论文标题
通过几乎Lyapunov函数和半决赛编程融合吸引子的近似值
Converging approximations of attractors via almost Lyapunov functions and semidefinite programming
论文作者
论文摘要
在本文中，我们将两种现有方法结合在一起，用于近似吸引子。其中一个通过与无限尺寸线性编程问题的解决方案相关的一台分布组合的吸引子近似。缺点是，这些集合不一定是阳性不变的。相反，第二种方法为吸引子提供了超级不变的超集。另一方面，他们的方法具有不利的不利条件，即不使用启发式方法，基本优化问题在计算上是不可计算的 - 并以损失保证的融合为代价。在本文中，我们结合了两种方法，结合了它们的技术，并通过基于凸优化的方形技术来使吸引子的收敛外近似值融合。该方法易于使用，并通过数值示例说明。
In this paper we combine two existing approaches for approximating attractors. One of them approximates the attractors arbitrarily well by sublevel sets related to solutions of infinite dimensional linear programming problems. A downside there is that these sets are not necessarily positively invariant. On the contrary, the second method provides supersets of the attractor which are positively invariant. Their method on the other hand has the disadvantage that the underlying optimization problem is not computationally tractable without the use of heuristics - and incorporating them comes at the price of losing guaranteed convergence. In this paper we marry both approaches by combining their techniques and we get converging outer approximations of the attractor consisting of positively invariant sets based on convex optimization via sum-of-squares techniques. The method is easy to use and illustrated by numerical examples.
