This paper addresses fault estimation and prescribed performance control for strict-feedback nonlinear systems subject to unknown time-varying faults. By introducing a novel intermediate variable for fault estimation, an adaptive fault estimator and a fault-tolerant controller are proposed. Utilizing a proof by contradiction, the designed prescribed performance control scheme resolves the complex coupling between fault estimation and adaptive control. Furthermore, all closed-loop signals are proven bounded, with both tracking and state errors converging to predesigned compact sets. Finally, numerical simulation on a single-link robot system validates the effectiveness of the proposed algorithm.

With the rapid rise and widespread adoption of social media, theoretical research on the dynamics of online information dissemination has become increasingly important. Therefore, we developed a new model of information diffusion that took into account the influence of information recipients on the diffusion of information. First, initially, the basic reproduction number of the model was calculated. Then, we analyzed the existence and stability of the equilibrium point. Next, based on the principle of Pontryagin's maximum principle, a control strategy was derived to effectively enhance the propagation of information. Numerical simulations verified the results of theoretical analysis. The results showed that increasing the proportion of propagators and the probability of beneficiaries transitioning into propagators significantly accelerated the speed and extent of information diffusion.