Jiaojiao Ren

This paper investigates the exponential $H_{\infty } $ stability of switching fuzzy vehicle lateral dynamics using an event-triggered reinforcement learning control strategy, which is fundamental for improving the performance, safety, and efficiency of transportation systems. A newly constructed vehicle model is proposed to comprehensively reflect the vehicle’s operating environment. By combining an event-triggered mechanism with our previously published switching law, frequent switchings are achieved without the restrictive condition $\tau _{a} \gt T$ . Reinforcement learning further reduces event triggers, lowering communication costs while maintaining system performance. Moreover, the maximum–minimum dwell time method is used to derive a non-weighted $L_{2}$ norm constraint, preserving the original interpretation of the $L_{2}$ norm inequality. Finally, a numerical example demonstrates the effectiveness of the proposed approach.

This paper investigates the stability of a delayed load frequency control (LFC) power system. Firstly, a dynamic LFC model is reconstructed to facilitate the development of a suitable Lyapunov-Krasovskii functional (LKF), which enables the derivation of stability conditions with reduced numerical complexity. Electric vehicles (EVs) are also incorporated into the LFC model to help mitigate frequency fluctuations. Secondly, a parameter-adjustable cubic function negative-determination condition is proposed, generalizing the existing condition in the literature as a special case and reducing its conservatism. Then, by combining the proposed negative-determination condition with the suitable LKF, new stability conditions are derived, enabling a more accurate determination of the allowable delay upper bound (ADUB). Furthermore, to improve computational efficiency in determining the ADUB, the suitable LKF not only provides stability conditions with lower complexity, reducing time per iteration, but also incorporates a binary search algorithm, significantly minimizing the total number of iterations required. Finally, case studies are presented to demonstrate the effectiveness of the proposed methods.

In this paper, a switching fuzzy model is firstly proposed for vehicle lateral dynamics, which comprehensively reflects practical vehicle changes, and its exponential $H_\infty$ output control is investigated. The event-triggered mechanism has proven to be significantly more effective than the time-triggered mechanism. By combining a new event-triggered mechanism with our previously published switching law, the relationship between event trigger points and system switching points is well handled. This allows for the realization of frequent switchings within an interevent interval. For the control objective of $H_\infty$ performance, by employing the maximum, minimum dwell time method, the weighted term $e^{-\alpha s}$ introduced by the average dwell time method is eliminated. Subsequently, the standard $L_{2}$ norm constraint is derived to ensure that the system does not blow up. By constructing a controller-mode-dependent Lyapunov functional and adopting the dynamic quantizers, the sufficient criteria of $H_\infty$ output control problem are presented. An example with numerical simulations is provided to validate the effectiveness.

In this paper, the Von Neumann conditions for the Upwind and Lax-Wendroff schemes of the Telegraph Equation are derived, but then prove to be contradicted with the proportional relation between time and space steps, determined by voltage and current waves’ propagation velocity. The contradiction implies that the stable Upwind and Lax-Wendroff schemes of the Telegraph Equation are not physically applicable.

In this paper, a theorem with very weak conditions on vector field functions for asymptotic stability of Caputo fractional order switching systems is proposed. Based on Vainikko’s lemmas, the Caputo fractional derivative of a continuously differentiable and convex Lyapunov function, along trajectories of any Caputo fractional order switching systems with vector field function being only continuous, proves to be continuous and have a very useful estimation. This weakens the smoothness requirement on the vector field functions for fractional stability analysis from differentiability as in existing results to only continuity. Finally, the numerical implementation of a Caputo fractional order switching system with only continuous vector field function illustrates the effectiveness of the proposed theorem.