Convergence Of Trajectories Research Articles

Dynamics of Particle Confined Between Oscillating and Fixed Walls

In this paper, we investigate the motion of a particle confined between the oscillating and fixed walls. As the particle collides with the moving wall in the phase of oscillations, when the wall velocity grows, the wall after collision catches up with the particle. This process can be repeated many times until in finite time interval the particle is found lying on the wall and continues its motion together with the wall. When the sign of the wall acceleration changes the particle detaches from the wall with zero velocity, so that it looks as if the particle “sticks” to the wall. It has been found that if the collision is inelastic, “sticking” leads to convergence of close trajectories except for the case of weak decay. On the contrary, in the case of elastic collision “sticking” of the particle causes even a more rapid divergence of theses trajectories.

State exact reconstruction for switched linear systems via a super-twisting algorithm

This article discusses the problem of state reconstruction synthesis for switched linear systems. Based only on the continuous output information, an observer is proposed ensuring the reconstruction of the entire state (continuous and discrete) in finite time. For the observer design an exact sliding mode differentiator is used, which allows the finite time convergence of the observer trajectories to the actual trajectories. The design scheme includes both cases: zero control input and nonzero control input. Simulations illustrate the effectiveness of the proposed observer.

Fractional standard map: Riemann–Liouville vs. Caputo

Properties of the phase space of the standard maps with memory obtained from the differential equations with the Riemann–Liouville and Caputo derivatives are considered. Properties of the attractors which these fractional dynamical systems demonstrate are different from properties of the regular and chaotic attractors of systems without memory: they exist in the asymptotic sense, different types of trajectories may lead to the same attracting points, trajectories may intersect, and chaotic attractors may overlap. Two maps have significant differences in the types of attractors they demonstrate and convergence of trajectories to the attracting points and trajectories. Still existence of the most remarkable new type of attractors, “cascade of bifurcation type trajectories”, is a common feature of both maps.

Trajectory Control of Scale-Free Dynamical Networks with Exogenous Disturbances

In this paper, the trajectory control of multi-agent dynamical systems with exogenous disturbances is studied. Suppose multiple agents composing of a scale-free network topology, the performance of rejecting disturbances for the low degree node and high degree node is analyzed. Firstly, the consensus of multi-agent systems without disturbances is studied by designing a pinning control strategy on a part of agents, where this pinning control can bring multiple agents' states to an expected consensus track. Then, the influence of the disturbances is considered by developing disturbance observers, and disturbance observers based control (DOBC) are developed for disturbances generated by an exogenous system to estimate the disturbances. Asymptotical consensus of the multi-agent systems with disturbances under the composite controller can be achieved for scale-free network topology. Finally, by analyzing examples of multi-agent systems with scale-free network topology and exogenous disturbances, the verities of the results are proved. Under the DOBC with the designed parameters, the trajectory convergence of multi-agent systems is researched by pinning two class of the nodes. We have found that it has more stronger robustness to exogenous disturbances for the high degree node pinned than that of the low degree node pinned.

Sampled‐data state feedback stabilization of a class of nonlinear systems based on Euler approximation

AbstractIn this paper, sampled‐data control of locally Lipschitz nonlinear systems is studied. The controller is designed entirely in the discrete‐time domain. The design is based on the approximate discrete‐time model of the continuous‐time system obtained using the Euler method. The analyses of the closed loop system establish trajectory convergence, which implies asymptotic/exponential convergence for arbitrarily small sampling time. The major contribution of this paper is that asymptotic/exponential convergence of the closed loop system is proved under some additional conditions for a sufficiently small but nonzero sampling time. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

The Concavity Assumption on Felicities and Asymptotic Dynamics in the RSS Model

An analysis of the RSS model in mathematical economics involves the study of an infinite-horizon variational problem in discrete time. Under the assumption that the felicity function is upper semicontinuous and “supported” at the value of the maximally-sustainable level of a production good, we report a generalization of results on the equivalence, existence and asymptotic convergence of optimal trajectories in this model. We consider two parametric specifications, and under the second, identify a “symmetry” condition on the zeroes of a “discrepancy function” underlying the objective function that proves to be necessary and sufficient for the asymptotic convergence of good programs. With a concave objective function, as is standard in the antecedent literature, we show that the symmetry condition reduces to an equivalent “non-interiority” condition.

