输入长时滞非线系统的延时补偿、跟踪和干扰抑制设计

With the development of scientific practice and theoretical research, nonlinear systems with long input delays become one of the research hotspots of control theory and control engineering. Based on Lyapunov method and continuous backstepping feedback transformations, time delay compensation, tracking and disturbance attenuation design for nonlinear systems with long input delays are systematically and profoundly investigated in this project. The research contains: the conditions of nonlinear systems being forward complete and backfard complete and the estimation of domain of attraction; the conditions and design of feedback stabilization for time delay compensation; the design for tracking and disturbances attenuation for uncertain systems and the corresponding inverse optimal control. The research objects are: to get constructing methods of continuous backstepping feedback transformation for time delay compensation; to design predictive control laws ahead of the length of time delay; to extend the results to the tracking, disturbances attenuation design for the uncertain nonlinear systems with long input delays; to obtain the inverse optimal function corresponding to the control law design and estimate dynamic performance of the closed-loop system. New theory for nonlinear systems with long input delays will be founded.

随着科学实践和理论研究的深入，输入长时滞非线性系统正在成为控制理论与工程研究的热点之一。本项目应用Lyapunov 方法和连续的Backstepping反馈变换，系统深入地研究输入长时滞非线性系统的延时补偿、跟踪和干扰抑制设计。研究内容包括：非线性系统为前向、后向完全的条件和吸引域估计；延时补偿的条件和反馈镇定设计；不确定系统的跟踪、干扰抑制的设计；及其相应的逆最优控制。研究的目标为：得到用于延时补偿设计的连续Backstepping反馈变换的构造方法；设计提前于时滞长度时间的预测控制律；并将获得的结果推广到输入长时滞非线性不确定系统的跟踪、干扰抑制等设计中，进而得到与这些控制律设计相对应的逆最优函数，以期对闭环系统的动态性能有所估计。由此建立输入长时滞非线性系统设计的新理论。

随着科学实践和理论研究的深入，输入时滞非线性系统正在成为控制理论与工程研究的热点之一。本项目应用无穷维Backstepping变换和Lyapunov泛函，系统深入地研究非线性常微分方程与波偏微分方程串接系统延时补偿设计; 输入时滞非线性系统延时补偿的通用镇定设计；输入时滞非线性不确定系统干扰抑制及逆最优控制。取得的主要成果为：得到用于延时补偿设计的无穷维Backstepping变换的构造方法；设计提前于时滞长度时间的预测控制律；并将获得的结果推广到输入时滞非线性不确定系统的干扰抑制和逆最优控制中，进而得到与这些控制律设计相对应的逆最优泛函。本项目的研究成果有助于解决石油钻井系统中钻柱的扭转振动，这对于优化钻井设计，降低钻井成本具有重要理论和实际意义。