Bifurcation control of nonlinear systems with time-periodic coefficients

Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251) Pub Date : 2003-12-01 DOI:10.1109/ACC.1999.782323

A. Dávid, S. Sinha

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引用次数: 16

Abstract

A technique for the bifurcation control of nonlinear systems with periodic coefficients is presented. In such systems, bifurcations occur when one of the Floquet multipliers becomes +1 , -1, or a pair of complex multipliers reaches magnitude 1. The stability of the bifurcated periodic or quasi-periodic orbit is guaranteed by employing a nonlinear state-feedback control. First the Lyapunov-Floquet transformation is applied such that the linear part of system equations becomes time-invariant. Then through an application of the time-periodic center manifold reduction and time-dependent normal form theory one can obtain a completely time-invariant form of the nonlinear equation for codimension one bifurcations. The time-invariant normal form is suitable for the application of control strategies developed for autonomous systems. Then by transforming the results back to the original variables, one obtains the gains for the time-varying controller. The control strategy is illustrated through an example of a parametrically excited simple pendulum undergoing a symmetry breaking bifurcation.

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具有时间周期系数非线性系统的分岔控制

提出了一种具有周期系数的非线性系统的分岔控制方法。在这样的系统中，当一个Floquet乘法器变成+1，-1，或者一对复乘法器达到1的量级时，就会发生分岔。采用非线性状态反馈控制保证了分岔周期或准周期轨道的稳定性。首先应用Lyapunov-Floquet变换使系统方程的线性部分变成定常的。然后，通过应用时间周期中心流形约简和时间相关范式理论，可以得到余维1分岔非线性方程的完全时不变形式。定常范式适合于自主系统控制策略的应用。然后将结果转换回原始变量，得到时变控制器的增益。通过一个参数激振单摆发生对称破缺分岔的例子说明了该控制策略。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251)

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