OVERTAKING OPTIMAL HARVESTING OF AGE-STRUCTURED PREDATOR-PREY SYSTEMS

This article is concerned with an optimal harvesting problem over an infinite horizon for age-dependent predator-prey system and the analysis of long-term behaviors of the optimal-controlled system. Instead of usual concepts, overtaking (or catching-up) optimality is adopted. First-order necessary conditions for optimal controller are carefully derived by means of Dubovitskii–Milyutin functional analytical extremum theory, which differs from the Lagrangian multipliers and the variation of calculus. Another focus of the article is the investigation of turnpike properties of population densities. Our results demonstrate the convergence of the optimal trajectories to an equilibrium in the sense of integral average, weak and point-wise, respectively. This research extend the results for linear equations of single species to situations of interacting species, and provide a unified framework for the treatment of multi-dimensional problems.

Convergence and divergence in plant community trajectories as a framework for monitoring wetland restoration progress

Summary 1. Environmental policies that use ecological restoration to offset the destruction of natural ecosystems assume that restorations readily compensate for the losses because they progress reliably and predictably over time, following deterministic successional trajectories. However, succession and restoration are spatially and historically contingent processes, often characterized by divergent trajectories that deviate from expectations. 2. We develop a framework for monitoring restorations that integrates two ideas from succession theory: convergence vs. divergence in species composition among successional sites, and progression towards vs. deviation from an expected community state. We apply this framework to short‐ and long‐term monitoring data from 11 restored wetlands in Illinois, USA, by comparing plant species composition among restored wetlands over time and between restored wetlands and two sets of reference wetlands (high integrity, ‘target’ wetlands and low integrity, degraded wetlands). 3. Over the first 4 years, restored wetlands that were initially similar in species composition diverged, progressing towards different high integrity target states. Planting a large number of native species in restorations increased their similarity to reference wetlands. 4. Over longer time scales (5–11 years post‐restoration), however, restored wetlands deviated from the ideal trajectory and converged upon the species composition of degraded wetlands, mainly because of non‐native species invasion. 5. Synthesis and applications. Framing restoration trajectories in terms of compositional convergence/divergence and progression towards/deviation from an acceptable range of reference sites is useful for monitoring restoration progress, identifying constraints to success and predicting restoration outcomes. Barriers to restoration, including non‐native species and a lack of native propagules, can limit long‐term progression towards target communities and constrain restoration to undesirable outcomes. Furthermore, convergence of restored wetlands on an undesirable community state limits the effectiveness of wetland mitigation policies.

Performance Analysis of Guidance Laws Based on Timescale Gap

An analytical treatment of performance analysis of guidance laws is possible only in simplistic scenarios. As the complexity of the guidance system increases, a search for analytical solutions becomes quite impractical. In this paper, a new performance measure, based upon the notion of a timescale gap that can be computed through numerical simulations, is developed for performance analysis of guidance laws. Finite time Lyapunov exponents are used to define the timescale gap. It is shown that the timescale gap can be used for quantification of the rate of convergence of trajectories to the collision course. Comparison between several guidance laws, based on the timescale gap, is presented. Realistic simulations to study the effect of aerodynamics and atmospheric variations on the timescale gap of these guidance laws are also presented.

Optimal controller synthesis for a class of LTI systems via switched feedback

We develop a switched feedback controller that optimizes the rate of convergence of the state trajectories to the origin for a class of second order LTI systems. Specifically, we derive an algorithm which optimizes the rate of convergence by employing a controller that switches between symmetric gains. As a byproduct of our investigation, we find that, in general, the controllers which optimize the rate of convergence switch between two linear subsystems, one of which is unstable. The algorithm we investigate will design optimal switching laws for the specific case of second order LTI plants of relative degree two.

Convergence of trajectories and optimal buffer sizing for AIMD congestion control

We study the interaction between the AIMD (Additive Increase Multiplicative Decrease) multi-socket congestion control and a bottleneck router with Drop Tail buffer. We consider the problem in the framework of deterministic hybrid models. First, we show that trajectories always converge to limiting cycles. We characterize the cycles. Necessary and sufficient conditions for the absence of multiple jumps in the same cycle are obtained. Then, we propose an analytical framework for the optimal choice of the router buffer size. We formulate this problem as a multi-criteria optimization problem, in which the Lagrange function corresponds to a linear combination of the average goodput and the average delay in the queue. Our analytical results are confirmed by simulations performed with MATLAB Simulink.

