Advances in computational Lyapunov analysis using sum-of-squares programming
Advances in computational Lyapunov analysis using sum-of-squares programming
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DOI：
10.3934/dcdsb.2015.20.2361
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发表时间：
2015-08
影响因子：
1.2
通讯作者：
James Anderson;A. Papachristodoulou
中科院分区：
文献类型：
--
作者：
James Anderson;A. Papachristodoulou
非线性动力系统平衡点的稳定性通常是用李雅普诺夫理论来确定的。这就需要构造一个类能量函数，称为Lyapunov函数，它满足一定的正性条件。与线性动力系统不同，对于一般的非线性系统，没有构造Lyapunov函数的算法方法。然而，如果感兴趣的系统按照多项式向量场演化，并且Lyapunov函数被约束为平方和多项式，则稳定性验证可以转化为半定(凸)优化程序。在这篇文章中，我们描述了平方和编程的最新进展，它促进了高级稳定性分析和控制设计。
The stability of an equilibrium point of a nonlinear dynamical system is typically determined using Lyapunov theory. This requires the construction of an energy-like function, termed a Lyapunov function, which satisfies certain positivity conditions. Unlike linear dynamical systems, there is no algorithmic method for constructing Lyapunov functions for general nonlinear systems. However, if the systems of interest evolve according to polynomial vector fields and the Lyapunov functions are constrained to be sum-of-squares polynomials then stability verification can be cast as a semidefinite (convex) optimization programme. In this paper we describe recent advances in sum-of-squares programming that facilitate advanced stability analysis and control design.