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.

@en

The present study aimed to compare survival to age 75 between men and women, by social circumstances and smoking behaviour. A 20 year follow up was carried out of a large representative cohort of Scottish men and women in the Renfrew and Paisley study, and was combined with Scottish mortality statistics. 6831 men and 7993 women aged 45-64 y at time of examination (between 1972 and 1976) were considered. Combining the estimates from the Renfrew and Paisley study with those from Scottish mortality statistics for men and women younger than 45 y of age, it was calculated that 28% of the male smokers and 44% of the male never smokers in disadvantaged social circumstances will have survived to age 75 y, compared with 46% and 56% of the female smokers and never smokers respectively. In more privileged social circumstances, 41% of the male smokers and 62% of the male never smokers will have survived to age 75 y, compared with 56% and 70% of the female smokers and never smokers respectively. The difference between male smokers in low social classes and female never smokers in high social classes is 42% in absolute terms (28% vs 70%), which gives an indication of the combined influence of gender, social circumstances and smoking on survival. These results show that gender, social circumstances and smoking are important determinants of mortality which have led to substantial differences in survival. The influence of additional factors related to mortality could usefully be compared to these to put their effects into perspective.@en