Fetal magnetocardiographic data processing

Event Abstract Back to Event Fetal magnetocardiographic data processing Silvia Comani1* 1 University of Chieti, Italy Fetal Magnetocardiography (fMCG) has been used to detect the fetal cardiac activity at different gestational ages and has progressively shown its potential for the non-invasive monitoring of the fetal heart function and well-being. Several signals are mixed in fMCG recordings, among which ambient noise and maternal cardiac activity primarily need to be suppressed because they may hinder the fetal cardiac signal. Among the several methods that have been used to disentangle the fetal cardiac signal, we employed independent component analysis (ICA) to obtain good separation of the fetal cardiac signals from fMCG data sets acquired at different gestational ages (15 to 38 weeks). Several factors, such as the identification of the fetal heartbeats, the signal-to-noise ratio of the fetal traces, the quality of the fetal signal waveform, the amount of residual maternal contamination in the fetal traces, can be evaluated to assess method performance. Once the fetal cardiac signal is separated, non linear parameters, such as entropy, can be evaluated to highlight the non linear behavior of the fetal heart along gestation. Moreover, the dynamical properties of the fetal cardiac system can be investigated by determining the properties of the attractors in the phase space, and by calculating the correlation dimensions and the Lyapunov exponents (LE) of the cardiovascular system along gestation. Those parameters permit to measure the rate of convergence or divergence of nearby trajectories of the dynamical system in the phase space, and can be considered dynamical indicators of chaos. Furthermore, the distribution of the LE can provide information on the possible deterministic nature of the system and on the number of degrees of freedom involved in the collected experimental data. Conference: Biomag 2010 - 17th International Conference on Biomagnetism , Dubrovnik, Croatia, 28 Mar - 1 Apr, 2010. Presentation Type: Oral Presentation Topic: Fetal and neonatal biomagnetism Citation: Comani S (2010). Fetal magnetocardiographic data processing. Front. Neurosci. Conference Abstract: Biomag 2010 - 17th International Conference on Biomagnetism . doi: 10.3389/conf.fnins.2010.06.00093 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 23 Mar 2010; Published Online: 23 Mar 2010. * Correspondence: Silvia Comani, University of Chieti, Chieti, Italy, comani@unich.it Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Silvia Comani Google Silvia Comani Google Scholar Silvia Comani PubMed Silvia Comani Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Life course determinants of racial and ethnic disparities in functional health trajectories.

Previous research has documented racial/ethnic disparities in functional health trajectories in old age, though little work has investigated the relative contribution of early and later life insults in their genesis. This paper uses two-part latent curve models to investigate the life course determinants of racial/ethnic disparities in functional health trajectories in the USA. We find that blacks and Hispanics have both a greater probability of having any limitation at baseline and more limitations on average among those who have any. Over time, there is convergence in trajectories between Hispanics and non-Hispanic whites, though the black-white gap remains constant. In addition, we find that disparities result from differential exposure to poor childhood health, early life socioeconomic deprivation, as well as adult health and socioeconomic attainment. However, the impact of childhood insults is largely mediated by more contemporaneous factors. We also find little evidence that the impact of life course factors varies across groups.

Convergence of trajectories and optimal buffer sizing for MIMD congestion control

We study the interaction between the MIMD (Multiplicative Increase Multiplicative Decrease) congestion control and a bottleneck router with Drop Tail buffer. We consider the problem in the framework of deterministic hybrid models. We study conditions under which the system trajectories converge to limiting cycles with a single jump. Following that, we consider the problem of the optimal buffer sizing in the framework of multi-criteria optimization in which the Lagrange function corresponds to a linear combination of the average throughput and the average delay in the queue. As case studies, we consider the Slow Start phase of TCP New Reno and Scalable TCP for high speed networks.

Are compensatory growth and catch-up growth two sides of the same coin?

Compensatory growth refers to an animal’s ability to grow extremely rapidly after it has experienced a period of reduced growth. It is also widely held that the growth trajectories of animals showing compensatory growth converge towards those followed by conspecifics that have experienced favorable growth conditions throughout their lives. In other words, it is often assumed that animals undergoing compensatory growth also show some recovery, and thereby exhibit catch-up growth. This belief has resulted in the terms compensatory growth, recovery growth, and catch-up growth being used as synonyms, and has also created some problems with regard to data analysis and interpretation. Following a discussion of methods of analysis and their limitations, a series of growth simulations is presented to illustrate why the terms should not be used as synonyms. The simulations, based upon the assumption that compensatory growth results in a restoration of body composition (using condition index as a surrogate), show that compensatory growth is not always accompanied by a convergence of growth trajectories. Compensatory growth can occur in the absence of catch-up growth, and the simultaneous observation of compensatory growth and a recovery of body mass is a special combination of events. Further, it is possible for growth trajectories to converge even when animals that have experienced a period of reduced growth do not display compensatory growth. Definitions are proposed that distinguish between the terms compensatory growth, recovery growth, and catch-up growth, and guidelines are given relating to the analysis of the results of fish compensatory growth studies.

