Fuzzy Adaptive Control for Stochastic Nonstrict Feedback Systems with Multiple Time-Delays: A Novel Lyapunov-Krasovskii Method

The motivation of this study is to solve the challenges posed by the nonstrict feedback structure and multiple timedelays factors in stochastic systems, which significantly complicate the structure of system structure and make the procedure of controller design more difficult. Firstly, a new LyapunovKrasovskii function is constructed in this study. A method is devised based on this function, which incorporates the characteristic of kernel functions in fuzzy logic systems and the concept of variable separation to effectively tackle challenges posed by complex system structures and time-delay factors, as well as reducing the burden of updating dynamic gains. Additionally, the application of the Nussbaum function technique efficiently resolves the issue of unknown control direction while ingeniously leveraging the distinctive properties of the Nussbaum function and the stochastic Barbalat's lemma. This approach provides a complete theoretical proof of the boundedness of the system signals and guarantees the asymptotically stable in probability. Ultimately, the proposed approach is validated by the exceptional performance of the simulation results for an electromechanical control system.