论文标题
与本地Lipschitz非线性的离散时间系统的轨迹和受控漏斗的联合合成
Joint Synthesis of Trajectory and Controlled Invariant Funnel for Discrete-time Systems with Locally Lipschitz Nonlinearities
论文作者
论文摘要
本文介绍了一种局部Lipschitz非线性系统的轨迹和不变漏斗（CIF）的联合合成算法。 CIF合成是指计算控制不变性集和相应反馈收益的过程。与现有的CIF合成方法相反，该方法使用预定义的名义轨迹计算CIF的工作旨在优化名义轨迹和CIF，以共同满足可行性条件，而无需放松约束并获得更高成本的名称轨迹。拟议的工作具有递归方案，主要优化轨迹更新和漏斗更新。轨迹更新步骤在确保CIF的可行性的同时优化了名义轨迹。然后，漏斗更新步骤计算名义轨迹周围的漏斗，以便CIF保证不变性属性。结果，使用了优化的轨迹和CIF，从控制定律的初始集合中传播的任何产生的轨迹都以计算的反馈增益在界面轨迹周围可行的区域内，在有界扰动的存在下。我们通过机器人技术的两种应用来验证提出的方法。
This paper presents a joint synthesis algorithm of trajectory and controlled invariant funnel (CIF) for locally Lipschitz nonlinear systems subject to bounded disturbances. The CIF synthesis refers to a procedure of computing controlled invariance sets and corresponding feedback gains. In contrast to existing CIF synthesis methods that compute the CIF with a pre-defined nominal trajectory, our work aims to optimize the nominal trajectory and the CIF jointly to satisfy feasibility conditions without the relaxation of constraints and obtain a more cost-optimal nominal trajectory. The proposed work has a recursive scheme that mainly optimize trajectory update and funnel update. The trajectory update step optimizes the nominal trajectory while ensuring the feasibility of the CIF. Then, the funnel update step computes the funnel around the nominal trajectory so that the CIF guarantees an invariance property. As a result, with the optimized trajectory and CIF, any resulting trajectory propagated from an initial set by the control law with the computed feedback gain remains within the feasible region around the nominal trajectory under the presence of bounded disturbances. We validate the proposed method via two applications from robotics.
