Laval Nozzle-based optimal intermittent control of stochastic nonlinear strict-feedback systems via deep neural networks

This paper proposes an optimal intermittent control strategy for a class of stochastic nonlinear strict-feedback systems with unknown dynamics. A novel concept, termed the ”Laval-Nozzle”, is introduced to precisely characterize the control performance of nonlinear systems under an event-triggered intermittent mechanism. Unlike existing methods, which focus on ensuring optimal predefined performance only within control intervals, this work establishes an optimal prescribed performance criterion for nonlinear systems based on the proposed Laval-Nozzle. The derived results capture the prescribed performance across both control and non-control intervals, thereby enhancing the overall effectiveness of the intermittent control strategy. Furthermore, unlike conventional approaches, we leverage deep neural networks (DNNs) to approximate highly complex functions, improving the estimation of unknown nonlinear dynamics. Simulation results validate the effectiveness of the proposed scheme, demonstrating that all signals in the closed-loop system remain stable in the mean-square sense, while tracking errors are constrained within a predefined set of functions.