具有局部Lipschitz非线性的离散时间系统轨迹与受控不变漏斗的联合综合
Joint Synthesis of Trajectory and Controlled Invariant Funnel for Discrete-time Systems with Locally Lipschitz Nonlinearities
AI总结：
本文提出一种轨迹与受控不变漏斗联合综合算法，针对局部Lipschitz非线性系统，通过递归交替优化标称轨迹与漏斗，在不放松约束下实现成本最优并保证有界扰动下的不变性，并在机器人应用中验证。
摘要：
本文针对受有界扰动影响的局部Lipschitz非线性系统，提出了一种轨迹与受控不变漏斗（CIF）的联合综合算法。CIF综合是指计算受控不变集及相应反馈增益的过程。与现有CIF综合方法使用预定义标称轨迹来计算CIF不同，我们的工作旨在联合优化标称轨迹与CIF，从而在不放松约束的情况下满足可行性条件，并获得更具成本最优性的标称轨迹。所提出的方法采用递归方案，主要交替进行轨迹更新和漏斗更新。轨迹更新步骤在保证CIF可行性的前提下优化标称轨迹。随后，漏斗更新步骤在标称轨迹周围计算漏斗，使CIF保证不变性性质。结果表明，借助优化后的轨迹与CIF，在存在有界扰动的情况下，由控制律以计算得到的反馈增益从初始集传播出的任意轨迹，都能保持在标称轨迹周围的可行区域内。我们通过机器人领域的两个应用验证了所提出的方法。
英文摘要：
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.
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