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首页> 美国政府科技报告 >Lyapunov-Based Feedback Control of Border Collision Bifurcations in Piecewise Smooth Systems.
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Lyapunov-Based Feedback Control of Border Collision Bifurcations in Piecewise Smooth Systems.

机译：基于Lyapunov的分段光滑系统中边界碰撞分岔的反馈控制。

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摘要

Feedback control of piecewise smooth discrete time systems that undergo border collision bifurcations is considered. These bifurcations occur when a fixed point or a periodic orbit of a piecewise smooth system crosses or collides with the border between two regions of smooth operation as a system parameter is quasi- statically varied. The goal of the control effort in this work is to modify the bifurcation so that the bifurcated steady state is locally attracting and locally unique. To achieve this, Lyapunov-based techniques are used. A sufficient condition for nonbifurcation with persistent stability in piecewise smooth maps of dimension n that depend on a parameter is derived. The derived condition is in terms of linear matrix inequalities. This condition is then used as a basis for the design of feedback controls to eliminate border collision bifurcations in piecewise smooth maps and to produce desirable behavior.

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