Actuators that lose effectiveness, together with disturbances entering through the same channel, can severely degrade the tracking performance of nonlinear control affine systems. This is particularly the case when the severity of the fault and the bounds of the disturbance are unknown.
The paper develops a framework for fault recovery that combines three elements: a Koopman based predictor for the detection and identification of faults from data, a polynomial chaos expansion (PCE) that quantifies the uncertainty and provides confidence bounds on the estimated fault parameters, and an adaptive deep neural network that compensates the remaining effects of fault and disturbance in closed loop. The plant is first rewritten into an effective input form, in which faults and disturbances appear as a single uncertainty of the input channel.
In the offline phase, expert demonstrations are generated for a range of fault and disturbance scenarios and a baseline network is trained by supervised learning. In order to decide which part of the network is adapted during operation, the average causal effect of each layer on the tracking error is evaluated and a single layer is selected. During operation, the module for fault detection and identification estimates the actuator effectiveness matrix and supplies a confidence bound that is used to reconfigure the nominal controller. An adaptive update law for the selected layer is proposed, and the uniform ultimate boundedness of the tracking error and of the weight errors is proven.
The estimates of the fault detection module tighten the residual bound and reduce the ultimate bound of the tracking error, with an explicit dependence on the accuracy of the estimation. The claims are validated numerically for a membrane reactor that has to follow a hydrogen demand, including fault scenarios outside the training data. Fault detection alone gives the lowest root mean square error, while its combination with the adaptive network reduces the largest tracking excursions.
The study was carried out at the Institute of Control Systems at Hamburg University of Technology within the Collaborative Research Centre CRC 1615 (SMART Reactors).
Srimanta Santra (2026). Koopman-PCE-based confidence-bounded fault diagnosis and recovery for hydrogen demand tracking in a membrane reactor. Computers and Chemical Engineering 213, 109728.
