Stability Analysis of Multi-Agent Tracking Systems with Quasi-Cyclic Switching Topologies

In this paper, the stability problem of a class of multi-agent tracking systems with quasi-cyclic switching topologies is investigated. The existing results of systems with switching topologies are usually achieved based on the assumption that the piecewise constant communication topologies are connected and the switchings are cyclic. The communication topologies are possible to be unconnected and it is difficult to guarantee the topologies switch circularly. The piecewise unconnected topology makes the interactive multi-agent tracking system to be an unstable subsystem over this time interval. In order to relax the assumption constraint, a quasi-cyclic method is proposed, which allows the topologies of multi-agent systems to switch in a less conservative way. Moreover, the stability of the tracking system with the existence of unstable subsystems is analyzed based on switched control theory. It is obtained that the convergence rate is affected by the maximum dwell time of unstable subsystems. Finally, a numerical example is provided to demonstrate the effectiveness of the theoretical results.

The dynamic behaviors of a supply chain with stock-dependent demand considering competition and deteriorating items

Purpose The purpose of this paper is to explore the dynamics and stability of switched supply system considering the influence of the retailer competition and deteriorating items. Design/methodology/approach A discrete dynamic switched model is developed to analyze the evolution process of the switched supply chain. The existence and the local stability of the switched supply chain are analyzed using an analytical method and a parameter plot basin. Findings The author finds the switched supply chain will exhibit stable, periodic, and divergent behaviors with different parameters due to the system’s switching mechanism and the switched supply chain presents complex dynamics when the stable and unstable subsystem coexist. Originality/value The originality and value of the research rests on this paper considering the influence of the retailers’ competition and deteriorating items on the supply chain dynamics under stock-dependent demand. The obtained results provide the decision maker with some guidelines on how to make stable designs for the switched supply chain design according to the parameter values.

LIFETIME OF 26S AND A LIMIT FOR ITS 2p DECAY ENERGY

The unknown isotope 26 S , expected to decay by two-proton (2p) emission, was studied theoretically and searched experimentally. The structure of this nucleus was examined within the relativistic mean field (RMF) approach. A method for taking into account the many-body structure in the three-body decay calculations was developed. The results of the RMF calculations were used as an input for the three-cluster decay model optimized for the study of a possible 2p decay branch of this nucleus. The experimental search for 26 S was performed by fragmentation of a 50.3 A MeV 32 S beam. No events of a particle-stable 26 S or 25 P (a presumably proton-unstable subsystem of 26 S ) were observed. Based on the obtained production systematics, an upper half-life limit of T1/2<79 ns was established from the time-of-flight through the fragment separator. Together with the theoretical lifetime estimates for two-proton decay, this gives a decay energy limit of Q2p>640 keV for 26 S . Analogous limits for 25 P are found as T1/2 < 38 ns and Qp>110 keV . In the case that the one-proton emission is the main branch of the 26 S decay, a limit Q2p>230 keV would follow for this nucleus. According to these limits, it is likely that 26 S resides in the picosecond lifetime range.

CRITERION OF CHAOS FOR SWITCHED LINEAR SYSTEMS WITH CONTROLLERS

In this paper, a sufficient criterion for time-invariant switched linear systems with controllers to be chaotic in the sense of Li–Yorke and Devaney is presented. The switched linear systems consist of an unstable subsystem with expanding flows and a controllable subsystem. It is exposed that the controllability of dynamic systems, instead of asymptotic stability, plays an important role in generating chaos. Finally, we give a numerical simulation for an example with some variable parameters to illustrate the validity of the result.

Real Time Estimation of Elastic Deformation for End-Point Tracking Control of Flexible Two-Link Manipulators

In this paper, an elastic-deformation estimator is proposed for real time end-point tracking control of a flexible two-link manipulator. Due to the noncolocated characteristics of the system, the inverse model (from end-point motion to control torques) is divided into two subsystems, namely, the stable subsystem and the unstable one, corresponding to the causal part and noncausal part of the system’s elastic motion, respectively. A digital filter is formulated to replace the unstable subsystem so as to estimate the noncausal part of the elastic motion associated with a specified end-point motion. For the design of the filter, the frequency response ratio between the filter and the unstable subsystem is used as the criterion, the objective of which is to have the frequency response ratio have zero phase shift as well as unity gain within a specified frequency range. It is shown that due to the noncausal characteristics of the unstable subsystem, preview information of the input trajectory is required for implementing the proposed filter, and the estimation accuracy increases as increasing the preview steps. Based on the stable subsystem and the proposed digital filter, a time-varying estimator is designed to estimate the elastic motion of the system when the end-point motion is specified. A command feedforward controller is then used to calculate the required control torques based on the estimated elastic deformation and the desired end-point motion. The computed torques along with a feedback controller then form a control scheme making the flexible two-link manipulator become capable of precision end-point tracking. Simulation results are presented to show the performance of the proposed end-point tracking scheme as well as the elastic-deformation estimator.