论文标题
非线性系统的L-1和L-侵入增益的多面体估计
Polyhedral Estimation of L-1 and L-infinity Incremental Gains of Nonlinear Systems
论文作者
论文摘要
我们提供了新颖的耗散性条件，以界定系统的增量L-1增益。此外，我们将现有的结果调整为L-侵增益的现有结果，并通过系统伴随将增量L-1和L-赋值收益界限相关联。我们基于基于优化的方法来构建多面体Lyapunov函数，我们利用这些条件来获得基于线性编程的算法，该算法可以根据给定候选候选的多面体存储函数或多面体组合提供越来越明显的增长界限。该算法还扩展了，以设计线性反馈控制器以进行性能，这是由增量增益的边界衡量的。我们将算法应用于几个数值示例，以说明这种方法的功率以及一些局限性。
We provide novel dissipativity conditions for bounding the incremental L-1 gain of systems. Moreover, we adapt existing results on the L-infinity gain to the incremental setting and relate the incremental L-1 and L-infinity gain bounds through system adjoints. Building on work on optimization based approaches to constructing polyhedral Lyapunov functions, we make use of these conditions to obtain a Linear Programming based algorithm that can provide increasingly sharp bounds on the gains as a function of a given candidate polyhedral storage function or polyhedral set. The algorithm is also extended to allow for the design of linear feedback controllers for performance, as measured by the bounds on the incremental gains. We apply the algorithm to a couple of numerical examples to illustrate the power, as well as some limitations, of this approach.
