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

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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.