Disturbance Attenuation in Nonlinear Control Systems

具有复杂非线性动力学行为的系统反馈律的设计是一个具有挑战性的研究课题，近年来引起了越来越多的关注。非线性控制理论的进步将大大改善轻型机械臂、高机动性飞机的自动驾驶仪和制导系统的控制系统设计，增加化工厂调节的灵活性和能效，便于在发生故障后实时重新配置控制系统。在必须面对的众多问题中，最重要的问题是设计反馈律，实现对规定的外生命令的跟踪和对外生干扰的抑制。控制系统中外生输入的跟踪/拒绝问题的方法取决于所选择的模型来描述预期会影响系统的外生输入族。如果没有可用的模型，一个吸引人的策略——在线性系统的情况下，它显示出自己非常强大和吸引人——是基于最坏的可能情况进行设计。例如，在频域，设计反馈律是为了使外源输入的频率响应的最大幅值最小。该研究项目将有助于将这些设计方法扩展到由非线性数学模型描述的系统。运用控制系统的几何理论、微分对策理论和动力系统的定性理论的方法和成果，研究的目的是建立足够一般的结果，反馈控制律的存在和实际设计，以实现未建模的外部干扰的衰减。

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.