SCATTERING-BASED CONTROL DESIGN FOR INTERCONNECTED AND NETWORKED SYSTEMS

本申请中提出的研究方案旨在发展基于系统地使用广义散射变换的非线性动力系统网络的模块化控制设计的新方法，并将其应用于实际工程问题。在申请人以前的工作中引入的广义散射变换是一种输入-输出变换，它允许将具有二次供给率的非线性耗散系统的动态行为呈现到指定的非平面锥体中。广义散射变换的这一性质使其成为一种有效的设计工具，尤其可用于动力系统的互连镇定，包括具有通信时滞的系统。提出的研究计划的长期目标是全面开发基于广义散射变换的技术，使这些技术成为强大和通用的工具，适用于广泛的系统和控制设计问题。具体的短期研究目标包括发展具有二次供电率的非线性耗散系统复杂网络的基于模块散射的设计方法，发展基于散射的控制设计方法，包括在存在通信约束(如不规则通信延迟、信息丢失、有限带宽)的情况下的设计，基于散射的切换耗散系统的控制设计，将基于散射的设计方法推广到具有非线性扇形边界的二次曲线系统的情况，将机器人的接触稳定性问题的设计方法扩展到多机器人交互，以及针对双边和多边遥操作机器人系统的广义基于散射的设计方法。在方法论方面，我们将研究现有的以及新出现的工程问题，其中控制设计直接使用或基于锥度和/或耗散性的概念，并系统地探索应用广义散射变换可以带来的额外自由度。所提出的研究方案将为耗散系统复杂网络的系统模块化设计带来新的强有力的方法，这些方法随后可以应用于涉及其组件之间的物理相互作用和/或信息交换的许多实际问题。在拟议的研究计划过程中接受的培训将为学员未来的职业成功提供坚实的背景，并将使他们在当今高科技就业市场上获得竞争优势。

The research program proposed in this application aims at development of novel methods of modular control design for networks of nonlinear dynamical systems based on systematic use of generalized scattering transformations, and their application to practical engineering problems. The generalized scattering transformation, which was introduced in the previous works of the applicant, is an input-output transformation which allows for rendering the dynamic behavior of a nonlinear dissipative system with quadratic supply rate into a prescribed non-planar cone. This property of generalized scattering transformation makes it an effective design tool which can, in particular, be used for stabilization of interconnections of dynamical systems, including those with communication delays. The long-term objective of the proposed research program is comprehensive development of generalized scattering transformation based techniques which will make these techniques powerful and versatile tools applicable to a wide range of systems and control design problems. The specific short-term research objectives include development of methods for modular scattering-based design for complex networks of nonlinear dissipative systems with quadratic supply rates, development of methods for scattering-based control design for cyberphysical systems, including design in the presence of communication constraints (such as irregular communication delays, information losses, limited bandwidth), scattering-based control design for switched dissipative systems, extension of the scattering-based design methods to the case of conic systems with nonlinear sector bounds, design methods for contact stability problem in robotics with extension to multi-robot interaction, as well as generalized scattering-based design methods for bilateral and multi-lateral teleoperator systems. In terms of methodology, we will look into existing as well as new and emerging engineering problems where the control design either directly employs or based on the notions of conicity and/or dissipativity, and systematically explore additional degrees of freedom that can be brought by application of the generalized scattering transformations. The proposed research program will lead to development of new powerful methods for systematic modular design of complex networks of dissipative systems, which can be subsequently applied to many practical problems that involve physical interaction and/or information exchange between their components. The training received over the course of the proposed research program will provide a solid background for the trainees' future professional success and will give them competitive advantage in today's high-tech job market.