Fault-Tolerant Controller Design with A Tolerance Measure for Systems with Actuator and Sensor Faults

This paper presents a fault-tolerant (FT) switching control system structure and proposes an FT controller design methodology for systems vulnerable to actuator and sensor faults. The working effectiveness of the i-th actuator/sensor (which is assumed to be known) is represented as a time varying parameter delta(i)(t) where delta(i)(t) is an element of {0, c(2), ... , c(s-1), 1} and where delta(i)(t) = 0 represents a component failure at time t while delta(i)(t) = c(j), for j = 2, ..., s - 1 (cf. delta(i)(t) = 1) represents a partially (cf. fully) working component. If the total number of components is m, then at any time t, there are s m fault scenarios. Recognizing that it is unlikely that all components will have serious faults at the same time, the design objective is to maintain an acceptable level of closed-loop performance only for those fault scenarios for which the minimum sum of working effectiveness of all components is assumed to be p, where 0 <= p <= m, so that p defines a fault-tolerance level for the controller. At the same time, the no-fault nominal performance is optimized. The FT controller is reconfigurable, but with the special structure that the system matrices are fixed while the switching is on the time varying parameters delta(i)(t); i = 1, ..., m. For systems with many potential component fault cases, a semidefinite relaxation FT control design procedure is proposed so as to overcome the combinatorial nature of the problem. A numerical example is given in the last section to demonstrate the efficiency of the FT controller design.