非线性系统的数据驱动迭代学习控制及其在康复机器人中的应用

This project investigates data driven iterative learning control for nonlinear systems and its application to rehabilitation robots. First, data driven iterative learning control is developed for nonlinear systems only with locally Lipschitz nonlinearities. The corresponding data driven iterative learning control algorithms are designed and new analysis methods and synthesis theories for the learning convergence are established in order to overcome the heavy dependence on the global Lipschitz condition of the key learning convergence theory that is built based on the contraction mapping principle. Then, optimization-based data driven iterative learning control algorithms are proposed such that the specified optimal learning performances can be achieved and the monotonic convergence of iterative learning processes can be guaranteed during the process of overcoming the effects of locally Lipschitz nonlinear dynamics. Next, robustness is exploited for data driven iterative learning control, which makes the learning systems with locally Lipschitz nonlinearities able to overcome nonrepetitive uncertainties in control environments, control tasks and plant models. Furthermore, experiments on the rehabilitation robot platforms are performed to validate the effectiveness of all the proposed data driven iterative learning control algorithms. This project can establish new fields and methods for the theoretical developments of both data driven control and iterative learning control and can also develop new ideas for the crossover studies on the two control problems, which provides effective data driven iterative learning control techniques for rehabilitation robots. Therefore, the studies of this project have both significant theoretical exploration value and broad application perspectives.

本项目研究非线性系统的数据驱动迭代学习控制及其在康复机器人中的应用。首先，开发局部Lipschitz非线性系统的数据驱动迭代学习控制，设计算法并建立新的学习收敛性分析方法及综合理论克服基于压缩映像的核心学习收敛理论关于全局Lipschitz条件的依赖。其次，提出基于目标优化的数据驱动迭代学习控制算法，实现指定的优化学习性能，在克服局部Lipschitz非线性动态影响的同时保证迭代学习过程的单调收敛性。然后，开展数据驱动迭代学习控制的鲁棒性研究，使局部Lipschitz非线性学习系统能克服控制环境、控制任务和对象模型等的非重复不确定性。此外，以康复机器人为平台，验证所提数据驱动迭代学习控制算法的有效性。本项目能建立数据驱动控制和迭代学习控制发展的新领域和新方法，开发两类控制问题交叉研究的新思路，为康复机器人提供有效的数据驱动迭代学习控制技术，因此其研究具有重要的理论探索价值和广阔的应用前景。

迭代学习控制作为一类智能控制方法，能够有效改善被控对象的瞬态性能和跟踪精度。然而，传统数据驱动迭代学习控制在局部Lipschitz非线性系统中难以应用，本项目针对此问题开展研究。具体地，建立了全新的迭代学习控制收敛性分析框架，使得迭代学习控制适用于仅满足局部Lipschitz条件的非线性被控系统；给出了关于优化目标泛函和优化方法选取的方法性指导规则，使得仅具有满足局部Lipschitz条件的非线性动态的被控系统在迭代学习控制过程中具有单调收敛性；基于已经建立的迭代学习控制收敛性双层动态分析方法，给出了关于鲁棒控制器设计的方法性指导，使得具有仅满足局部Lipschitz条件的非线性动态的被控系统能够克服迭代变化的非重复不确定性；并开发了手部康复机器人仿真实验平台对上述非线性数据驱动迭代学习控制方法进行验证。.本项目共发表论文34篇，其中包括SCI检索期刊论文24篇；出版专著1部；获得中国仪器仪表学会科学技术发明奖二等奖1项；获得国际会议最佳论文奖1项；申请/授权发明专利6项。通过本项目的研究，有效解决了数据驱动迭代学习控制无法应用于局部Lipschitz非线性系统的问题，从鲁棒和优化两个角度给出全新的局部Lipschitz非线性系统数据驱动迭代学习控制设计和分析方案，由此推动了迭代学习控制在实际应用中的发展。