Fault-tolerant control of sampled-data nonlinear distributed parameter systems

This work presents an integrated fault detection and fault-tolerant control architecture for spatially-distributed systems described by highly-dissipative systems of nonlinear partial differential equations with actuator faults and sampled measurements. The architecture consists of a family of nonlinear feedback controllers, observer-based fault detection filters that account for the discrete measurement sampling, and a switching law that reconfigures the control actuators following fault detection. An approximate model that captures the dominant dynamics of the infinite-dimensional system is embedded in the control system to provide the controller and fault detection filter with estimates of the measured output between sampling instances. The model state is then updated using the actual measurements whenever they become available from the sensors. A sufficient condition for stability of the sampled-data nonlinear closed-loop system is derived in terms of the sampling rate, the model accuracy, the controller design parameters and the spatial placement of the control actuators. This characterization is used to derive rules for fault detection and actuator reconfiguration. The results are demonstrated through an application to the problem of stabilizing the zero solution of the Kuramoto-Sivashinsky equation.