CAREER: Robustness Analysis in the Design of Nonlinear Feedback

拟议的研究将集中在严格分析特殊类别的本质上非线性反馈设计，应用于自调谐，δ - σ调制器，反复位发条和计算机模拟运动。该研究的一个主要目的是证明如何将鲁棒性的局部分析用于本质上非线性反馈系统的全局分析，从而产生任何其他方法都无法比拟的结果。另一个总体目标是提出新的解决方案，并分析几个众所周知的非线性反馈问题的已知“特设”解决方案。继电器反馈系统分析。研究了具有线性时变装置的继电器反馈的反馈互连问题。这种互连引起自振荡（极限环）的情况将是最令人感兴趣的。将推导出这种极限环的全局稳定性的充分条件，并估计存在外部输入时振荡的灵敏度。特别对基于继电器的PID反馈自整定进行了分析。另一个应用将是分析δ - σ调制器。总的来说，研究项目的这一部分旨在弥补缺乏适合于严格分析分段线性系统的方法。具有幅度和速率约束的反馈控制。研究具有控制信号速率和幅度约束的线性和轻度非线性系统的控制问题。主要目标将是提高控制响应的速度和效率，用诱导范数和表征暂态行为的其他参数表示。另一个目的是为不同的反复位绕组设计的比较研究提供严格的基础。计算机动画的反馈控制。本部分课题涉及开环不稳定物体实时动态模拟计算机动画的可行性研究。“物体”将是一个关节上的三维系统，通常在任何时候都有一个或两个关节端接触地面，并通过关节之间的角度协调变化来保持稳定。最终，该物体将具有人体的大部分动力学特征，通过初始模型将具有较少的自由度。目标是教会物体在重力的作用下“行走”。人体运动的稳定性很可能是由自主神经系统控制的几个反馈回路保证的。然而，定义这些反馈的实际控制律是未知的。提出的研究的主要目的是表明，使用先进的非线性反馈控制方法，有可能找到开环运动的实时稳定算法，至少在简化模型的情况下是这样。本研究也将针对重复开环不稳定运动的稳定算法进行研究。综合教育软件。该提案的教育部分旨在为“系统与信号”本科班开发一个集成软件包和特殊方法，为最先进的，以学习为基础的，以实践为导向的教育提供工具。该系统将提供(a)以计算机辅助多媒体介绍课程概念；(b)学生使用随机生成的操练问题进行自我训练；(c)用于正式测试的自动问题生成和评估程序；(d)允许进一步积累知识的开放式架构。最终，拟议的发展应促进大学教育形式的重大变化。* * *

9624885 Megretski The proposed research will concentrate on rigorous analysis of special classes of essentially nonlinear feedback design with application in self-tuning, delta-sigma modulators, anti-reset windup, and computer simulated locomotion. One major objective of the research is to demonstrate how the local analysis of robustness can be used in the global analysis of essentially nonlinear feedback systems, to produce results not matched by any other approach. Another general objective is to propose new solutions, and analyze the known "ad-hoc" solution to several well-known nonlinear feedback problems. Analysis of relay feedback systems. Feedback interconnection of a relay feedback with a linear time-variant plant will be considered. The situation in which such interconnection induces self-oscillation (a limit cycle) will be of most interest. Sufficient conditions for the global stability of such limit cycles will be derived, and the sensitivity of the oscillations in the presence of external inputs will be estimated. In particular, analysis of relay-based self-tunning of PID feedback will be done. Another application will be the analysis of delta- sigma modulators. In general, this part of the research project is aimed to compensate for the lack of methods suitable for rigorous analysis of piecewise linear systems. Feedback control with magnitude and rate constraints. The problem of control of linear and mildly nonlinear systems with constraints imposed on control signal rate and magnitude will be considered. The prime objective will be to improve the speed and efficiency of the control response, expressed in terms of induced norms and other parameters characterizing the transient behavior. Another objective is to provide a rigorous basis for a comparative study of different anti-reset windup designs. Feedback control of computer animation. This part of the project involves research on the feasibility of real-time dynamically simulate d computer animation of an open-loop unstable object. The "object" will be a three-dimensional system on joints, normally having at any time one or two joint ends touching the ground, and maintaining stability by changing the angles between the joints in a coordinated manner. Ultimately, the object will have most of the dynamical features of a human body, through the initial models will have less degrees of freedom. The goal is to teach the object to "walk" in the presence of the gravity force. It is most likely that the stability of the human body motion is ensured by several feedback loops governed by the autonomic nervous system. However, the actual control laws defining these feedbacks are not known. The main objective of the proposed research is to show that, using an advanced nonlinear feedback control methodology, it is possible to find algorithms for real- time stabilization of the open-loop locomotion, at least in the case of a simplified model. The research will also be aimed at studying the algorithms for stabilization of repetitive open-loop unstable motion. Integrated educational software. The educational component of the proposal is aimed at the development of an integrated software package and special methodology for the undergraduate class in "Systems and signals", to provide a tool for state-of- the-art, learning based, and practice-oriented education. The system will provide (a) computer-assisted multimedia-based presentations of course concepts; (b) student self-training using random generators of drill problems; (c) automatic problem generation and evaluation programs for official testing; (d) an open architecture allowing further accumulation of the knowledge. Ultimately, the proposed development should facilitate a major change in the forms of the university education. ***