Mathematical Sciences: Feedback Design for Nonlinear Systems

本研究的目的是建立一个系统的 非线性系统响应成形方法 目的是控制或 对系统行为的影响最小。 一个更长期的目标， 目前还在试验阶段， 利用奇异非线性行为来实现系统 这是线性系统无法实现的。 本研究的重点是发展一种稳定的理论， 状态响应和“非线性”的意外解决方案 调节器问题”，从平衡的小偏差。 一个相当有前途的新领域涉及一种结构， 解决监管问题，似乎特别 适合于计算实现的结果， 反馈律 事实上，计算需要离线 一个非线性偏微分方程的解 显然，对于非线性系统， 线性控制系统方程

The goal of this research is to develop a systematic approach to shaping the response of nonlinear systems to applied forcing mechanisms with the aim of controlling or at least influencing the system behavior. A longer term goal, currently being pursued only at an experimental level, is also to take advantage of exotic nonlinear behavior to achieve a system response which cannot be realized with a linear system. This proposal focuses on the development of a theory of steady- state response and to an unanticipated solution of the "nonlinear regulator problem", for small deviations from an equilibrium. One rather promising new frontier involves a structure of the solution of the regulator problem which seems particularly amenable to a computational implementation of the resulting feedback law. Indeed, the compution requires the off-line solution of a nonlinear partial differential equation which is apparently the analogue, for nonlinear systems, of the Riccati equation of linear control systems.