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

0203387LIN本程序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，即使是局部的，也不能通过任何平滑的反馈来处理。非光滑反馈设计提供了克服系统的一些拓扑障碍的可能性，这些障碍不能通过平滑控制来解决，例如，全局镇定不能通过任何线性或平滑状态反馈镇定的非线性系统。这项研究将解决非线性控制领域中一些最关键和最具挑战性的问题，包括全局强镇定、实用的输出跟踪以及具有不可控不稳定线性化的非线性参数系统的自适应控制。我们发展的一条独特的线索是显式构造类齐次Lyapunov函数和非Lipschitz连续控制器，基于从微分几何控制理论、齐次系统理论以及反馈控制设计技术的综合，用于非线性系统的控制，其雅可比线性化包含与右半平面上的特征值相关的不可控模式。许多具有实际意义的控制系统(如互联网网络、制造系统、仿生执行器系统、电刺激肌肉、水下或航天飞行器等)都具有用现有反馈设计方法无法处理的真正的非线性特征，并且大多数系统本质上是平滑的。事实上，主动研究的一个目标就是将一个物理动态系统转换为一个线性系统，对它来说，发达的现代控制技术(线性系统理论)是很容易应用的。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，这些设计方法在一些新的现实问题中并没有得到广泛的应用，例如复杂网络的控制(如互联网或电力系统网络)或复杂武器(如导弹和先进战斗机)的位置和速度控制。这项研究的目的是寻找方法来利用由物理力与物理系统的内在非线性或复杂的相互作用所引起的潜在的戏剧性的、尽管不直观的影响。这项研究的主要成果将是用于动态系统控制的新的非光滑反馈设计方法。预计使用非平滑控制的系统化方法的好处将被广泛认识，特别是在可以找到许多非平滑控制应用的行业(例如，制造业、航空航天、电力和生物医学工程)。

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.