ROBUST CONTROL OF SPATIOTEMPORAL CHAOS IN COUPLED MAP LATTICES

In this paper, a new method for controlling spatiotemporal chaos in discrete-time spatially extended systems modeled by coupled map lattices is proposed. This method is based on quasi-sliding mode using a Lyapunov function. This method enables the system to drive the chaotic motion toward any desired trajectory via a sliding surface in the error space. The controller also guarantees finite time convergence of the state trajectory. The main advantage of this method is its robustness with respect to additive uncertainties and its applicability for all types of coupled map lattices. A diffusively coupled map lattice is used as an example to demonstrate the method. Simulation results reveal the robustness and the effectiveness of the method in controlling spatiotemporal chaos in coupled map lattices.

A Neuro-Sliding-Mode Control With Adaptive Modeling of Uncertainty for Control of Movement in Paralyzed Limbs Using Functional Electrical Stimulation

During the past several years, several strategies have been proposed for control of joint movement in paraplegic subjects using functional electrical stimulation (FES), but developing a control strategy that provides satisfactory tracking performance, to be robust against time-varying properties of muscle-joint dynamics, day-to-day variations, subject-to-subject variations, muscle fatigue, and external disturbances, and to be easy to apply without any re-identification of plant dynamics during different experiment sessions is still an open problem. In this paper, we propose a novel control methodology that is based on synergistic combination of neural networks with sliding-mode control (SMC) for controlling FES. The main advantage of SMC derives from the property of robustness to system uncertainties and external disturbances. However, the main drawback of the standard sliding modes is mostly related to the so-called chattering caused by the high-frequency control switching. To eliminate the chattering, we couple two neural networks with online learning without any offline training into the SMC. A recurrent neural network is used to model the uncertainties and provide an auxiliary equivalent control to keep the uncertainties to low values, and consequently, to use an SMC with lower switching gain. The second neural network consists of a single neuron and is used as an auxiliary controller. The control law will be switched from the SMC to neural control, when the state trajectory of system enters in some boundary layer around the sliding surface. Extensive simulations and experiments on healthy and paraplegic subjects are provided to demonstrate the robustness, stability, and tracking accuracy of the proposed neuroadaptive SMC. The results show that the neuro-SMC provides accurate tracking control with fast convergence for different reference trajectories and could generate control signals to compensate the muscle fatigue and reject the external disturbance.

Some Characterizations of Global Exponential Stability of a Generic Class of Continuous-Time Recurrent Neural Networks

This paper reveals two important characterizations of global exponential stability (GES) of a generic class of continuous-time recurrent neural networks. First, we show that GES of the neural networks can be fully characterized by global asymptotic stability (GAS) of the networks plus the condition that the maximum abscissa of spectral set of Jacobian matrix of the neural networks at the unique equilibrium point is less than zero. This result provides a very useful and direct way to distinguish GES from GAS for the neural networks. Second, we show that when the neural networks have small state feedback coefficients, the supremum of exponential convergence rates (ECRs) of trajectories of the neural networks is exactly equal to the absolute value of the maximum abscissa of spectral set of Jacobian matrix of the neural networks at the unique equilibrium point. Here, the supremum of ECRs indicates the potentially fastest speed of trajectory convergence. The obtained results are helpful in understanding the essence of GES and clarifying the difference between GES and GAS of the continuous-time recurrent neural networks.

The Expert Control Designing of Tanker Ship Maneuvering by Optimal Control as a Reference Model

Fuzzy logic control (FLC) system is a control system which is working based on error input data, rate of error, and accelaret of error of controlling variable. Using some rules of FAM (Fuzzy Associate Memory) which is constructed for resulting a decision can be used to actuator of controller. This paper is des-cribing about designing fuzzy logic as a control system for ship maneuvering, which is input for FLC are yaw error, yaw rate, and tracking error while the output of fuzzy logic control is command rudder signal. FLC con-sists of two units of controller; it is first controller unit work for autopilot and second controller unit for offset track. Interference function for FLC is Sugeno – Takagi which represent mathematic equation from input vari-able of FLC. Gain control of FLC based on least square estimation of error yaw, yaw rate, and output control signal relationship from LQR/LTR as a model reference control. Dynamic model of ship maneuvering has been derived on 3 dof with Clarke hydrodynamic coefficient. The capability of logic fuzzy control has been shown on simulation, for tanker ship model without interference or within interference. Robust of fuzzy logic control has been got from trajectory convergence error of yaw and yaw rate error when on turning simulation or off turning simulation toward the sector (0, 0).

Exact Observer for Switching Linear Systems via Super-Twisting Algorithm

Abstract This paper discusses the problem of observability synthesis of switching systems. Based only on the continuous output information, an observer is proposed ensuring the reconstruction of the entire state (continuous and discrete) in finite time. For the observer design a exact sliding mode differentiator is used, which allows the finite time convergence of the observer trajectories to the original trajectories. The observer design includes both cases zero control input and nonzero control input. Simulations illustrate the effectiveness of the proposed observation scheme.