A Behavioral Approach to Dissipativity Analysis in Nonlinear Systems, with Applications to Human/Robot Interfaces

本项目将集中研究非线性系统性能研究中的一些基本悬而未决的问题。一旦这些问题得到解决，由此产生的理论将被应用于各种系统的稳定性分析，在这些系统中，单个或多个人类操作员与活跃的非线性机器人设备处于反馈回路中，因此受到外力的影响。拟议工作的目标有三个。首先，建立了非线性系统的性能与鲁棒稳定性之间的关系。这种关系是许多现代线性鲁棒控制技术的重要组成部分，但相关结果在非线性系统中的推广还没有得到充分的发展。事实上，初步研究表明，当使用基于耗散性的标准准则(例如L2增益或无源性)时，鲁棒稳定性并不意味着时不变非线性系统的性能。该项目的一个目标是确定哪些较弱的耗散性版本会导致性能和健壮稳定性之间的理想等价性。为此，提出了一种新版本的耗散性，称为条件耗散性，该项目的一部分将是确定其关键性质。为了提供足够的分析工具来满足第一个项目目标，将在Willems工作的基础上开发非线性系统模型的行为方法。特别是，对于分析非线性系统模型特别重要的概念(如拉萨尔的S不变原理)将在行为的背景下制定。该项目这一部分的预期结果将证明，行为方法为分析和设计提供了某些优势，这是非线性系统模型的标准方法所不具备的。最后，根据前两个项目目标开发的理论将应用于触觉显示器和双边遥操作系统等人机接口的稳定性分析。在这类系统中，操作者直接接触到一个主动的机器人设备，并受到通过非线性反馈回路施加的力的影响。这种反馈系统的稳定性不仅对于人类操作者的安全，而且对于通过力反馈对虚拟或物理环境的准确触觉感知都是重要的。本项目将极大地扩展关于这些系统稳定性的已知结果，并为系统设计提供指导。事实上，这将是第一次解决多用户系统的稳定性问题，即多个人类操作员通过自己的局部机器人设备同时相互作用以及与虚拟或物理环境交互的系统。任何依赖于性能和鲁棒稳定性之间关系的非线性系统设计技术的应用都将直接受益于在该项目过程中发展的理论。特别是，该项目将为触觉显示器和双边遥操作系统等机器人系统的设计者提供有用的指导，使他们的系统以稳定的方式工作。因此，该项目有可能提高这些系统在计算机辅助设计、制造和医学等领域的各种实施的质量。

This project will focus on the investigation of some of the basic unresolved issues in the study of the performance properties of nonlinear systems. Once these issues have been addressed, the resulting theory will be applied to the stability analysis of various systems in which single or multiple human operators are in feedback loops with active nonlinear robotic devices and are thus subject to applied forces. The objectives of the proposed work are threefold. First,the relationship between performance and robust stability for nonlinear systems will be established. This relationship is an essential part of many modern linear robust control techniques, but extensions of the relevant results to nonlinear systems have not yet been fully developed. Indeed, preliminary investigations have revealed that robust stability does not imply performance for time-invariant nonlinear systems when standard dissipativity-based criteria are used (such as L2-gain or passivity). One goal of this project is to determine which weaker versions of dissipativity lead to the desired equivalences between performance and robust stability. To this end,a new version of dissipativity called conditional dissipativity is proposed, and part of this project will be to identify its key properties.To provide analysis tools sufficient for meeting the first project objective, a behavioral approach to nonlinear system models will be developed based on the work of Willems. In particular, concepts especially important for the analysis of nonlinear system models (such as LaSalle 's invariance principle) will be worked out in a behavioral context. An expected outcome of this part of the project will be the demonstration that the behavioral approach offers certain advantages to both analysis and design not available with standardapproaches to nonlinear system models. Finally, the theory developed according to the first two project objectives will be applied to the stability analysis of human/machine interfaces such as haptic displays andbilateral teleoperation systems. In such systems, a human operator is in direct contact with an active robotic device and is subject to forces applied through a nonlinear feedback loop.The stability of such a feedback system is important not only for the safety of the human operator but also for the accurate tactile perception of the virtual or physical environment via the force feedback.This project will significantly extend the knownresults on the stability of these systems and provide guidelines for system design. In fact, it will be the first to address stability issues for multi-user systems, that is, systems in which multiple human operators interact simultaneously with each other and with virtual or physical environments by means of their own ocal robotic devices.Any application of nonlinear system design techniques which relies on the relationship between performance and robust stability will directly benefit from the theory developed during the course of this project. In particular, this project will provide designers of robotic systems such as haptic displays and bilateral teleoperation systems with useful guidelines for making their systems work in a stable manner. This project thus has the potential for improving the quality of various implementations of these systems in such areas as computer-aided design, manufacturing and medicine.