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

本计画将集中于非线性系统性能研究中一些基本未解决的问题。 一旦这些问题得到解决，所得到的理论将被应用到各种系统的稳定性分析，其中单个或多个人类操作员在反馈回路中与主动非线性机器人设备，从而受到施加的力。 拟议工作的目标有三个方面。 首先，将建立非线性系统的性能和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，但相关结果的扩展到非线性系统尚未得到充分发展。 事实上，初步的研究表明，鲁棒稳定性并不意味着性能的时不变的非线性系统时，使用标准的耗散为基础的标准（如L2增益或无源性）。 该项目的一个目标是确定哪些较弱版本的耗散导致性能和鲁棒稳定性之间的理想等价。 为此，我们提出了一种新的耗散性，称为条件耗散性，并确定其关键特性。为了提供满足第一个项目目标所需的分析工具，我们将在Willems工作的基础上开发一种非线性系统模型的行为方法。 特别是，对于非线性系统模型（如拉萨尔的不变性原理）的分析特别重要的概念将在行为背景下制定。 该项目的这一部分的预期成果将是演示的行为方法提供了一定的优势，分析和设计不提供与standardapproaches非线性系统模型。 最后，根据前两个项目目标开发的理论将被应用到人/机界面的稳定性分析，如触觉显示器和双边遥操作系统。 在这样的系统中，操作员与主动机器人设备直接接触，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操作员的安全很重要，而且对通过力反馈对虚拟或物理环境的准确触觉感知也很重要。本项目将显著扩展这些系统稳定性的已知结果，为系统设计提供指导。 事实上，它将是第一个解决多用户系统稳定性问题的系统，即，多人操作员通过他们自己的本地机器人设备同时相互交互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此过程中发展的理论。项目 特别是，该项目将提供设计师的机器人系统，如触觉显示器和双边遥操作系统的有用的指导方针，使他们的系统工作在一个稳定的方式。 因此，该项目有可能提高这些系统在计算机辅助设计、制造和医药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.