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

本提案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。主要目标是开发非光滑反馈设计方法，通过可测量信号实现全局稳定、自适应调节和输出跟踪，用于一类具有不稳定/不可检测线性化的重要非线性系统，这些系统无法通过任何光滑反馈处理，即使是局部。非光滑反馈设计提供了克服平滑控制无法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无法稳定的非线性系统，因为线性化系统具有与右半平面上的特征值相关的不可控模式。本提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，以鲁棒方式实现全局强稳定性，即以对系统中的扰动和参数不确定性不敏感的方式实现。本提案的另一个重点将是通过测量反馈为固有非线性系统发展新的输出跟踪理论。目标是使被控装置跟踪所需的参考信号。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保证渐近跟踪。在假设线性化系统至少部分可控和可观测的前提下，通过中心流形理论对这些鲁棒性进行了非线性模拟。然而，对于线性化不可观测和不可控的非线性系统的输出调节，研究结果却很少。我们的初步分析表明，非线性调节问题需要一个新的表述。事实上，提案中的一些戏剧性的例子表明，虽然渐进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。该项目的一个重要组成部分将是在非线性参数化存在的情况下，为具有不可控/不可观测线性化的非线性系统建立全局实际输出跟踪的一般理论。理论研究将得到几个新应用的补充。特别是，将开发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拮抗仿生驱动系统的输出跟踪/调节，通过非光滑测量反馈。智力优势：该计划不仅将提供一个总体框架，非线性系统的控制与不可控/不可观察的线性化通过非光滑测量反馈，但也作出了根本性的贡献，一些重要的和具有挑战性的开放问题，如输出反馈稳定，输出跟踪和调节，真正的非线性系统，不能由现有的光滑综合技术控制。所提出的研究将产生新的见解，推动非光滑控制理论的发展，并进一步促进非光滑设计方法的发展及其在大类固有非线性系统中的应用。更广泛的影响：拟议的研究将对开发新一代非线性控制技术产生巨大影响，重点是开发计算效率高且实际可行的非光滑控制工具和算法，用于关键生物医学控制应用和实现工程系统（例如移动机器人，欠驱动机械系统和仿生或生物启发系统）的高性能操作。将非光滑控制方法应用于仿生系统有可能克服设计仿生机器人（例如，类蟑螂六足机器人）、功能性电刺激肌肉和其他人造设备的一些基本困难，这些人造设备的嵌入式控制系统可以在现实世界中自主运行，从而显着提高第一代仿生系统的性能。该计划的成果被设想为显著提高工程和生物启发系统的可操作性和效率提供新的途径，创造商业或生物医学应用机会，并最终产生经济效益

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