Disturbance Attenuation in Nonlinear Control Systems

系统反馈律的设计 具有复杂的非线性动力学特性 行为是一项具有挑战性的研究任务， 近年来引起了越来越多的兴趣。 非线性控制理论的发展将 大大改善控制系统的设计 用于轻型机器人手臂，用于自动驾驶仪， 高度可折叠的飞行器的导航系统， 提高灵活性和能源效率， 化工厂的调节，便于实时 控制系统的重新配置， 发生故障。 在众多问题中， 这是必须面对的，最重要的一个问题是， 反馈律的设计实现了对 规定的外源命令和拒绝 外生干扰 的途径 跟踪/拒绝外来投入的问题 在控制系统中取决于所选择的模型 来描述一系列的外生输入， 预计会影响系统。 如果没有模型， 这是一个有吸引力的策略，它揭示了 它本身就非常强大和有吸引力， 线性系统-是基于最坏的设计 可能的情况。 例如，在频率 域，反馈律被设计为 使频率的最大振幅最小化 对外部输入的反应。 本研究 该项目将有助于扩大这些 系统设计方法， 非线性数学模型 使用方法 它是由控制的几何理论 系统，微分对策理论和 动力系统定性理论，目的 研究的目的是建立足够普遍的 关于存在和实际设计的结果 反馈控制律实现衰减 未建模的外部干扰。

The design of feedback laws for systems characterized by complicated nonlinear dynamical behavior is a challenging research task which has attracted an increasing interest in recent years. Advances in nonlinear control theory will substantially improve the design of control systems for light-weighted robot arms, for autopilots and guidance systems of highly maneuverable aircrafts, increase the flexibility and energy efficiency in the regulation of chemical plants, facilitate the real-time reconfiguration of a control system after the occurrence of a failure. Among the many problems which must be confronted, a most important one is the desing of feedback laws achieving tracking of prescribed exogenous commands and rejection of exogenous disturbances. The approaches to the problem of tracking/rejection of exogenous inputs in a control system depend upon the model chosen to describe the family of exogenous inputs which are expected to affect the system. If no model is available, an appealing strategy -which revealed itself very powerful and attractive in the case of linear systems- is to base the design on the worst possible situation. For instance, in the frequency domain, the feedback laws are designed so as to minimize the maximal amplitude of the frequency response to the exogenous inputs. This research project would contribute to the extension of these design methodologies to systems described by nonlinear mathematical models. Using methods and results from the geometric theory of control systems, the theory of differential games and the qualitative theory of dynamical system, the purpose of the research is to establish sufficiently general results about existence and actual design of feedback control laws achieving attenuation of unmodeled external disturbances.