Global Control of Nonlinear Systems with Uncontrollable Unstable Linearization: A Non-Smooth Feedback Framework

0203387林本计划将系统地开发一种非光滑反馈设计方法，用于控制真正的非线性系统，这些系统可能无法通过任何光滑反馈处理，即使是局部的。非光滑反馈设计提供了克服光滑控制无法解决的系统拓扑障碍的可能性，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。该研究将解决非线性控制领域的一些最关键和最具挑战性的问题，包括全局强镇定，实用输出跟踪和自适应控制的非线性参数化系统的不可控不稳定线性化。 在我们的发展中的一个独特的线程是显式的构造类似的李雅普诺夫函数和非Lipschitz连续控制器，基于微分几何控制理论，齐次系统理论，以及发展的反馈控制设计技术的方法，控制非线性系统的雅可比线性化包含不可控的模式与右半平面上的特征值。 这一工作还将包括一类重要的非线性系统的几何特征和高阶标准形。许多具有实际意义的控制系统（例如互联网网络、制造系统、仿生致动器系统、电刺激肌肉、水下或航空航天器等）具有现有反馈设计方法无法处理的真正非线性特性;大部分都是光滑的。实际上，积极研究的目标一直是将物理动态系统转换为线性系统，对于该线性系统，发展良好的现代控制技术（线性系统理论）是容易适用的。这些“线性化”技术由于通过反馈消除系统的非线性或忽略动态系统的复杂性而具有严重的局限性。因此，这些设计方法在许多新的现实问题中没有得到广泛的应用，例如复杂网络（如互联网或电力系统网络）的控制或复杂武器（如导弹和先进战斗机）的位置和速度控制。本研究的目的是找到方法来利用潜在的戏剧性，虽然非直观的，所造成的固有的非线性或复杂的相互作用的物理力与物理系统的影响。拟议的研究的主要成果将是新的，非光滑的反馈设计方法控制的动态系统。预计使用非光滑控制的系统方法的好处将得到广泛的赞赏，特别是在工业（如制造业，航空航天，电力和生物医学工程），可以找到许多非光滑控制的应用。

0203387LinThis program will systematically develop a nonsmooth feedback design methodology for the control of genuinely nonlinear systems that may not be dealt with, even locally, by any smooth feedback. Nonsmooth feedback designs offer the potential to overcome some topological obstructions of the system that cannot be addressed by smooth controls, for example, to globally stabilize a nonlinear system that is not stabilizable by any linear or smooth state feedback. The research will address some of the most critical and challenging issues in the field of nonlinear control, including global strong stabilization, practical output tracking and adaptive control for nonlinearly parameterized systems with uncontrollable unstable linearization. A unique thread in our development is the explicit construction of homogeneous-like Lyapunov functions and non-Lipschitz continuous controllers, based on a synthesis of methods drawn from differential geometric control theory, homogeneous systems theory, as well as the development of feedback domination design techniques for the control of nonlinear systems whose Jacobian linearization contains uncontrollable modes associated with eigenvalues on the right-half plane. This work will also include a geometric characterization and a higher-order normal form for a significant class of nonlinear systems.Many control systems of practical importance (e.g. internet network, manufacturing systems, biomimetic actuator systems, electrically stimulated muscles, underwater or aerospace vehicles and so on) have genuinely nonlinear characteristics that cannot be dealt with by existing feedback design methods; most of them are smooth in nature. In fact, a goal of active research has been to transform a physical dynamic system into a linear one for which the well-developed modern control techniques (linear systems theory) are readily applicable. These "linearizing" techniques have serious limitations due to canceling the system nonlinearity by feedback or neglecting the complexity of dynamic systems. Consequently, these design methods have not found wide applications in a number of new real-world problems, such as control of complex network (e.g. internet or power systems network) or controlling the position and speed in sophisticated weapons (e.g. missiles and advanced combat aircraft). The purpose of this research is to find ways to take advantage of the potentially dramatic, though nonintuitive, effects caused by the inherent nonlinearity or complex interactions of physical forces with physical systems. The main outcome of the proposed research will be new, nonsmooth feedback design methodologies for the control of dynamic systems. It is expected that the benefits to a systematic approach towards using nonsmooth control will be becoming widely appreciated, particularly in industries (e.g. manufacturing, aerospace, power and biomedical engineering) where many applications of nonsmooth control can be found.