedmann equation which arises in an extension of general relativity which accommodates a time-dependent fundamental length L(t), we consider cosmological models where the scale factor diverges with an essential singularity at a finite future time. Such models have no dark energy in the conventional sense of energy possessing a simple pressure–energy relationship. Data on supernovae restrict the time from the present until the Rip to be longer than the current age of the Universe.

Design of an adaptive predictive controller for steam generators

The water level control of a nuclear steam generator is very important to secure the sufficient cooling inventory for the nuclear reactor and, at the same time, to prevent the damage of turbine blades. The dynamics of steam generators is very different according to power levels and changes as time goes on. The generalized predictive control method is used to solve an optimization problem for the finite future time steps at current time and to implement only the first control input among the solved optimal control inputs of several time steps. A recursive parameter estimation algorithm estimates on-line the mathematical model of steam generator every time step to generate the linear controller design model. In this work, by combining these generalized predictive control method and recursive parameter estimation algorithm, a new controller is designed to control the water level of nuclear steam generators. It is shown through application to a linear model and a nonlinear model of steam generators that the proposed controller has good performance.

On dynamical properties of general dynamical systems and differential inclusions

Let F be a general dynamical system defined on a complete locally compact metric space X. We give a slightly improved version of the Lyapunov characterization of asymptotic stability in one of our previous works and provide a short self-contained proof for the existence of arbitrarily small positively invariant neighborhoods of compact asymptotically stable sets in the present context. Based on these results, we prove that the uniform attractors of F are connected and are stable with respect to perturbations under appropriate conditions. We are also interested in the dynamical properties of differential inclusion: x′(t)∈f(x(t)) on R m . First, we show that if no solutions of the system blow up in finite future time, then its reachable mapping F is a general dynamical system. Then we discuss some asymptotic stability properties of the system. In particular, we prove that if there exists a nonempty compact connected subset M of R m such that M attracts a neighborhood of itself, then the system has a connected uniform attractor A . We also prove that A is stable with respect to both internal and external perturbations. More precisely, we prove that when λ>0 is sufficiently small, the perturbed system: x′(t)∈ con f(x(t)+λ B 1)+λ B 1 has a connected uniform attractor A λ ; moreover, δ H ( A λ, A)→0 as λ→0, where δ H (· ,·) is the Hausdorff distance in R m .

On the use and the performance of software reliability growth models

We address the problem of predicting future failures for a piece of software. The number of failures occurring during a finite future time interval is predicted from the number failures observed during an initial period of usage by using software reliability growth models. Two different methods for using the models are considered: straightforward use of individual models, and dynamic selection among models based on goodness-of-fit and quality-of-prediction criteria. Performance is judged by the relative error of the predicted number of failures over future finite time intervals relative to the number of failures eventually observed during the intervals. Six of the former models and eight of the latter are evaluated, based on their performance on twenty data sets. Many open questions remain regarding the use and the performance of software reliability growth models.