Linear acceleration-based redundancy resolution schemes that diverge in finite time

A mean field game approach for a class of linear quadratic discrete choice problems with congestion avoidance

A finite time synergetic control scheme for robot manipulators

In this article, we present a novel method that results in efficient minimum norm solution for the rate coordination problem in redundant manipulators. The theory is developed based upon a geometric interpretation that, for minimum norm criterion, vectors orthogonal to constraint space should pass through the origin of the solution space. It is shown that, for any spatial manipulator with 1, 2, or 3 degrees of redundancy, the minimum norm rate solution can be derived in analytic closed form. An example of the analytic formulation is given for a 3R planar case, substantiated with simulation results. The behavior of this algorithm in nonredundant and near singular situations is also discussed. The method offers an equivalent but much more efficient alternative to using the pseudoinverse in redundancy resolution and, in fact, is applicable to any underdetermined linear system. An alternative formulation of pseudoinverse arrived at in the course of the development is also presented. © 1992 John Wiley & Sons, Inc.

Long range scattering for the modified Schrödinger map in two space dimensions

A neural network adaptive control scheme for robot manipulators is proposed which consists of one Adaline network to identify structured system dynamics and another one to compensate for both structured and unstructured dynamic uncertainties. The former is trained offline using an LMS (least mean square) type algorithm, while the latter uses an online stable weight updating mechanism determined using Lyapunov theory. Since Adaline nets match robot regressor dynamics perfectly, the training processes of the resulting simple neural networks are computationally efficient and the proposed adaptive control scheme has very high potential in real-time applications. The proposed control scheme is illustrated by simulation and comparison studies. >

Fault Tolerant Control Scheme for Robotic Manipulators Affected by Torque Faults

This paper presents a distributed, robust, finite-time secondary control for both voltage and frequency restoration of an islanded microgrid with droop-controlled inverter-based distributed generators (DGs). The distributed cooperative secondary control is fully distributed (i.e., uses only the information of neighboring DGs that can communicate with one another through a sparse communication network). In contrast to existing distributed methods that require a detailed model of the system (such as line impedances, loads, other DG units parameters, and even the microgrid configuration, which are practically unknown), the proposed protocols are synthesized by considering the unmodeled dynamics, unknown disturbances, and uncertainties in their models. The other novel idea in this paper is that the consensus-based distributed controllers restore the islanded microgrid's voltage magnitudes and frequency to their reference values for all DGs within finite time, irrespective of parametric uncertainties, unmodeled dynamics, and disturbances, while providing accurate real-power sharing. Moreover, the proposed method considers the coupling between the frequency and voltage of the islanded microgrid. Unlike conventional distributed controllers, the proposed approach quickly reaches consensus and exhibits a more accurate robust performance. Finally, we verify the proposed control strategy's performance using the MATLAB/SimPowerSystems toolbox.

Since population models are often subject to environmental noise, in this paper we stochastically perturb the Lotka-Volterra model with variable delay \(\dot{x}(t)=\text{diag}(x(t))\big{[}b+Ax(t)+Bx(t-\delta(t))\big{]}\) into the It\(\hat{\text{o}}\) form \(\text{d}x(t)=\text{diag}(x(t))\big{[}\big{(}b+Ax(t)+Bx(t-\delta(t))\big{)}\text{d}t+\sigma\text{d}w(t)\big{]}\). We show that under certain conditions, the deterministic delay equation and the perturbed delay equation have similar behaviour in the sense that both have positive solutions which will not explode to infinity in a finite time and, in fact, will be ultimately bounded.KeywordsStochastic Lotka-Volterra modelVariable delayUltimate boundednessItô’s formulaAMR Subject Classifications34K4060H1060J65

A nonclassical fourth-order partial differential equation describing blow-up instability in self-oscillatory systems is studied. Several classes of exact solutions of this equation are constructed. It is shown that these solutions include ones growing to infinity in a finite time, ones bounded globally in time, and ones bounded on any finite time interval, but not globally.

Considering stochastic perturbations of white and color noises, we introduce the Markov switched stochastic Nicholson-type delay system with patch structure. By constructing a traditional Lyapunov function we show that solutions of the addressed system are not only positive, but also do not explode to infinity in finite time and, in fact, are ultimately bounded. Then we estimate its ultimate boundedness, moment, and Lyapunov exponent. Finally, we present an example of numerical simulations to verify theoretical results.

Toda hierarchy with indefinite metric

Small-noise limit of the quasi-Gaussian log-normal HJM model

In this paper, we consider the Cauchy problem for the nonlinear Schr&#246;dinger equation with combined power-type nonlinearities, which is masscritical/supercr-itical, and energy-subcritical. Combing Du, Wu and Zhang' argument with the variational method, we prove that if the energy of the initial data is negative (or under some more general condition), then the <i>H</i>¹-norm of the solution to the Cauchy problem will go to infinity in some finite time or infinite time.

We continue the study (initiated in [1]) of Borel measures whose time evolution is provided by an interacting Hamiltonian structure. Here, the principal focus is the development and advancement of deficency in the measure caused by displacement of mass to infinity in finite time. We introduce - and study in its own right - a regularization scheme based on a dissipative mechanism which naturally degrades mass according to distance traveled (in phase space). Our principal results are obtained based on some dynamical considerations in the form of a condition which forbids mass to return from infinity.

This paper discusses a randomized n-species delay Lotka-Volterra competition system. We show that the positive solution of the associated stochastic delay differential equation does not explode to infinity in a finite time. In addition the existence uniqueness and boundedness of the positive solutions are studied.