Controller verification in adaptive learning systems towards trusted autonomy

With the increasing levels of adaptation and autonomy in complex cyber-physical systems (CPS), the traditional notion that such systems can be fully tested and validated offline is becoming an impossible task. It is virtually impossible to analyze or test ahead of time all the possible parameter values resulting from the uncertainty in system operational and environmental conditions. This paper considers the problem of online controller verification in a class of first-order nonlinear uncertain systems incorporating neural network based learning algorithms. Based on several critical assumptions, an on-line neural network model is employed to ensure robustness and fault-tolerance to certain modeling uncertainty and physical faults under consideration. However, these assumptions may be violated in the presence of software faults or unanticipated physical faults in the closed-loop system, leading to unstable learning behaviors and controller malfunctions. Based on Lyapunov stability theory, a online controller verification scheme is developed to detect such unstable learning behaviors by continuously monitoring the decrease of Lyapunov functions. Adaptive thresholds for detecting malfunctions of the adaptive learning controller are derived, ensuring the robustness with respect to modeling uncertainty and neural network approximation error. Additionally, the detectability conditions are investigated, characterizing the class of detectable software faults and unanticipated hardware faults. An upper bound on the detection time of controller malfunction is also derived. Some simulation results using a two-tank system are shown to illustrate the effectiveness of the controller verification method.