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

点击翻译按钮获取中文摘要

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.