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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。
Aiming at a kind of system that is disturbed continuously, a concept of preserving attractor disturbance disturbance is proposed. Combined with the backstepping design, the Barbalat lemma and the Lyapunov analysis method, a quadratic matrix inequality condition is given. A scalar adaptive robust control law is designed for this kind of system, which suppresses the state of the controlled system in a bounded attractor Inside. This quadratic matrix inequality is transformed into an easy to solve linear matrix inequality. Furthermore, the criterion of minimizing the attractor is given by the linear matrix inequality, so that the disturbance rejection can be further optimized. As an application, this paper first analyzes the rolling motion of a certain type of fishery ship in random waves, and then uses the designed disturbance rejection control law as the steering torque to apply it to the yawning control of fishery ships, and through numerical simulation, Paul Attractor rudder roll effect.