保吸引子的扰动抑制及其在舵减摇中的应用

针对一类受到持续扰动的系统，提出了保吸引子扰动抑制的概念。结合反步设计、Barbalat引理和Lyapunov分析方法，给出一个二次矩阵不等式条件，为这类系统设计了标量自适应鲁棒控制律，将受控系统的状态抑制在一个有界的吸引子内。这个二次矩阵不等式被转化为易于求解的线性矩阵不等式。并进一步利用线性矩阵不等式给出使吸引子最小化的判据，从而使扰动抑制进一步优化。作为应用，该文首先分析某型渔政船在随机斜浪中的横摇运动，然后将设计的扰动抑制控制律作为操舵力矩，运用于渔政船的横摇控制，并通过数值仿真验证了保吸引子舵减摇的效果。

GUARANTEED ATTRACTOR DISTURBANCE REJECTION AND ITS APPLICATION IN RUDDER ROLL STABILIZATION

The notation of a guaranteed attractor disturbance rejection is presented for a class of system with persistent disturbance. Based on a back stepping design, Barbalat lemma and Lyapunov theory, and by solving a quadratic matrix inequality (QMI), an adaptive scalar robust controller is designed for a class of this kind of system to suppress its states to a bounded attractor, and the QMI is transformed into linear matrix inequality (LMI). The further criterion of the attractor’s minimization is brought forward in the form of LMI, and so further optimizes the effect of disturbance rejection control. As application, the roll motion of a fishery administration ship in the random oblique wave is discussed. Then the designed disturbance rejection controller is used as rudder moment to control its roll motion, and the effect of the guaranteed attractor roll stabilization is verified.