A Set-theoretic Reconfiguration Feedback Control Scheme Against Simultaneous Stuck Actuators

This paper presents a fault tolerant control scheme for constrained discrete time linear systems against stuck actuators and bounded disturbances. The results here proposed are a significant generalization of a similar algorithm which has been designed only to manage healthy/out-of-service actuator units. A key feature of the proposed scheme consists of taking advantage of polyhedral algebra and computational geometry concepts in order to characterize the reconfiguration logic of the proposed fault tolerant architecture. This is achieved by describing the plant via a set of a finite number of piecewise affine systems capable to cover all of the admissible faulty stuck scenarios. It is then proved that one-step sequences of controllable sets can be formally defined within a piecewise affine system paradigm under the key property that each region is a polyhedron.