Systematic Synthesis of Passive Fault-Tolerant Augmented Neural Lyapunov Control Laws for Nonlinear Systems

Performance and closed-loop stability of control systems can be jeopardised by actuator faults. Actuator redundancy in combination with appropriate control laws can increase the resiliency of a system to both loss of efficiency or jamming. Passive Fault-Tolerant Control (FTC) systems aim at designing a unique control law with guaranteed stability in both nominal and faulty scenarios. In this work, a novel machine learning-based method is devised to systematically synthesise control laws for systems affected by actuator faults, whilst formally certifying the closed-loop stability. The learning architecture trains two Artificial Neural Networks, one representing the control law, and the other resembling a Control Lyapunov Function (CLF). In parallel, a Satisfiability Modulo Theory solver is employed to certify that the obtained CLF formally guarantees the Lyapunov conditions. The method is showcased for two scenarios, one encompassing the stabilisation of an inverted pendulum with redundant actuators, whilst the other covers the control of an Autonomous Underwater Vehicle. The framework is shown capable of synthesising both linear and nonlinear control laws with minimal hyperparameter tuning and within limited computational resources.