论文标题
使用移位的形状函数和R-Composition估算非对称和无界吸引力区域
Estimation of non-symmetric and unbounded region of attraction using shifted shape function and R-composition
论文作者
论文摘要
提出了一种使用正方形编程之和的一般数值方法，以解决估计非线性多项式系统渐近稳定平衡点的吸引力区域（ROA）的问题。该方法基于Lyapunov理论，并定义了形状函数以扩大局部Lyapunov函数的可证明子集。与以平衡点为中心的形状函数的现有方法相反，所提出的方法利用了移动的形状函数（SSF），其中心迭代向新获得的不变子集的边界移动，以改善ROA估计。生成了一组具有相应SSF的转移中心，以产生精确的ROA的经过验证的子集，然后采用组成方法，即R-Composition，仅通过仅单个但较丰富的水平集来以紧凑的形式表达这些独立的集合。提出的方法表示为RCOMSSF，为一般ROA估计问题带来了显着改善，尤其是对于非对称或无限的ROA，同时将计算负担保持在合理的水平。文献的几个基准示例证明了它的有效性和优势。
A general numerical method using sum of squares programming is proposed to address the problem of estimating the region of attraction (ROA) of an asymptotically stable equilibrium point of a nonlinear polynomial system. The method is based on Lyapunov theory, and a shape function is defined to enlarge the provable subset of a local Lyapunov function. In contrast with existing methods with a shape function centered at the equilibrium point, the proposed method utilizes a shifted shape function (SSF) with its center shifted iteratively towards the boundary of the newly obtained invariant subset to improve ROA estimation. A set of shifting centers with corresponding SSFs is generated to produce proven subsets of the exact ROA and then a composition method, namely R-composition, is employed to express these independent sets in a compact form by just a single but richer-shaped level set. The proposed method denoted as RcomSSF brings a significant improvement for general ROA estimation problems, especially for non-symmetric or unbounded ROA, while keeping the computational burden at a reasonable level. Its effectiveness and advantages are demonstrated by several benchmark examples from literature.
