Design Theory for Fault Tolerant Control Systems

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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.