Porubov Alexey, Andrievsky Boris
Institute of Problems in Mechanical Engineering, Bolshoy 61, V.O., Saint-Petersburg 199178, Russia
St. Petersburg State University, 7-9, Universitetskaya nab., V.O., Saint-Petersburg 199034, Russia.
Philos Trans A Math Phys Eng Sci. 2017 Mar 6;375(2088). doi: 10.1098/rsta.2016.0212.
A general form of a distributed feedback control algorithm based on the speed-gradient method is developed. The goal of the control is to achieve nonlinear wave localization. It is shown by example of the sine-Gordon equation that the generation and further stable propagation of a localized wave solution of a single nonlinear partial differential equation may be obtained independently of the initial conditions. The developed algorithm is extended to coupled nonlinear partial differential equations to obtain consistent localized wave solutions at rather arbitrary initial conditions.This article is part of the themed issue 'Horizons of cybernetical physics'.
基于速度梯度法的分布式反馈控制算法的一般形式被开发出来。控制的目标是实现非线性波的局域化。通过正弦 - 戈登方程的例子表明，单个非线性偏微分方程的局域波解的产生和进一步稳定传播可以独立于初始条件而获得。所开发的算法被扩展到耦合非线性偏微分方程，以在相当任意的初始条件下获得一致的局域波解。本文是主题为“控制论物理学的前沿”特刊的一部分。
