A new approach to the reconfigurable control of piecewise affine (PWA) systems after actuator and sensor faults is presented. The approach extends the concept of virtual actuators and virtual sensors from linear to PWA systems on the basis of the fault-hiding principle. The weak fault-hiding goal is introduced as a relaxation of the asymptotic fault-hiding goal. Sufficient linear matrix inequality conditions for the existence of input-to-state stabilizing virtual actuators and sensors are given that lead to a tractable computational algorithm. The stability of the reconfigured closed-loop system is verified. The approach is evaluated using a system of interconnected tanks.
I. IIn this paper, a new reconfigurable control strategy for piecewise affine (PWA) systems is presented. Reconfigurable control responds to severe component failures that break the control loop by restructuring the control loop on-line [1]. Control reconfiguration is an active fault-tolerant control methodology that uses the estimatef of the fault f , which is obtained from a diagnosis component (FDI) (Fig. 1). As opposed to passive fault-tolerant control approaches [2], [3], in reconfigurable control the controller is changed to match the faulty plant once the fault has been isolated [4]. For switched systems, adaptive schemes [5] and output feedback controller redesign have been developed (see for example [6]). For PWA systems, model-predictive control has been used for fault-tolerant control [7]. y d f fû r Controller Plant FDI Control reconfiguration Execution -Supervision Fig. 1. Active fault-tolerant control scheme.This approach is based on the idea of keeping the nominal controller in the loop by inserting a reconfiguration block between the faulty plant and the nominal controller when a fault occurs. The reconfiguration block is chosen to hide the fault from the controller and, at the same time, to ensure that the faulty plant controlled by the nominal controller together with the reconfiguration block remains globally input-to-state stable. The fault-hiding approach was previously developed for linear and Hammerstein systems and lead to virtual actuators for the actuator fault case and to virtual sensors for the sensor fault case (see [8]-[12]); until now, the faulthiding approach was not available for PWA systems. The extension from linear to PWA systems is hard due to the following complexity property: For continuous PWA systems with more than 2 states, the problem of deciding whether or not all system trajectories are bounded is undecidable [13].The motivation for studying PWA systems is at least twofold. Firstly, PWA systems are receiving wide attention due to the fact that the PWA framework [14] provides a way to describe dynamic systems exhibiting switching between a multitude of linear dynamic regimes, see also [15]. Such switching can be due to piecewiselinear characteristics such as dead-zone, saturation, hysteresis or relays. Secondly, PWA systems may result from piecewise linear approximations of complex nonlinea...