含正弦扰动奇异摄动时滞系统的最优减振控制

研究奇异摄动时滞系统在正弦扰动下的最优减振控制问题．基于奇异摄动的快慢分解理论,将原最优控制问题转化为无时滞快子问题和受扰线性时滞慢子问题,通过摄动法和前馈补偿技术求解时滞慢子系统的最优控制问题,得到了系统的前馈反馈组合控制(FFCC)律及其存在唯一性条件．FFCC律由线性解析项和共态向量无穷级数和表示的时滞补偿项组成,其中线性解析项可通过求解Riccati方程和Sylvester方程得到,时滞补偿项通过递推求解共态向量方程得到,仿真算例表明了方法的有效性．

Optimal damping control for singularly perturbed time-delay systems with sinusoidal disturbances

The optimal damping control design for singularly perturbed time-delay systems affected by external sinu- soidal disturbances is considered.Based on the slow-fast decomposition theory of singular perturbation,the system is first decomposed into a fast subsystem and a slow time-delay subsystem with disturbances.Then,the perturbation method is proposed to solve the slow time scale time-delay optimal control problem,and the feedforward compensation technique is used to reject the disturbances.The conditions of existence and uniqueness of the feedforward and feedback composite control (FFCC) law are also obtained.The FFCC law consists of linear analytic terms and a time-delay compensation term which is a series sum of adjoint vectors.The linear analytic terms can be found by solving Riccati matrix equation and Sylvester equation respectively.The compensation term can be approximately obtained by a recursion formula of adjoint vector equation.Finally,numerical examples are presented to illustrate the effectiveness of the proposed design method.