On the Stability of Swarm Consensus Under Noisy Control

Representation of a swarm of independent robotic agents under graph-theoretic constructs allows for more formal analysis of convergence properties. We consider the local and global convergence behavior of an N-member swarm of agents in a modified consensus problem wherein the connectivity of agents is governed by probabilistic functions. The addition of a random walk control ensures ε-stability of the swarm consensus. Simulation results are given to show the rate of convergence to consensus and planned experiments are described.

The Levenberg-Marquardt-Type Methods for a Kind of Vertical Complementarity Problem

Two kinds of the Levenberg-Marquardt-type methods for the solution of vertical complementarity problem are introduced. The methods are based on a nonsmooth equation reformulation of the vertical complementarity problem for its solution. Local and global convergence results and some remarks about the two kinds of the Levenberg-Marquardt-type methods are also given. Finally, numerical experiments are reported.

A decomposition method for a semilinear boundary value problem with a quadratic nonlinearity

The author adapts the decomposition method of Adomian to find a series solution of a one-dimensional boundary value problem for a semilinear heat equation with a quadratic nonlinearity. Local and global convergence results are obtained.