We propose a method to outer bound forward reachable sets on finite horizons for uncertain nonlinear systems with polynomial dynamics. This method makes use of time-dependent polynomial storage functions that satisfy appropriate dissipation inequalities that account for time-varying uncertain parameters, L2 disturbances, and perturbations characterized by integral quadratic constraints (IQCs) with both hard and soft factorizations. In fact, to our knowledge, this is the first result introducing IQCs to reachability analysis, thus allowing for various types of uncertainty, including unmodeled dynamics. The generalized S-procedure and Sum-of-Squares techniques are used to derive algorithms with the goal of finding the tightest outer bound with a desired shape. Both pedagogical and practically motivated examples are presented, including a 7-state F-18 aircraft model.

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不确定非线性系统使用耗散不等式的可达性分析

对于具有多项式动力学的不确定非线性系统，我们提出了一种在有限范围内外界前向可达集的方法。该方法利用瞬态多项式存储函数，该函数满足适当的耗散不等式，这些不等式考虑了随时间变化的不确定参数、L2 干扰和以具有硬和软分解的积分二次约束 (IQC) 为特征的扰动。事实上，据我们所知，这是第一个将 IQC 引入可达性分析的结果，从而允许各种类型的不确定性，包括未建模的动态。广义 S 过程和平方和技术用于推导算法，目标是找到具有所需形状的最紧密外界。提供了教学和实践动机的例子，