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

这项提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。主要目的是针对一类具有不可镇定/不可检测线性化的非线性系统，发展非光滑反馈设计方法，通过可测信号实现全局镇定、自适应调节和输出跟踪，这些非线性系统即使在局部也不能用任何平滑反馈来处理。非光滑反馈设计是为了克服某些不能用平滑控制解决的拓扑障碍，例如，全局镇定不能用任何线性或光滑状态反馈镇定的非线性系统，因为线性化系统在右半平面上具有与特征值相关的不可控模式。该方案的基本研究内容是设计实现全局强稳定性的非光滑局部状态或输出反馈控制器，即以一种对系统中的扰动和参数不确定性不敏感的方式，即以一种健壮的方式实现。该方案的另一个重点将是通过测量反馈为固有的非线性系统发展一种新的输出跟踪理论。目标是使受控对象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确保渐近跟踪。利用中心流形理论，在线性化后的系统至少部分可控且能观测的假设下，建立了这些鲁棒性的非线性模拟。然而，对于线性化不能观测和不能控制的非线性系统的输出调节，目前还知之甚少。我们的初步分析表明，需要一种新的形式来解决非线性调节器问题。事实上，该提案中的一些戏剧性例子表明，虽然渐近输出跟踪通常是不可能的，即使是局部的，但实际的输出跟踪是可以实现的。这个项目的一个重要组成部分将是建立一个在存在非线性参数的情况下，具有不可控/不可观测线性化的非线性系统的全局实用输出跟踪的一般理论。理论研究将通过几个新的应用来补充。特别是，将要发展的非光滑控制理论将被用来解决困难的控制问题，包括欠驱动机械系统的输出反馈镇定和对抗性仿生驱动系统的输出跟踪/调节。智能优点：该程序不仅为具有不可控/不可观测线性化的非线性系统的非光滑测量反馈控制提供了一个通用的框架，而且对于现有平滑综合技术不能控制的真正的非线性系统，如输出反馈镇定、输出跟踪和调节等一些重要和具有挑战性的开放问题做出了基础性贡献。这项研究将带来新的见解，推动非光滑控制理论的发展，并进一步促进针对一大类固有非线性系统的非光滑设计方法及其应用的发展。广泛影响：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，重点是开发计算高效且实用可行的非光滑控制工具和算法，用于关键的生物医学控制应用，以及实现工程系统(如移动机器人、欠驱动机械系统、仿生或生物启发系统)的高性能运行。将非光滑控制方法应用到仿生系统中，有可能克服仿生机器人(如仿蟑螂六足机器人)、功能性电刺激肌肉和其他人造设备的一些基本困难，使嵌入的控制系统能够在现实世界中自主运行，从而显著提高第一代仿生系统的性能。这一计划的成果预计将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