A Lyapunov Treatment of Swarm Coordination Under Conflict

2009 ◽  
Author(s):  
Paul McCullough ◽  
Mark Bacon ◽  
Nejat Olgac ◽  
Daniel A. Sierra
Keyword(s):  
Stability Analysis ◽  
Control Strategy ◽  
Interaction Force ◽  
Equal Mass ◽  
Local Vectors ◽  
Two Phases ◽  
Integrator Model ◽  
Force Profiles ◽  
Double Integrator ◽  
Approach Phase

This document considers hostile conflicts between two swarms, called pursuers and evaders, based on a double integrator model. In order to convert the marginally stable dynamics into stable-capture behavior, we introduce a control strategy based on the relative positions and velocities of opposing swarm members. To evaluate its effectiveness, a Lyapunov-based stability analysis is performed. For simplicity, this document considers swarms with equal membership strengths and equal mass only. The modeling is based on a set of suggested interaction force profiles, which are functions of local vectors. The group pursuit is conceived in two phases: the approach phase during which the two swarms act like two individuals; and the assigned pursuit phase where each pursuer is assigned to an evader.

Swarm Coordination Under Conflict and Use of Enhanced Lyapunov Based Controller

2009 ◽  
Author(s):  
Daniel A. Sierra ◽  
Paul McCullough ◽  
Nejat Olgac ◽  
Eldridge Adams
Keyword(s):  
Stability Analysis ◽  
Distributed Control ◽  
Complex Nature ◽  
Control Logic ◽  
Group Pursuit ◽  
Dissipative Control ◽  
Multi Agent ◽  
Two Phases ◽  
The Stability ◽  
Approach Phase

We consider hostile conflicts between two multi-agent swarms. First, we investigate the complex nature of a single pursuer attempting to intercept a single evader (1P-1E), and establish some rudimentary rules of engagement. We elaborate on the stability repercussions of these rules. Second, we extend the modelling and stability analysis between multi-agent swarms of pursuers and evaders. The present document considers only swarms with equal membership strengths for simplicity. This effort is based on a set of suggested momenta deployed on individual agents. Due to the strong nonlinearities, Lyapunov-based stability analysis is used. The control of a group pursuit is divided into two phases: the approach phase during which the two swarms act like individuals in the 1P-1E interaction; and the assigned pursuit phase where each pursuer is assigned to an evader. A dissipative control momentum was suggested in an earlier publication, which caused undesirable control chatter. This study introduces a distributed control logic which ameliorates the chatter problems considerably.

scholarly journals Untangling superposed double layer and structural forces across confined nanoparticle suspensions

2021 ◽  
Author(s):  
Michael Ludwig ◽  
Regine von Klitzing
Keyword(s):  
Double Layer ◽  
Interaction Force ◽  
Charged Surfaces ◽  
Structural Forces ◽  
Nanoparticle Suspensions ◽  
Confined Suspensions ◽  
Force Profiles

Complete interaction force profiles of charged surfaces across confined suspensions were successfully described using a superposition of double layer and structural forces.

Control Strategy and Stability Analysis of Impedance Isolated Medium Voltage UPS in Off-grid Operation

2021 ◽  
Author(s):  
Ganghua Zhang ◽  
Yaoyao Xiao ◽  
Mingyu Han ◽  
Wenping Zuo ◽  
Meng Zhou ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Control Strategy ◽  
Medium Voltage ◽  
Grid Operation

Maximizing Walking Step Length for a Near Omni-Directional Hexapod Robot

2004 ◽  
Author(s):  
James P. Schmiedeler ◽  
Nathan J. Bradley ◽  
Brett Kennedy
Keyword(s):  
Stability Analysis ◽  
Step Length ◽  
Static Stability ◽  
Optimization Approach ◽  
Computationally Efficient ◽  
Constant Height ◽  
Planning Algorithm ◽  
Two Phases ◽  
The Stability ◽  
Path Planning Algorithm

A foot path planning algorithm is presented for a robot with six limbs symmetrically located on the faces of its hexagonal body, enabling it to walk at a constant height with an alternating tripod gait. The symmetry results in near omni-directional locomotion capability, so the algorithm is formulated for walking in any direction and at any height. The approach is to determine the maximum length foot path through each limb’s workspace and then modify those foot paths based upon static stability analysis. The stability analysis is conducted in two phases to ensure stability without excessively reducing step length. Compared to an optimization approach, the algorithm yields foot paths within 9.1% of the maximal foot paths for all directions and heights. Unlike the optimization approach, the developed algorithm is computationally efficient enough to be implemented in realtime.

scholarly journals Neural Network Inverse Model Control Strategy: Discrete-Time Stability Analysis for Relative Order Two Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
M. A. Hussain ◽  
Jarinah Mohd Ali ◽  
M. J. H. Khan
Keyword(s):  
Neural Network ◽  
Stability Analysis ◽  
Discrete Time ◽  
Control Strategy ◽  
Direct Method ◽  
Time Derivative ◽  
Inverse Model ◽  
Relative Order ◽  
Time Stability ◽  
Model Control

This paper discusses the discrete-time stability analysis of a neural network inverse model control strategy for a relative order two nonlinear system. The analysis is done by representing the closed loop system in state space format and then analyzing the time derivative of the state trajectory using Lyapunov’s direct method. The analysis shows that the tracking output error of the states is confined to a ball in the neighborhood of the equilibrium point where the size of the ball is partly dependent on the accuracy of the neural network model acting as the controller. Simulation studies on the two-tank-in-series system were done to complement the stability analysis and to demonstrate some salient results of the study.

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