Nonsmooth Measurement Feedback Control of Genuinely Nonlinear Systems with Applications to Biologically-Inspired Systems

真正非线性系统的非平滑测量反馈控制及其在仿生系统中的应用

• 批准号: 0400413
• 负责人: Wei Lin
• 金额: --
• 依托单位: Case Western Reserve University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-07-01 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0400413&HistoricalAwards=false
• 关键词: Nonsmooth; Measurement; Feedback; Control; Genuinely

This proposal aims to address some of the most fundamental and challenging issues in the field of nonlinearcontrol. The main objectives are to develop nonsmooth feedback design approaches achieving global stabilization,adaptive regulation and output tracking, via measurable signals, for a significant class of nonlinear systems withunstabilizable/undetectable linearization, which cannot be dealt with by any smooth feedback, even locally. Nonsmoothfeedback designs ofer the potential to overcome certain topological obstacles that cannot be addressed by smoothcontrols, for example, to globally stabilize a nonlinear system that is not stabilizable by any linear or smooth statefeedback, because the linearized system has uncontrollable modes associated with eigenvalues on the right-half plane.The basic research components of this proposal are to design nonsmooth partial state or output feedback controllersthat achieve global strong stability and do so in a robust fashion, that is, in a manner which is not sensitive toperturbations and parametric uncertainties in the system.The other focal points of this proposal will be the development of a new output tracking theory for inherentlynonlinear systems by measurement feedback. The objective is to make the controlled plant track a desired referencesignal. A key feature of the classical servomechanism theory is the ability to absorb the effect of modeling errors andto secure asymptotic tracking in the presence of uncertainties. A nonlinear analogue of these robustness properties wasdeveloped via center manifold theory, under the assumption that the linearized system is controllable and observable,at least partially. However, little result is known on the output regulation of nonlinear systems whose linearizationis unobservable and uncontrollable. Our preliminary analysis suggests that a new formulation to the nonlinear reg-ulator problem is needed. Indeed, some dramatic examples in the proposal indicate that while asymptotic outputtracking is usually not possible, even locally, practical output tracking is achievable. One of important componentsof this project will be to establish a general theory for global practical output tracking of nonlinear systems withuncontrollable/unobservable linearization, in the presence of nonlinear parameterization.The theoretical research will be complemented by several novel applications. In particular, the nonsmooth controltheory to be developed will be used to address diffcult control problems including output feedback stabilization ofunderactuated mechanical systems and output tracking/regulation of antagonistic biomimetic actuation systems, bynonsmooth measurement feedback.Intellectual Merits: This program will not only provided a general framework for the control of nonlinear systemswith uncontrollable/unobservable linearization by nonsmooth measurement feedback, but also make a fundamentalcontribution to a number of important and challenging open problems such as output feedback stabilization, outputtracking and regulation, for genuinely nonlinear systems that cannot be controlled by existing smooth synthesis tech-niques. The proposed research will yield new insight, advance the state-of-the-art of nonsmooth control theory, andfurther facilitate the development of nonsmooth design methods and their applications for a large class of inherentlynonlinear systems.Broader Impact: The proposed research will have enormous impact on developing a new generation of nonlinearcontrol technologies, with emphasis on the development of computationally efficient and practically feasible nonsmoothcontrol tools and algorithms, for critical biomedical control applications and for achieving high-performance operationof engineering systems (e.g. mobile robots, underactuated mechanical systems, and biomimetic or biologically-inspiredsystems). Applications of the nonsmooth control methods to biomimetic systems have the potential to overcome somefundamental diffculties in designing biologically-inspired robots (e.g. cockroach-like hexapod robots), functional elec-trical stimulation muscles, and other man-made devices whose embedded control systems can function autonomouslyin the real world, thus improving significantly performance of the first generation biomimetic systems. The outcomesof this program are envisioned to provide new avenues for a significant improvement of operability and efficiencyof engineering and biologically-inspired systems, to create commercial or biomedical application opportunities, andeventually to result in economic benefits.1

该建议旨在解决非线性控制领域中一些最基本和最具挑战性的问题。本文的主要目标是针对一类非线性系统，通过可测信号实现全局镇定、自适应调节和输出跟踪，这类非线性系统具有不可镇定/不可检测线性化，不能用任何光滑反馈来处理，即使是局部的。非光滑反馈设计具有克服光滑控制不能解决的某些拓扑障碍的潜力，例如，全局稳定任何线性或光滑状态反馈都不能稳定的非线性系统，因为线性化系统具有与右边的特征值相关联的不可控模式，该方案的基本研究内容是设计非光滑部分状态或输出反馈控制器，使其实现全局强稳定性，并以鲁棒的方式实现。的方式，即以一种方式，这是不敏感的扰动和参数的不确定性在系统中。这一建议的其他重点将是一个新的输出跟踪理论的发展inherentlynonlinear系统的测量反馈。目标是使被控对象跟踪期望的参考信号。经典伺服机构理论的一个关键特征是能够吸收建模误差的影响，并在存在不确定性的情况下确保渐近跟踪。这些鲁棒性的非线性模拟开发通过中心流形理论，假设线性化系统是可控的和可观的，至少部分。然而，对于线性化后的不可观测和不可控的非线性系统，其输出调节的研究成果却很少。我们的初步分析表明，一个新的提法，非线性regulator问题是必要的。事实上，提案中的一些戏剧性的例子表明，虽然渐近输出跟踪通常是不可能的，即使是局部的，实际的输出跟踪是可以实现的。本项目的一个重要组成部分是在非线性参数化条件下，建立不可控/不可观测线性化非线性系统全局实际输出跟踪的一般理论，并通过一些新的应用来补充理论研究。特别是，将要发展的非光滑控制理论将用于解决困难的控制问题，包括欠驱动机械系统的输出反馈稳定和对抗性仿生驱动系统的输出跟踪/调节，通过非光滑测量反馈。该程序不仅为不可控/不可观测线性化非线性系统的非光滑测量反馈控制提供了一个通用框架，而且对于一些重要的和具有挑战性的开放问题，如输出反馈镇定，输出跟踪和调节，对于现有的光滑综合技术不能控制的真正的非线性系统，也做出了根本性的贡献。该研究将产生新的见解，推进非光滑控制理论的最新发展，并进一步促进非光滑设计方法的发展及其在一大类固有非线性系统中的应用。这项研究将对开发新一代非线性控制技术产生巨大影响，重点在于开发计算上有效且实际上可行的非平滑控制工具和算法，用于关键的生物医学控制应用和实现工程系统的高性能操作（例如移动的机器人、欠驱动机械系统和仿生或生物启发系统）。非光滑控制方法在仿生系统中的应用有望克服仿生机器人（如蟑螂机器人）、功能性电刺激肌肉以及其他人造设备设计中的一些基本困难，使其嵌入式控制系统能够在真实的世界中正常工作，从而显著提高第一代仿生系统的性能。该计划的成果旨在为工程和生物启发系统的可操作性和效率的显着改善提供新的途径，以创造商业或生物医学应用机会，并最终产生经济效益。