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In this paper, we propose a new solution to the motion planning and control problem for a team of carlike mobile robots traversing in an extended dynamic environment. Motivated by the emerging necessity to avoid or defend against a swarm of autonomous robots, the wide array of obstacles in this dynamic environment for the first time includes a swarm of boids governed separately by a system of ordinary differential equations. The swarm exhibits collective emergent behaviors, whereas the carlike mobile robots safely navigate to designated targets. We present a set of nonlinear continuous controllers for obstacle, collision, and swarm avoidance. The controllers provide a collision-free trajectory within a constrained workspace cluttered with various fixed and moving obstacles while satisfying the nonholonomic and kinodynamic constraints associated with the vehicular robotic system. An advantage of the proposed method is the ease in deriving the acceleration-based control laws from the Lyapunov-based control scheme. The effectiveness of the control laws is demonstrated via computer simulations. The novelty of this paper lies in the simplicity of the controllers and the ease in the treatment of an extended dynamic environment, which includes swarm avoidance. [ABSTRACT FROM AUTHOR]

The benefits for the advancement and enhancement of assistive technology are manifold. However, improving accessibility for persons with disabilities (PWD) to ensure their social and economic inclusion makes up one of the major ones in recent times. This paper presents a set of new nonlinear time-invariant stabilizing controllers for safe navigation of an autonomous nonholonomic rear-wheel drive wheelchair. Autonomous wheelchairs belong to the category of assistive technology, which is most sought in current times due to its usefulness, especially to the less abled (physically and/or cognitively), hence helping create an inclusive society. The wheelchair navigates in an obstacle-ridden environment from its start to final configuration, maintaining a robust obstacle avoidance scheme and observing system restrictions and dynamics. The velocity-based controllers are extracted from a Lyapunov function, the total potentials designed using the Lyapunov based Control Scheme (LbCS) falling under the classical approach of the artificial potential field method. The interplay of the three central pillars of LbCS, which are safety, shortness, and smoothest course for motion planning, results in cost and time effectiveness and the velocity controllers' efficiency. Using the Direct Method of Lyapunov, the stability of the wheelchair system has been proved. Finally, computer simulations illustrate the effectiveness of the set of new controllers., Competing Interests: The authors declare that they have no competing interests., (© 2021 Kumar et al.)

In this paper, fractional-order time delay system modeling is presented using Haar wavelet operational matrix of integration. Therefore, it does not require any prior knowledge of transfer function structure or partial information about fractional differentiation order. It allows the estimation of the implicit time delay parameter together with other model parameters by utilizing new delay operational matrix of Haar wavelet based on Riemann-Liouville definition. The proposed technique reduces the complexity of identification by converting the complex fractional calculus equations into simple algebra. The efficacy of the approach is verified on various integer and non-integer (fractional) order systems in simulation. For realistic condition, proposed method is verified in the presence of noise in simulation and also demonstrated on the real-time process control temperature system., (Copyright © 2018. Published by Elsevier Ltd.)

A reason for applying the direct method of Lyapunov to artificial neural networks (ANNs) is to design dynamical neural networks so that they exhibit global asymptotic stability. Lyapunov functions that frequently appear in the ANN literature include the quadratic function, the Persidskii function, and the Luré-Postnikov function. This contribution revisits the quadratic function and shows that via Krasovskii-like stability criteria, it is possible to have a very simple and systematic procedure to obtain not only new and generalized results but also well-known sufficient conditions for convergence established recently by non-Lyapunov methods, such as the matrix measure and nonlinear measure.

In this paper, the reported numbers of HIV-positive individuals in Fiji between and including the years 1989 and 2002 have been used to study the dynamics of the observed HIV-positive population size. The Fiji data showed a pattern that appears to begin to approximate the "S" shaped growth pattern. It is well-known in the mathematics literature that this nonlinear pattern is a natural growth phenomenon and that there are suitable mathematical equations--from the classical Verhulst equation to the recent Tsoularis equation--that can be used to study it. These equations generate two-dimensional curves, the uses of which are case-dependent. In this paper, the curves used are the Logistic Curve and the Gompertz Curve, which are known to be relatively accurate in predicting the short-term behaviour of the observed HIV-positive population size at the initial stages of growth. This study showed that the curves, based on the 1989-2002 data, gave the scenarios in which new reported cases could stabilize by 2005 or 2013. Based on the 1989-2001 data, both curves gave the worst-case scenario of continuous increase till the year 2020 when the numbers could begin to stabilize.