Oscillation of Third-Order Neutral Delay Differential Equations

The purpose of this paper is to examine oscillatory properties of the third-order neutral delay differential equation [a(t)(b(t)(x(t)+p(t)x(σ(t)))′)′]′+q(t)x(τ(t))=0. Some oscillatory and asymptotic criteria are presented. These criteria improve and complement those results in the literature. Moreover, some examples are given to illustrate the main results

A Critical Escape Probability Formulation for Enhancing the Transient Stability of Power Systems with System Parameter Design

For the enhancement of the transient stability of power systems, the key is to define a quantitative optimization formulation with system parameters as decision variables. In this paper, we model the disturbances by Gaussian noise and define a metric named Critical Escape Probability (CREP) based on the invariant probability measure of a linearised stochastic processes. CREP characterizes the probability of the state escaping from a critical set. CREP involves all the system parameters and reflects the size of the basin of attraction of the nonlinear systems. An optimization framework that minimizes CREP with the system parameters as decision variablesis is presented. Simulations show that the mean first hitting time when the state hits the boundary of the critical set, that is often used to describe the stability of nonlinear systems, is dramatically increased by minimizing CREP. This indicates that the transient stability of the system is effectively enhanced. It also shown that suppressing the state fluctuations only is insufficient for enhancing the transient stability. In addition, the famous Braess' paradox which also exists in power systems is revisited. Surprisingly, it turned out that the paradoxes identified by the traditional metric may not exist according to CREP. This new metric opens a new avenue for the transient stability analysis of future power systems integrated with large amounts of renewable energy.Comment: 15 pages, 4 figures, 2 table

Input-To-State Stability for a Class of Switched Stochastic Nonlinear Systems by an Improved Average Dwell Time Method

This paper investigates the input-to-state stable in the mean (ISSiM) property of the switched stochastic nonlinear (SSN) systems with an improved average dwell time (ADT) method in two cases: (i) all of the constituent subsystems are ISSiM and (ii) parts of the constituent subsystems are ISSiM. First, an improved ADT method for stability of SSN systems is introduced. Then, based on that not only a new ISSiM result for SSN systems whose subsystems are ISSiM is presented, but also a new ISSiM result for such systems in which parts of subsystems are ISSiM is established. In comparison with the existing ones, the main results obtained in this paper have some advantages. Finally, an illustrative example with numerical simulation is verified the correctness and validity of the proposed results

Input-To-State Stability for a Class of Switched Stochastic Nonlinear Systems by an Improved Average Dwell Time Method

This paper investigates the input-to-state stable in the mean (ISSiM) property of the switched stochastic nonlinear (SSN) systems with an improved average dwell time (ADT) method in two cases: (i) all of the constituent subsystems are ISSiM and (ii) parts of the constituent subsystems are ISSiM. First, an improved ADT method for stability of SSN systems is introduced. Then, based on that not only a new ISSiM result for SSN systems whose subsystems are ISSiM is presented, but also a new ISSiM result for such systems in which parts of subsystems are ISSiM is established. In comparison with the existing ones, the main results obtained in this paper have some advantages. Finally, an illustrative example with numerical simulation is verified the correctness and validity of the proposed results

NetGPT: A Native-AI Network Architecture Beyond Provisioning Personalized Generative Services

Large language models (LLMs) have triggered tremendous success to empower daily life by generative information, and the personalization of LLMs could further contribute to their applications due to better alignment with human intents. Towards personalized generative services, a collaborative cloud-edge methodology sounds promising, as it facilitates the effective orchestration of heterogeneous distributed communication and computing resources. In this article, after discussing the pros and cons of several candidate cloud-edge collaboration techniques, we put forward NetGPT to capably deploy appropriate LLMs at the edge and the cloud in accordance with their computing capacity. In addition, edge LLMs could efficiently leverage location-based information for personalized prompt completion, thus benefiting the interaction with cloud LLMs. After deploying representative open-source LLMs (e.g., GPT-2-base and LLaMA model) at the edge and the cloud, we present the feasibility of NetGPT on the basis of low-rank adaptation-based light-weight fine-tuning. Subsequently, we highlight substantial essential changes required for a native artificial intelligence (AI) network architecture towards NetGPT, with special emphasis on deeper integration of communications and computing resources and careful calibration of logical AI workflow. Furthermore, we demonstrate several by-product benefits of NetGPT, given edge LLM's astonishing capability to predict trends and infer intents, which possibly leads to a unified solution for intelligent network management \& orchestration. In a nutshell, we argue that NetGPT is a promising native-AI network architecture beyond provisioning personalized generative services