Design Theory for Fault Tolerant Control Systems

控制器的设计问题，使控制系统保持稳定的情况下，其组件的故障，从三个方面进行了讨论；(1)具有时滞系统的鲁棒控制器设计理论。讨论了部件失效导致系统参数摄动的鲁棒控制问题。针对具有时滞的线性系统，提出了该理论。利用算子李雅普诺夫方程和里卡蒂方程的性质，用算子微分方程描述系统，得到了一个广泛适用的一般理论。(2)用H控制理论设计的系统的增益余量。H*控制理论在设计鲁棒控制系统方面受到广泛关注。讨论了用H*理论设计系统的两个最关键的问题；(a)保持闭环稳定性的增益余量；(b)保证最优性的增益上限。导出了系统具有无限大增益裕度，并保证了该增益范围内的最优性。(3)抑制扰动影响的设计理论。某一类部件故障可以被建模为对标称系统的扰动。从以下几个方面讨论了干扰衰减问题：(a)包含最优性的H_2 /H*混合问题，(b)与微分对策的关系，(c)渐近干扰衰减问题，(d)有限视界问题。

Design problems of a controller, which enable the control system to remain stable in case of failure in its components, are discussed from three directions ;(1) Design theory of a robust controller for the system with time-delay. A robust control problem for the case when failure of components results in perturbation of system parameter is discussed. The theory is developed for the linear system with time-delay. A widely applicable general theory es developed by describing the system with an operator differential equation and by utilizing a property of a operator Liapunov and Riccati equations.(2) Gain margin of a system designed by an H control theory. H* control theory is attracting a wide attention for designing a robust control system. Two most crucial topics on the system designed by an H*theory are discussed ; (a) Gain margin under which stability of a closed loop is preserved, and (b) Upper limit of gain which assures the optimality. It is derived that the system has an infinitely large gain margin, and the optimality is assured for that range of gain.(3) Design theory to supperss the effect of disturbance. Some class of component failure can be modeled as disturbance to the nominal system. A disturbance attenuation problem is discussed with respect to the following issues ; (a) H_2 /H* mixed problem to include the optimality, (b) Relation to the differential game, (c) Asymptotic disturbance attenuation problem, and (d) A finite horizon problem.