Equal coaxial symmetrically located helical vortices translate and rotate steadily while preserving their shape and relative position if they move in an unbounded inviscid incompressible fluid. In ...this paper, the linear and angular velocities of this set of vortices (
$U$
and
$\unicodeSTIX{x1D6FA}$
respectively) are computed as the sum of the mutually induced velocities found by Okulov (J. Fluid Mech., vol. 521, 2004, pp. 319–342) and the self-induced velocities found by Velasco Fuentes (J. Fluid Mech., vol. 836 2018). Numerical computations of the velocities using the Helmholtz integral and the Biot–Savart law, as well as numerical simulations of the flow evolution under the Euler equations, are used to verify that the theoretical results are accurate for
$N=1,\ldots ,4$
vortices over a broad range of values of the pitch and radius of the vortices. An analysis of the flow topology in a reference system that translates with velocity
$U$
and rotates with angular velocity
$\unicodeSTIX{x1D6FA}$
serves to determine the capacity of the vortices to transport fluid.
The surveillance or monitoring of places is crucial to ensuring security, protecting people and assets, preventing crimes, and detecting emergencies, to mention some. Unmanned Aerial Vehicles (UAVs) ...play a vital role in these applications, offering versatility, agility, and aerial vision. A crucial step for such tasks is to protect the UAV path ahead. This paper focuses on a methodology harnessing the unpredictable nature of chaotic systems to generate trajectories around a closed area or contour. However, although a vast quantity of research papers mention the use of chaotic path generation, they have yet to learn about the control system and the dynamics affecting the UAV, where developing the control theory is challenging. In this paper, we design controllers based on predetermined-time stability, ensuring the achievement of the desired trajectory before a specified time. Additionally, adjusting control parameters is a crucial step during the control design, impacting the control performance. Hence, we present a method to optimize and adapt controller parameters through evolutionary optimization, demonstrating precision enhancement. We validate the proposed system’s performance and the controllers through numerical simulations, indicating that the UAV effectively and accurately follows some types of chaotic trajectories like a square contour, aiming at the feasibility of this methodology in real UAV surveillance applications.
•Design of Predefined-Time Control (PTC) for chaotic trajectory tracking with UAVs.•Generation of complex and unpredictable trajectories based on chaotic systems.•Optimization of controller parameters by Differential Evolution metaheuristic.•Lyapunov analysis for the design and convergence of Predefined-Time Controllers.
Abstract The Gaia mission has provided astrometric observations of unprecedented accuracy for more than 156,000 asteroids. The reported astrometric uncertainties are of the order of milliarcseconds, ...about 2 orders of magnitude smaller than that of traditional ground-based observations. The accuracy of Gaia data requires a high-fidelity orbit determination process, especially in the observation modeling. We present a statistical analysis of Gaia Focused Product Release to test the accuracy of the reported positions and associated uncertainties. We find that center-of-light offsets due to phase variations need to be modeled to properly fit the observational data. Prediction tests show that the uncertainty in the fitted orbits can be optimistic unless the observational uncertainty is inflated to account for errors in finding the center-of-mass of the body. Moreover, errors in the masses of small-body perturbers can cause differences in the orbital solution that exceed formal uncertainties of the best constrained orbits. As an example, we provide an update of the impact hazard analysis of 1950 DA, one of the asteroids observed by Gaia, and find that the impact probability in the year 2880 increases to 3.8 × 10 −4 .
Abstract We characterize asteroid (16) Psyche using high-precision astrometry, including the recent Gaia Focused Product Release. The gravitational perturbations of Psyche on other asteroids can be ...observable in the case of mutual encounters. Using a least squares approach, we estimate the mass of Psyche by fitting astrometric data of asteroids that come within 0.05 au of Psyche. Combining the resulting individual estimates, we find GM = 1.601 ± 0.017 km 3 s −2 . This result is robust against variations in the orbit determination setup and specific data set used. The volume and equivalent radius of Psyche are currently constrained by occultations and radar and optical imaging to (5.75 ± 0.19) × 10 6 km 3 and 111 − 0.5 + 2 km, respectively. Given the volume of Psyche, our mass estimate corresponds to a bulk density of 4172 ± 145 kg m −3 , which is compatible with an M-type taxonomic classification. Finally, the phase-dependent photocenter offset is visible in the residuals of Gaia astrometric observations of Psyche. This effect is consistent with the size of Psyche.
Abstract
The catalog of km-sized near-Earth objects (NEOs) is nearly complete. Typical impact monitoring analyses search for possible impacts over the next 100 yr and none of the km-sized objects ...represent an impact threat over that time interval. Assessing the impact risk over longer timescales is a challenge since orbital uncertainties grow. To overcome this limitation we analyze the evolution of the minimum orbit intersection distance (MOID), which bounds the closest possible encounters between the asteroid and the Earth. The evolution of the MOID highlights NEOs that are in the vicinity of the Earth for longer periods of time, and we propose a method to estimate the probability of a deep Earth encounter during these periods. This metric is used to rank the km-sized catalog in terms of their long-term impact hazard to identify targets of potential interest for additional observation and exploration.
ABSTRACT This article describes a control approach for obtaining predefined‐time robust tracking in multiplicative systems despite positive, bounded, and unknown multiplicative disturbances. The ...proposed approach is distinguished by imposing predefined‐time convergence, a topic previously studied in conventional calculus in the context of multiplicative systems. Multiplicative calculus is recognized as a beneficial tool that complements standard calculus by simplifying the modeling and comprehension of numerous processes. Simulations are carried out to illustrate that the given control strategy enforces convergence before a predefined time instant and, while inducing robustness against system uncertainties. The findings of this article pave the way for further research into predefined‐time synchronization of multiplicative oscillator systems, which would bring promising implications for data encryption and secure communication.
Stability analysis plays an essential role in control systems design. This analysis can be done using different techniques that show the equilibrium points are stable (or unstable). This paper ...focuses on fractional systems of order 0 < α < 1 modeled by the Atangana–Baleanu derivative of Riemann–Liouville type (ABR), which allows consistent modeling of a large class of physical systems with complex dynamics. The main contribution of the paper consists of some novel inequalities for the Atangana–Baleanu derivative of the Riemann–Liouville type. Furthermore, the proposed study allows considering both quadratic and convex Lyapunov functions to analyze stability in ABR systems by applying the Direct Lyapunov Method.
In this article, the estimation problem in a class of nonlinear fractional-order systems is solved by a stable estimator that generalizes the classical exponential observers, establishing a new class ...called Mittag–Leffler observers. The solution to the linear quadratic regulator problem is proposed to design optimal control laws for fractional-order linear systems and its applications. All the results are based on the Caputo derivative for commensurate fractional-order systems. Numerical simulations validate the proposed theory.
This paper proposes the study of a newer class of integro-differential operators, which allow analysing a more general family of dynamical systems, with not necessarily integer-order differentiable ...solutions, and based on Volterra integral equations of the second kind. One of the main advantages of the present study is that the proposed operators include, in particular cases, some classical and modern formulations of fractional- and distributed-order derivatives. In contrast to conventional methodologies, the integer-order differentiability of the solution is not assumed, allowing to deem on a more general class of dynamical systems and non-smooth techniques for robust stabilisation. The formal presentation of novel tools could result in high interest for robust control of more varied dynamical processes. Representative simulations are also presented in order to highlight the feasibility of the proposed methods.
In this work, a class of chaotic nonlinear fractional systems of commensurate order called Liouvillian systems is considered to solve the problem of generalized synchronization. To solve this ...problem, the master and the slave systems are expressed in the Fractional Generalized Observability Canonical Form (FGOCF), then a fractional-order dynamical control law is designed to achieve the generalized synchronization. The encryption of color images is presented as an application to the proposed synchronization method, the encryption algorithm allows to decrypt data without loss. The synchronization and its applications are then illustrated with numerical examples.
